# This file contains miscellaneous (mathematical) bib entries ## with emphasis on Optimization and Matrix Theory. ### IMPORTANT NOTE!!! The 'string' definitions for journals is given ### below in this file .master.bib. #### #### This is also available as the #### Bibliography on optimization and matrix theory #### with URL http://liinwww.ira.uka.de/bibliography/Math/optimization.html #### as part of: # The Collection of Computer Science Bibliographies # at URL http://liinwww.ira.uka.de/bibliography/index.html ### ### I will also include these in the dedicated file .strings.bib ### If you are now using another file other than .master.bib ##### (e.g. .psd.bib) then you should include .master.bib FIRST #### in the \bibliography line, i.e. \bibliography{.master,....} ##### #### #### The string definitions are in this file .master.bib # author: Henry Wolkowicz (University of Waterloo) # personal URL: http://orion.math.uwaterloo.ca:80/~hwolkowi # this file has URL: # http://orion.math.uwaterloo.ca:80/~hwolkowi/henry/reports/master.bib.gz # This file does not contain my personal publications which are in # the file with URL: # http://orion.math.uwaterloo.ca:80/~hwolkowi/henry/reports/publs.bib.gz # # # keywords from Stewart's bibfile # cs : computer science # csd : CS decomposition # eig : eigenvalue problems # eriv : errors in variables # geig : generalized eigenvalue problems # ginv : generalized inverse # gsvd : generalized singular value decomposition # iter : iterative methods # la : linear algebra # lsq : least squares # math : mathematics # lud : LU decomposition # na : numerical analysis # nla : numerical linear algebra # nlop : nonlinear equations and optimization # prll : parallel computations # pert : perturbation theory # qrd : QR decomposition # regr : regression # stat : statistics # svd : singular value decomposition # New keywords # sdp : semidefinite programming # coneprog : cone programming # trg : trust regions # cdtprob : Celis-Dennis-Tapia two trust regions problem # qap : quadratic assignment problem # lsopt : large scale optimization # ilp : integer linear programming # ipg : interior point algorithms # qp : quadratic programming ################################### ################################### ################################### ################################### ####string definitions start - always in .master.bib file first. #### i.e. changes are made in this file and copied to .strings.bib ############# ############# ########### definitions from Sturm start here #### definitions are put at start - others follow below. @STRING{ SV = "Springer-Verlag" } @STRING{ MGH = "Mc{G}raw-Hill" } @STRING{ W = "Wiley" } @STRING{ JW = "John Wiley" } @STRING{ WI = "Wiley-Interscience" } @STRING{ PH = "Prentice-Hall" } @STRING{ AW = "Addison-Wesley" } @STRING{ PUP = "Princeton University Press" } @STRING{ AP = "Academic Press" } @STRING{ CUP = "Cambridge University Press" } @STRING{ OUP = "Oxford University Press" } @STRING{ ESP = "Elsevier Science Publisher B.V." } @STRING{ KAP = "Kluwer Adademic Publishers" } @STRING{ NY = "New York" } @STRING{ B = "Berlin" } @STRING{ NJ = "New Jersey" } @STRING{ NH = "North-Holland" } @STRING{ EIEUR = "Econometric Institute, Erasmus University Rotterdam" } @STRING{ ROT = "Rotterdam, The Netherlands" } @STRING{ S = "STURM, J.F."} @STRING{ SZ = "STURM, J.F. and Zhang, S."} @STRING{ LSZ = "LUO, Z.-Q. and STURM, J.F. and ZHANG, S."} @STRING{ LS = "LUO, Z.-Q. and STURM, J.F."} ########### definitions from Sturm end here ############################################# ############################################# # The following is from V. Balakrishnan on SDP and systems control @string{ csm= {IEEE Control Syst.\ Mag.} } @string{ tac= {IEEE Trans.\ Aut.\ Control} } @string{ scl= {Syst.\ Control Letters} } @string{ arc= {Automation and Remote Control} } @string{ cdc= {Proc.\ IEEE Conf.\ on Decision and Control} } ############################################# @string{ ijrnc= {Int.\ J.\ Robust and Nonlinear Control} } @string{ acc= {Proc.\ American Control Conf.} } @string{ aut= {Automatica} } @string{ tcst= {IEEE Trans.\ Control Sys.\ Tech.} } @string{ csm= {IEEE Control Syst.\ Mag.} } @string{ tac= {IEEE Trans.\ Aut.\ Control} } @string{ JASA= {J. Amer. Statistical Association} } @string{ scl= {Syst.\ Control Letters} } @string{ arc= {Automation and Remote Control} } @string{ cdc= {Proc.\ IEEE Conf.\ on Decision and Control} } @string{ ieep= {IEE Proc.} } ############################################# ############################################# ##from Bertsimis ############################################# @string{ICTA = {IEE Proc. -Control Theory Appl.}} @String{IROS="IEEE Int. Conf. on Intelligent Robot Systems"} @String{ICRA="Proc. IEEE Int. Conf. on Robotics and Automation"} @String{IJRR = {Int. J. of Robot. Res.}} @String{ITSMC ={IEEE Trans. Syst., Man, Cybern.}} @String{ICMFIIS={Proc. IEEE/SICE/RSJ Int. Conf. on Multisensor Fusion and Integration for Intelligent Systems}} ############################################# ############################################# ############################################# ####Start of strings - alphabetical order of journals - #### changed in master.bib first @string{toms = "ACM Transactions on Mathematical Software"} @STRING{aer = "American Economic Review"} @STRING{ajae = "Americal Journal of Agricultural Economics"} @STRING{amerm = "Amer. Math. Monthly"} @STRING{AMERMlong = "The American Mathematical Monthly"} @STRING{amers = "Amer. Statist."} @STRING{AMERlong = "The American Statistician"} @STRING{aor = "Ann. of Oper. Res."} @STRING{AORlong = "Annals of Operations Research"} @string{adm = "Ann. Discrete Math."} @string{ADMlong = "Annals of Discrete Mathematics"} @STRING{ams = "Annals of Mathematical Statistics"} @STRING{apmo = "Appl. Math. Optim."} @STRING{APMOlong = "Applied Mathematics and Optimization"} @STRING{ apnum = "Appl. Numer. Math."} @STRING{ APNUMlong = "Applied Numerical Mathematics"} @string{bell = "The Bell System Technical Journal"} @string{ coap = "Comput. Optim. Appl."} @string{ coa = "Comput. Optim. Appl."} @string{ COAPlong = "Computational Optimization and Applications"} @STRING{cjm = "Canadian Journal of Mathematics"} @string{cacm = "Communications of the ACM"} @STRING{ cor = "Comput. Oper. Res." } @STRING{ CORlong = "Computer and Operations Research" } @string{comp = "Computing"} STRING{ CRAS = "Compt Rend Acad. Sci." } @STRING{ CM = "Contemporary Mathematics" } @STRING{ C = "Cybernetics" } @STRING{cmj = "Czechoslovak Math. J."} @STRING{dam = "Discrete Applied Mathematics"} @STRING{dm = "Discrete Mathematics"} @STRING{ ECPE = "Eng. Costs and Prod. Econ." } @string{electjc = "Electronic J. Combinatorics"} @string{ela = "Electronic J. Linear Algebra"} @string{elalong = "The Electronic JOURNAL of Linear Algebra"} @STRING{ejc = "European Journal of Combinatorics"} @STRING{ ejor = "European J. Oper. Res."} @STRING{ EJORlong = "European J. of Operational Research"} @STRING{ glasgow = "Glasgow Math. J."} @STRING{ glasgowlong = "Glasgow Mathematical Journal"} @string{jogo = "J. Global Optim."} @string{globalopt = "J. Global Optim."} @string{GLOBALOPTlong = "Journal of Global Optimization"} @STRING{ IEEEinfo = "IEEE Trans. Inform. Theory"} @STRING{ IEEEinfolong = "IEEE Transactions on Information Theory"} @string{ieeetc = "IEEE Trans. Computers"} @string{ijnme = "International Journal for Numerical Methods in Engineering"} @STRING{ IJOPM= "Int. J. Oper. Prod. Manag." } @STRING{ IJPE = "Int. J. Prod. Econ." } @STRING{ IJPR = "Int. J. Prod. Res." } @STRING{imajna = "IMA Journal of Numerical Analysis"} @string{ja = "Journal of Algorithms"} @STRING{ JAMS = "J. Australian Math. Soc."} @STRING{ JAMSlong = "J. of the Australian Mathematical Society"} @string{ JCAM = {J. of Comput. Appl. Mathem.}} @string{ JCAMlong = {J. of Computational and Applied Mathematics}} @STRING{jacm = "J. Assoc. Comput. Mach."} @STRING{JACMlong = "Journal of the Association of Computing Machinery"} @string{jco = "J. Comb. Optim."} @string{JCOlong = "Journal of Combinatorial Optimization"} @STRING{jct = "Journal of Combinatorial Theory"} @STRING{jcta = "Journal of Combinatorial Theory (A)"} @STRING{jctb= "Journal of Combinatorial Theory (B)"} @STRING{jof= "J. Finance"} @STRING{joflong= "Journal of Finance"} @STRING{jmaa = "J. Math. Anal. Appl."} @STRING{JMAAlong = "Journal of Mathematical Analysis and Applications"} @STRING{ JORS = "J. Oper. Res. Soc." } @STRING{ JRAM = "J. f{\"u}r die reine und angewandte {M}athematik"} @STRING{ JRC = "J. of Regional Science" } @string{jota = "J. Optim. Theory Applic."} @STRING{JOTAlong = "Journal of Optimization Theory and Applications"} @STRING{jrs = "Journal of Regional Science"} @STRING{ JRNBS= "J. of Research of the National Bureau of Standards"} @STRING{jrssa = "Journal of the Royal Statistical Society: Series~A"} @string{laa = "Linear Algebra Appl."} @string{opte = "Optimization and Engineering"} @string{LAAlong = "Linear Algebra and its Applications"} @string{lama = "Linear and Multilinear Algebra"} @STRING{ms = "Management Sci."} @STRING{MSlong = "Management Science"} @STRING{ MA = "Mathematische Annalen" } @string{mcomp = "Math. Comp."} @string{MCOMPlong = "Mathematics of Computation"} @STRING{ MP = "Math. Program." } @string{mprog = "Math. Program."} @STRING{MPROGlong = "Mathematical Programming"} @STRING{mp = "Math. Program."} @string{MPlong = {Mathematical Programming}} @STRING{mpa = "Math. Program., Series A"} @STRING{mps = "Math. Program. Studies"} @STRING{mpb = "Math. Program., Series B"} @STRING{ MPS = "Mathematical Programming Study" } @STRING{mor = "Math. Oper. Res."} @STRING{ MORlong = "Mathematics of Operations Research" } @STRING{mathz = "Math. Z."} @STRING{ nrlq = "Naval Res. Logist. Quart." } @STRING{ NRLQlong = "Naval Research Logistics Quarterly" } @STRING{ NRL = "Naval Research Logistics" } @STRING{ N = "Networks" } @string{opte = "Optim. Eng." } @string{OPTIMA = "Optima"} @STRING{ OPTI = "Optimization" } @string{ oms = "Optim. Methods Softw."} @string{ OPSlong = "Optimization Methods and Software"} @string{ornl = "Oak Ridge National Laboratory"} @STRING{orl = "Operations Research Letters"} @STRING{or = "Operations Research"} @STRING{jorlong = "Journal of the Operations Research Society"} @STRING{jor = "Oper. Res."} @STRING{jors = "Oper. Res."} @STRING{ ORQ = "Operations Research Quarterly" } @STRING{pjm = "Pacific Journal of Mathematics"} @string{pc = "Parallel Computing"} @STRING{pams = "Proceedings of the American Mathematical Society"} @STRING{rsue = "Regional Science and Urban Economics"} @STRING{restud = "Review of Economics Studies"} @STRING{ SIAM = "SIAM" } @string{sijam = "SIAM J. Appl. Math."} @string{SIJAMlong = "SIAM J. ON Applied Mathematics"} @STRING{siad = "SIAM J. Algebraic Discrete Methods"} @STRING{SIADlong = "SIAM Journal on Algebraic and Discrete Methods"} @string{sdma = "SIAM J. Discrete Math."} @string{SDMAlong = "SIAM Journal on Discrete Mathematics"} @string{SIAGOPT = "SIAG/OPT Views-and-News"} @STRING{ SRev = "SIAM Review" } @STRING{ SJC = "SIAM J. on Computing" } @STRING{ SJCO = "SIAM J. Control Optim." } @STRING{ SJMA = "SIAM J. Math. Anal." } @string{SJMAA = "SIAM J. Matrix Anal. Appl."} @STRING{sijc = "SIAM J. on Computing"} @STRING{SIJClong = "SIAM Journal on Computing"} @string{sico = "SIAM J. Control Optim."} @string{SICOlong = "SIAM J. on Control and Optimization"} @string{simax = "SIAM J. Matrix Anal. Appl."} @string{SIMAXlong = "SIAM J. on Matrix Analysis and Applications"} @string{sinum = "SIAM J. Numer. Anal."} @string{SINUMlong = "SIAM J. on Numerical Analysis"} @STRING{sjna = "SIAM J. Numer. Anal."} @STRING{SJNAlong = "SIAM J. on Numerical Analysis"} @string{siopt = "SIAM J. Optim."} @string{SIOPTlong = "SIAM Journal on Optimization"} @string{sissc = "SIAM J. on Scientific and Statistical Computing"} @string{sir = "SIAM Review"} ### start strings from Goemans @string{stoc95 = "Proc. of the 27th {ACM} Symp. on Theory Comput."} @string{stoc97 = "Proc. of the 29th {ACM} Symp. on Theory Comput."} @string{stoc98 = "Proc. of the 30th {ACM} Symp. on Theory Comput."} @string{stoc99 = "Proc. of the 31st {ACM} Symp. on Theory Comput."} @string{focs97 = "Proc. 38th Symp. on Found. of Comp. Sci."} @string{soda00 = "Proc.11th {ACM-SIAM} Symp. on Disc. Algs."} ### end strings from Goemans @STRING{tr = "Transportation Research"} @STRING{ts = "Transportation Science"} @STRING{tams = "Transactions of the American Mathematical Society"} @STRING{ TS = "Transportation Science" } @STRING{utilmath = "Util. Math."} @STRING{UTILMATHlong = "Utilitas Mathematica"} ########################end of string definitions######### ####################################### ####################################### ####additions from Dima feb/2014 @article{BW80, Author = {Borwein, J.M. and Wolkowicz, H.}, Coden = {JAMADS}, Date-Added = {2014-02-01 12:14:44 -0500}, Date-Modified = {2014-02-01 12:16:40 -0500}, Fjournal = {Australian Mathematical Society. Journal. Series A}, Issn = {0263-6115}, Journal = {J. Austral. Math. Soc. Ser. A}, Mrclass = {90C25}, Mrnumber = {614086 (83b:90121)}, Mrreviewer = {B. T. Polyak}, Number = {3}, Pages = {369--380}, Title = {Facial reduction for a cone-convex programming problem}, Volume = {30}, Year = {1980/81}, Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=614086}} @article {JeyakumarLi:14, AUTHOR = {Jeyakumar, V. and Li, G. Y.}, TITLE = {Trust-region problems with linear inequality constraints: exact {SDP} relaxation, global optimality and robust optimization}, JOURNAL = MP, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Optimization Society}, VOLUME = {147}, YEAR = {2014}, NUMBER = {1-2, Ser. A}, PAGES = {171--206}, ISSN = {0025-5610}, MRCLASS = {90C20 (90C22)}, MRNUMBER = {3258522}, MRREVIEWER = {Jinyan Fan}, DOI = {10.1007/s10107-013-0716-2}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s10107-013-0716-2}, } @article{R97, Author = {Ramana, M.V.}, Coden = {MHPGA4}, Date-Added = {2014-02-01 12:21:47 -0500}, Date-Modified = {2014-02-01 12:22:15 -0500}, Doi = {10.1016/S0025-5610(96)00082-2}, Fjournal = {Mathematical Programming}, Issn = {0025-5610}, Journal = MP, Mrclass = {90C60 (49N15)}, Mrnumber = {1461379 (98j:90098)}, Mrreviewer = {Vaithilingam Jeyakumar}, Note = {Semidefinite programming}, Number = {2, Ser. B}, Pages = {129--162}, Title = {An exact duality theory for semidefinite programming and its complexity implications}, Url = {http://dx.doi.org/10.1016/S0025-5610(96)00082-2}, Volume = {77}, Year = {1997}, Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=1461379}} @article{BW81, Author = {Borwein, J.M. and Wolkowicz, H.}, Coden = {JMANAK}, Date-Added = {2014-02-01 12:16:06 -0500}, Date-Modified = {2014-02-01 12:16:54 -0500}, Doi = {10.1016/0022-247X(81)90138-4}, Fjournal = {Journal of Mathematical Analysis and Applications}, Issn = {0022-247X}, Journal = {J. Math. Anal. Appl.}, Mrclass = {90C48 (90C25)}, Mrnumber = {641348 (83d:90236)}, Mrreviewer = {S. Zlobec}, Number = {2}, Pages = {495--530}, Title = {Regularizing the abstract convex program}, Url = {http://dx.doi.org/10.1016/0022-247X(81)90138-4}, Volume = {83}, Year = {1981}, Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=641348}} @article{LSZ97, Author = {Z.-Q. Lio and J. Sturm and S. Zhang }, Date-Added = {2014-02-01 12:24:49 -0500}, Date-Modified = {2014-02-01 12:26:46 -0500}, Journal = {Technical Report 9719/A, Erasmus University Rotterdam, Econometric Institute, The Netherlands}, Title = {Duality results for conic convex programming}, Year = {1997}} @article{MW13, Author = {Waki, H. and Muramatsu, M.}, Coden = {JOTABN}, Date-Added = {2014-02-01 12:32:15 -0500}, Date-Modified = {2014-02-01 12:32:49 -0500}, Doi = {10.1007/s10957-012-0219-y}, Fjournal = {Journal of Optimization Theory and Applications}, Issn = {0022-3239}, Journal = {J. Optim. Theory Appl.}, Mrclass = {90C22}, Mrnumber = {3063940}, Number = {1}, Pages = {188--215}, Title = {Facial reduction algorithms for conic optimization problems}, Url = {http://dx.doi.org/10.1007/s10957-012-0219-y}, Volume = {158}, Year = {2013}, Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=3063940}} @techreport{P00, Author = {G. Pataki}, Date-Added = {2014-02-01 12:34:17 -0500}, Date-Modified = {2014-02-01 12:35:32 -0500}, INSTITUTION = {Columbia University}, address = {New York}, Title = {A simple derivation of a facial reduction algorithm and extended dual systems}, Year = {2000}} ####################################### %AAAAAAAAAAAA @ARTICLE {Aa:71, author = "J.O. AASEN", title = "On the reduction of a symmetric matrix to tridiagonal form", journal = "BIT", year = "1971", volume = "11", pages = "233-242"} @article{abrams:706, AUTHOR = {Abrams, R.A.}, collaboration = {}, title = {Projections of Convex Programs with Unattained Infima}, publisher = {SIAM}, year = {1975}, journal = {SIAM Journal on Control}, volume = {13}, number = {3}, pages = {706-718}, url = {http://link.aip.org/link/?SJC/13/706/1}, doi = {10.1137/0313040} } @techreport{IyigunBenisrael:10, AUTHOR = "C. Iyigun and A. Ben-Israel", TITLE = "Contributions to the multi-facility location problem", TYPE = "Technical Report", NUMBER = "Sept-10", INSTITUTION = "RUTCOR, Rutgers University", YEAR = "2010", } @article {MR0449686, AUTHOR = {Abrams, R.A. and Ben-Israel, A.}, TITLE = {Optimality conditions and recession cones}, JOURNAL = {Operations Res.}, FJOURNAL = {Operations Research}, VOLUME = {23}, YEAR = {1975}, NUMBER = {3}, PAGES = {549--553}, ISSN = {0030-364X}, MRCLASS = {90C25}, MRNUMBER = {MR0449686 (56 \#7987)}, MRREVIEWER = {J. Parida}, } @article {MR80c:90121, AUTHOR = {Abrams, R. A. and Wu, C.T.}, TITLE = {Projection and restriction methods in geometric programming and related problems}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {26}, YEAR = {1978}, NUMBER = {1}, PAGES = {59--76}, ISSN = {0022-3239}, CODEN = {JOTABN}, } @article {MR58:4328, AUTHOR = {Abrams, R. and Kerzner, L.}, TITLE = {A simplified test for optimality}, JOURNAL = {J. Optim. Theory Appl.}, VOLUME = {25}, YEAR = {1978}, NUMBER = {1}, PAGES = {161--170}, } @article {MR2735944, AUTHOR = {Zhu, Z. and So, A.M.-C. and Ye, Y.}, TITLE = {Universal rigidity and edge sparsification for sensor network localization}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {20}, YEAR = {2010}, NUMBER = {6}, PAGES = {3059--3081}, ISSN = {1052-6234}, MRCLASS = {52C25 (05C85 68M10 90C22)}, MRNUMBER = {2735944}, DOI = {10.1137/090772009}, URL = {http://dx.doi.org.offcampus.lib.washington.edu/10.1137/090772009}, } @article {MR0249108, AUTHOR = {Ben-Israel, A.}, TITLE = {Theorems of the alternative for complex linear inequalities}, JOURNAL = {Israel J. Math.}, FJOURNAL = {Israel Journal of Mathematics}, VOLUME = {7}, YEAR = {1969}, PAGES = {129--136}, ISSN = {0021-2172}, MRCLASS = {90.60 (15.00)}, MRNUMBER = {0249108}, MRREVIEWER = {M. F. Smiley}, DOI = {10.1007/BF02771659}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/BF02771659}, } @article {MR56:7987, AUTHOR = {Abrams, R.A. and Ben-Israel, A.}, TITLE = {Optimality conditions and recession cones}, JOURNAL = {Operations Res.}, VOLUME = {23}, YEAR = {1975}, NUMBER = {3}, PAGES = {549--553}, } @article {MR55:2140, AUTHOR = {Abrams, Robert A.}, TITLE = {Consistency, superconsistency, and dual degeneracy in posynomial geometric programming}, JOURNAL = {Operations Res.}, VOLUME = {24}, YEAR = {1976}, NUMBER = {2}, PAGES = {325--335}, } @article {MR54:2200, AUTHOR = {Abrams, Robert A.}, TITLE = {Degenerate quadratic programming and $l\sb{p}$ approximation problems}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {55}, YEAR = {1976}, NUMBER = {2}, PAGES = {266--271}, } @article {MR51:9814, AUTHOR = {Abrams, R. A.}, TITLE = {Projections of convex programs with unattained infima}, JOURNAL = {SIAM J. Control}, VOLUME = {13}, YEAR = {1975}, PAGES = {706--718}, } @techreport{AdachiIwataNakatsukasaTakeda:15, AUTHOR = "S. Adachi and S. Iwata and Y. Nakatsukasa and A. Takeda", TITLE = "Solving the Trust Region Subproblem by a Generalized Eigenvalue Problem", TYPE = "Technical Report", INSTITUTION = "Mathematical Engineering, The University of Tokyo", YEAR = "2015", } @article{Adachi, author = "Adachi, S. and Iwata, S. and Nakatsukasa, Y. and Takeda, A.", title = "Solving the trust-region subproblem by a generalized eigenvalue problem", journal = "SIAM J. Optimiz.", volume = 27, year = 2017, pages = "269-291"} @inproceedings{jain2010guaranteed, title={Guaranteed rank minimization via singular value projection}, author={Jain, P. and Meka, R. and Dhillon, I.S}, booktitle={Advances in Neural Information Processing Systems}, pages={937--945}, year={2010} } @techreport{SakaueNakatTakedaIwata:15, AUTHOR = "S. Sakaue and Y. Nakatsukasa and A. Takeda and S. Iwata", TITLE = "A Polynomial-Time Algorithm for Nonconvex Quadratic Optimization with Two Quadratic Constraints", TYPE = "Technical Report", INSTITUTION = "Mathematical Engineering, The University of Tokyo", YEAR = "2015", } @ARTICLE {AdDe:94, author = "W.P. ADAMS and P.M. DEARING", title = "On the equivalence between roof duality and {L}agrangian duality for unconstrained $0-1$ quadratic programming problems", journal = "Discrete Appl. Math.", year = "1994", volume = "48", pages = "1-20"} @inproceedings{AdJo:94, author="W.P. ADAMS and T.A. Johnson", title="Improved linear programming-based lower bounds for the quadratic assignment problem", booktitle="Proceedings of the DIMACS Workshop on Quadratic Assignment Problems", editors="P. Pardalos and H. Wolkowicz", Publisher="American Mathematical Society", series="DIMACS Series in Discrete Mathematics and Theoretical Computer Science", pages="43--75", volume= "16", year = "1994" } @techreport{Agarwaletal:13, AUTHOR = "A. Agarwal and J.M. Phillips and H. Daum\'{e} III and Venkatasubramanian S", TITLE = "Sensor Network Localization for Moving Sensors", TYPE = "Technical Report", INSTITUTION = "Dept.\ of Comp.\ Sc., University of Maryland", YEAR = "2013", } @ARTICLE {AgrawalDingSY:12, author = "S. Agrawal and Y. Ding and A. Saberi and Y. Ye", title = "Price of Correlations in Stochastic Optimization", pages = "229-232", year = "2012", journal = "Operations Research", volume = "60", number = "1", pages = "150-162" } @ARTICLE {DingGeHeryan:18, author = "Y. Ding and D. Ge and S. He and C. Ryan", title = "A Non-Asymptotic Approach to Analyzing Kidney Exchange Graphs", pages = "918-935", year = "2018", journal = "Operations Research", volume = "66", number = "4" } @ARTICLE {DingMcCormickNagarajan:18, author = "Y. Ding and T. McCormick and M. Nagarajan", title = "A Fluid Model for an Overloaded Bipartite Queueing System with Scoring-Based Priority Rules", pages = "", year = "2018", journal = "Operations Research", volume = "under review", number = "" } @ARTICLE {Agg:66, author = "J.C. AGGERI", title = "Les fonctions convexes continue et le th\'eor\`eme de {K}rein-{M}ilman", journal = "C.R. Acad. Sci. Paris", year = "1966", volume = "262", pages = "229-232"} @ARTICLE {AgLe:65, author = "J.C. AGGERI and C. LESCARRET", title = "Fonctions convexes duales associ\'ees \'a une couple d`ensembles mutuellement polaires", journal = "C.R. Acad. Sci. Paris", year = "1965", volume = "260", pages = "6011-6014"} @BOOK {AhHoUl:74, author = "A.V. AHO and J.E. HOPCROFT and J.D. ULLMAN", title = "The Design and Analysis of Computer Algorithms", publisher = "Addison-Wesley", year = "1974", series = "Reading", address = "Massachusetts"} @article {MR2000c:65064, AUTHOR = {AIRAPETYAN, R.G. and RAMM, A.G. and SMIRNOVA, A.B.}, TITLE = {Continuous analog of the {G}auss-{N}ewton method}, JOURNAL = {Math. Models Methods Appl. Sci.}, FJOURNAL = {Mathematical Models \& Methods in Applied Sciences}, VOLUME = {9}, YEAR = {1999}, NUMBER = {3}, PAGES = {463--474}, ISSN = {0218-2025}, MRCLASS = {65J22 (47J25 65J15)}, MRNUMBER = {2000c:65064}, MRREVIEWER = {Stefano Serra Capizzano}, } @article {MR2486048, AUTHOR = {Ai, W. and Zhang, S.}, TITLE = {Strong duality for the {CDT} subproblem: a necessary and sufficient condition}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {19}, YEAR = {2008}, NUMBER = {4}, PAGES = {1735--1756}, ISSN = {1052-6234}, MRCLASS = {90C20 (90C33 90C51)}, MRNUMBER = {2486048 (2010a:90061)}, MRREVIEWER = {Vaithilingam Jeyakumar}, DOI = {10.1137/07070601X}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/07070601X}, } @ARTICLE {AlFe:85, author = "M. AL-BAALI and R. Fletcher", title = "Variational methods for nonlinear least squares", journal = "J. Opl. Res. Soc.", year = "1985", volume = "36", pages = "405-421", note = "Also available as Technical Report NA/71, Department of Mathematical Sciences, University of Dundee, 1983"} @article {MR0107973, AUTHOR = {Akaike, H.}, TITLE = {On a successive transformation of probability distribution and its application to the analysis of the optimum gradient method}, JOURNAL = {Ann. Inst. Statist. Math. Tokyo}, FJOURNAL = {Annals of the Institute of Statistical Mathematics}, VOLUME = {11}, YEAR = {1959}, PAGES = {1--16}, ISSN = {0020-3157}, MRCLASS = {65.00}, MRNUMBER = {0107973 (21 \#6694)}, MRREVIEWER = {G. E. Forsythe}, } @article{Akutsu:97, AUTHOR = "T. Akutsu", TITLE = "{NP}-hardness results for protein side-chain packing", JOURNAL = "Genome Informatics", VOLUME = "8", YEAR = "1997", PAGES = "180--186", } @article{Alrajehetal:13, title = "Localization Techniques in Wireless Sensor Networks", author = "Alrajeh, N.A. and Bashir, M. and Shams, B.", year = "2013", pages = "1550--1477", URL = "https://doi.org/10.1155/2013/304628", journal = "International Journal of Distributed Sensor Networks", volume = "9", number = "6", publisher = "SAGE Publications", abstract = "The important function of a sensor network is to collect and forward data to destination. It is very important to know about the location of collected data. This kind of information can be obtained using localization technique in wireless sensor networks (WSNs). Localization is a way to determine the location of sensor nodes. Localization of sensor nodes is an interesting research area, and many works have been done so far. It is highly desirable to design low-cost, scalable, and efficient localization mechanisms for WSNs. In this paper, we discuss sensor node architecture and its applications, different localization techniques, and few possible future research directions. AB - The important function of a sensor network is to collect and forward data to destination. It is very important to know about the location of collected data. This kind of information can be obtained using localization technique in wireless sensor networks (WSNs). Localization is a way to determine the location of sensor nodes. Localization of sensor nodes is an interesting research area, and many works have been done so far. It is highly desirable to design low-cost, scalable, and efficient localization mechanisms for WSNs. In this paper, we discuss sensor node architecture and its applications, different localization techniques, and few possible future research directions." } @incollection {MR94k:65076, AUTHOR = {ALLGOWER, E.L. and GEORG, K.}, TITLE = {Continuation and path following}, BOOKTITLE = {Acta numerica, 1993}, PAGES = {1--64}, PUBLISHER = {Cambridge Univ. Press}, ADDRESS = {Cambridge}, YEAR = {1993}, MRCLASS = {65H20 (90C30)}, MRNUMBER = {94k:65076}, MRREVIEWER = {K. B{\"o}hmer}, } @ARTICLE {AlGe:80, author = "E. ALLGOWER and K. GEORG", title = "Simplicial and continuation methods for approximating fixed points and solutions to systems of equations", journal = "SIAM Rev.", year = "1980", volume = "22", pages = "28-85"} @article{all, AUTHOR = "J.C.\ ALLWright", TITLE = "On Maximizing the Minimum Eigenvalue of a Linear Combination of Symmetric Matrices", JOURNAL = simax, VOLUME = "10", NUMBER ="3", YEAR = "1989", PAGES = "347--382", } @article {amestoyLiPralet:07, AUTHOR = {AMESTOY, P.R. and LI, X.S. and PRALET, S.}, TITLE = {Unsymmetric ordering using a constrained {M}arkowitz scheme}, JOURNAL = simax, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {29}, YEAR = {2007}, NUMBER = {1}, PAGES = {302--327}, } @article {AmoiaMichSant:81, AUTHOR = {AMOIA, V. and DEMICHELI, G. and SANTOMAURO, M.}, TITLE = {Computer-oriented formulation of transition-rate matrices via {K}ronecker algebra}, JOURNAL = {IEEE Trans. Reliability}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Reliability}, VOLUME = {R-30}, YEAR = {1981}, NUMBER = {2}, PAGES = {123-132} } @Article{An2005, author="An, L.T.H. and Tao, P.D.", title="The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems", journal="Annals of Operations Research", year="2005", month="Jan", day="01", volume="133", number="1", pages="23--46", abstract="The DC programming and its DC algorithm (DCA) address the problem of minimizing a function f=g−h (with g,h being lower semicontinuous proper convex functions on Rn) on the whole space. Based on local optimality conditions and DC duality, DCA was successfully applied to a lot of different and various nondifferentiable nonconvex optimization problems to which it quite often gave global solutions and proved to be more robust and more efficient than related standard methods, especially in the large scale setting. The computational efficiency of DCA suggests to us a deeper and more complete study on DC programming, using the special class of DC programs (when either g or h is polyhedral convex) called polyhedral DC programs. The DC duality is investigated in an easier way, which is more convenient to the study of optimality conditions. New practical results on local optimality are presented. We emphasize regularization techniques in DC programming in order to construct suitable equivalent DC programs to nondifferentiable nonconvex optimization problems and new significant questions which have to be answered. A deeper insight into DCA is introduced which really sheds new light on DCA and could partly explain its efficiency. Finally DC models of real world nonconvex optimization are reported.", issn="1572-9338", doi="10.1007/s10479-004-5022-1", url="https://doi.org/10.1007/s10479-004-5022-1" } @article {MR2029522, AUTHOR = {L.T.H. An and P.D. Tao and D.N. H{\`a}o}, TITLE = {On the ill-posedness of the trust region subproblem}, JOURNAL = {J. Inverse Ill-Posed Probl.}, FJOURNAL = {Journal of Inverse and Ill-Posed Problems}, VOLUME = {11}, YEAR = {2003}, NUMBER = {6}, PAGES = {545--577}, ISSN = {0928-0219}, MRCLASS = {90C30 (49K40 65J20 90C55)}, MRNUMBER = {MR2029522 (2004j:90114)}, MRREVIEWER = {Jos{\'e} Mario Mart{\'{\i}}nez}, } @article{AnerssonMausserRosenUryasev, author = {Andersson, F. and Mausser, H. and Rosen, D. and Uryasev, S.}, year = {2001}, month = {01}, pages = {273-291}, title = {Credit Risk Optimization with Conditional Value-at Risk Criterion}, volume = {89}, journal = MP, doi = {10.1007/PL00011399} } @article{ANDERSEN:95:D, author = "E.D. Andersen and K.D. Andersen", title = "{Presolving in linear programming}", journal = mprog, volume = 71, number = 2, pages = "221--245", year = 1995 } @incollection{andersen2000mosek, title={The MOSEK interior point optimizer for linear programming: an implementation of the homogeneous algorithm}, author={Andersen, E.D. and Andersen, K.D.}, booktitle={High performance optimization}, pages={197--232}, year={2000}, publisher={Springer} } @article {MR3569612, AUTHOR = {Fountoulakis, K. and Gondzio, J.}, TITLE = {Performance of first- and second-order methods for {$\ell_1$}-regularized least squares problems}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {65}, YEAR = {2016}, NUMBER = {3}, PAGES = {605--635}, ISSN = {0926-6003}, MRCLASS = {90C25 (65K10 90-04)}, MRNUMBER = {3569612}, MRREVIEWER = {Ya-Feng Liu}, DOI = {10.1007/s10589-016-9853-x}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10589-016-9853-x}, } @incollection {MR1777460, AUTHOR = {Altman, A. and Gondzio, J.}, TITLE = {Regularized symmetric indefinite systems in interior point methods for linear and quadratic optimization}, NOTE = {Interior point methods}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods and Software}, VOLUME = {11/12}, YEAR = {1999}, NUMBER = {1-4}, PAGES = {275--302}, ISSN = {1055-6788}, MRCLASS = {90C51 (90C05)}, MRNUMBER = {1777460}, DOI = {10.1080/10556789908805754}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1080/10556789908805754}, } @article {MR2776704, AUTHOR = {Colombo, M. and Gondzio, J. and Grothey, A.}, TITLE = {A warm-start approach for large-scale stochastic linear programs}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {127}, YEAR = {2011}, NUMBER = {2, Ser. A}, PAGES = {371--397}, ISSN = {0025-5610}, MRCLASS = {90C15 (60C05 90C06 90C51)}, MRNUMBER = {2776704}, DOI = {10.1007/s10107-009-0290-9}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s10107-009-0290-9}, } @incollection{int:Andersen26, author = "E.D. Andersen and J. Gondzio and C. M{\'esz\'aros} and X.~XU", title = "Implementation of interior-point methods for large scale linear programs", editor = " T. Terlaky", booktitle = "Interior point methods of mathematical programming", pages ="189--252", publisher = "Kluwer, Dordrecht, The Netherlands", year = "1996"} @article{mybib:GG-oops, author = {J. Gondzio and A. Grothey}, title = {Exploiting Structure in Parallel Implementation of Interior Point Methods for Optimization}, journal = "Computational Management Science", volume = "6", year = "2009", pages = "135--160" } @incollection{mybib:GG-10e9, author = "J. Gondzio and A. Grothey", title = "Direct Solution of Linear Systems of Size $10^9$ Arising in Optimization with Interior Point Methods", booktitle = "Parallel Processing and Applied Mathematics", series = "Lecture Notes in Computer Science", editor = "R. Wyrzykowski and J. Dongarra and N. Meyer and J. Wasniewski", publisher = "Springer-Verlag", address = "Berlin", year = "2006", volume = "3911", pages = "513--525" } @incollection{mybib:GG-CompFin, author = "J. Gondzio and A. Grothey", title = "Solving nonlinear financial planning problems with $10^9$ decision variables on massively parallel architectures", booktitle = "Computational Finance and its Applications II", series = "WIT Transactions on Modelling and Simulation", editor = "M. Costantino and C.A. Brebbia", publisher = "WIT Press", year = "2006", volume = "43", pages = "??--??" } @ARTICLE {AnderYe:96, author = "E.D. Andersen and Y. YE", title = "Combining interior-point and pivoting algorithms for linear programming", journal = "Management Science", year = "1996", volume = "42", pages = "1719-1731"} @ARTICLE {AnOs:77a, author = "M.R. ANDERSON and M.R. OSBORNE", title = "Discrete nonlinear approximation problems in polyhedral norms", journal = "Numer. Math.", year = "1977", volume = "28", pages = "143-156"} @ARTICLE {AnOs:77b, author = "M.R. ANDERSON and M.R. OSBORNE", title = "Discrete nonlinear approximation problems in polyhedral norms: A {L}evenberg algorithm", journal = "Numer. Math.", year = "1977", volume = "28", pages = "157-170"} @book {AnNa:87, author = "E. ANDERSON and P. NASH", title = "Linear Programming in Infinite Dimensional Spaces", publisher = "John Wiley and Sons", year = "1987"} @TECHREPORT {AndVic:96, author = "D.A. ANDREWS and L.N. VICENTE", title = "Characterization of the smoothness and curvature of a marginal function for a trust-region problem", institution = "Department of Mathematical Sciences, Rice University", year = "1996", number = "CRPC-TR96-13", address = "Houston, TX"} @techreport {Andrei:04, author = "N. ANDREI", title = "On the complexity of {\em {MINOS}} package for linear programming", school = "Research Institute for Informatics", volume = "13", year = "2004", pages = " ", number = "1", address = "Bucharest"} @article {MR2424936, AUTHOR = {Andrei, Neculai}, TITLE = {An unconstrained optimization test functions collection}, JOURNAL = {Adv. Model. Optim.}, FJOURNAL = {Advanced Modeling and Optimization. The Electronic International Journal}, VOLUME = {10}, YEAR = {2008}, NUMBER = {1}, PAGES = {147--161}, ISSN = {1841-4311}, MRCLASS = {90C26 (90-00)}, MRNUMBER = {2424936 (2009f:90078)}, } @article {MR94e:90089, AUTHOR = {ANJOS, M. F.}, TITLE = {A modified {B}royden update with interpolation}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {14}, YEAR = {1993}, NUMBER = {6}, PAGES = {1359--1367}, ISSN = {1064-8275}, CODEN = {SJOCE3}, } @preamble{ "\def\cprime{$'$} " } @article {MR1724764, AUTHOR = {ANSTREICHER, K.M.}, TITLE = {Linear programming in {$O((n\sp 3/\ln n)L)$} operations}, NOTE = {Dedicated to John E. Dennis, Jr., on his 60th birthday}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {9}, YEAR = {1999}, NUMBER = {4}, PAGES = {803--812 (electronic)}, ISSN = {1095-7189}, MRCLASS = {90C05 (90C60)}, MRNUMBER = {MR1724764 (2000k:90025)}, MRREVIEWER = {E. G. Gol{\cprime}shte{\u\i}n}, } @TECHREPORT {AnVi:93, author = "K.M. ANSTREICHER and J-P. VIAL", title = "On the convergence of an infeasible primal-dual interior-point method for convex programming", institution = "Universite de Geneve", year = "1993"} @ARTICLE {AM:85, author = "N. ALON and V.D. MILMAN", title = "$\lambda_1$, Isoperimetric inequalities for graphs and superconcentrators", journal = "JCT", year = "1985", volume = "38", pages = "73-88"} @techreport{applegate2021practical, title={Practical Large-Scale Linear Programming using Primal-Dual Hybrid Gradient}, author={D. Applegate and M. Diaz and O. Hinder and H. Lu and M. Lubin and B. {O}'{D}onoghue and Warren Schudy}, year={2021}, eprint={2106.04756}, archivePrefix={arXiv}, primaryClass={math.OC} } @BOOK {Apos:57, author = "T.M. APOSTOL", title = "Mathematical Analysis", publisher = "Addison-Wesley", year = "1957", series = "Reading", address = "Massachusetts"} @PHDTHESIS {Vann:83, author = "A. VANNELLI", title = "Solution techniques for 0-1 indefinite quadratic programming problems with applications in decomposition", school = "University of Waterloo", year = "1983", address = "Waterloo, Canada"} @TECHREPORT {ArVa:93, author = "S. AREIBI and A. VANNELLI", title = "Personal communication", institution = "University of Waterloo", year = "1993", address = "Waterloo, Ontario, Canada"} @techreport{at, AUTHOR = "M.\ ARGAEZ and R.A.\ Tapia", TITLE = "On the global convergence of a modified augmented {L}agrangian linesearch interior-point {N}ewton method for nonlinear programming", TYPE = "Technical Report", NUMBER = "95-38", INSTITUTION = "Dept.\ of Comp.\ and Appl.\ Math., Rice University", YEAR = "1997", } @article{goldstein:323, author = {T. Goldstein and S. Osher}, collaboration = {}, title = {The Split Bregman Method for L1-Regularized Problems}, publisher = {SIAM}, year = {2009}, journal = {SIAM Journal on Imaging Sciences}, volume = {2}, number = {2}, pages = {323-343}, keywords = {constrained optimization; L1-regularization; compressed sensing; total variation denoising}, url = {http://link.aip.org/link/?SII/2/323/1}, doi = {10.1137/080725891} } @article {WenYinzhanggoldfarb:11, AUTHOR = {Z. Wen and W. Yin and H. Zhang and D. Goldfarb}, TITLE = {ON THE CONVERGENCE OF AN ACTIVE SET METHOD FOR $\ell_1$ MINIMIZATION}, JOURNAL = oms, VOLUME = {to appear}, YEAR = {2011}, NUMBER = {}, PAGES = {}, } @article {MR2735964, AUTHOR = {Yin, W.}, TITLE = {Analysis and generalizations of the linearized {B}regman model}, JOURNAL = {SIAM J. Imaging Sci.}, FJOURNAL = {SIAM Journal on Imaging Sciences}, VOLUME = {3}, YEAR = {2010}, NUMBER = {4}, PAGES = {856--877}, ISSN = {1936-4954}, MRCLASS = {68U10 (65K10 90C25 90C51 94A12)}, MRNUMBER = {2735964 (2011j:68172)}, MRREVIEWER = {Patrick L. Combettes}, } @article {MR2603887, AUTHOR = {Hale, E.T. and Yin, W. and Zhang, Y.}, TITLE = {Fixed-point continuation applied to compressed sensing: implementation and numerical experiments}, JOURNAL = {J. Comput. Math.}, FJOURNAL = {Journal of Computational Mathematics}, VOLUME = {28}, YEAR = {2010}, NUMBER = {2}, PAGES = {170--194}, ISSN = {0254-9409}, CODEN = {JCMMEB}, MRCLASS = {65K10}, MRNUMBER = {2603887 (2011b:65095)}, MRREVIEWER = {Vera A. Roshchina}, } @article{yin:143, author = {W. Yin and S. Osher and D. Goldfarb and J. Darbon}, collaboration = {}, title = {Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing}, publisher = {SIAM}, year = {2008}, journal = {SIAM Journal on Imaging Sciences}, volume = {1}, number = {1}, pages = {143-168}, keywords = {$\ell_1$-minimization; basis pursuit; compressed sensing; iterative regularization; Bregman distances}, url = {http://link.aip.org/link/?SII/1/143/1}, doi = {10.1137/070703983} } @article{hale:1107, author = {E.T. Hale and W. Yin and Y. Zhang}, collaboration = {}, title = {Fixed-Point Continuation for $\ell_1$-Minimization: Methodology and Convergence}, publisher = {SIAM}, year = {2008}, journal = {SIAM Journal on Optimization}, volume = {19}, number = {3}, pages = {1107-1130}, keywords = {$\ell_1$ regularization; fixed-point algorithm; $q$-linear convergence; continuation; compressed sensing}, url = {http://link.aip.org/link/?SJE/19/1107/1}, doi = {10.1137/070698920} } @article {MR1977792, AUTHOR = {Williams, P.J. and El-Bakry, A.S. and Tapia, R.A.}, TITLE = {Using indicators in finite termination procedures}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods \& Software}, VOLUME = {18}, YEAR = {2003}, NUMBER = {1}, PAGES = {39--52}, ISSN = {1055-6788}, MRCLASS = {90C51 (90C05)}, MRNUMBER = {1977792 (2004c:90099)}, MRREVIEWER = {Hiroshi Yabe}, DOI = {10.1080/1055678031000066598}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1080/1055678031000066598}, } @incollection {MR1747275, AUTHOR = {Williams, P. J. and El-Bakry, A.S. and Tapia, R.A.}, TITLE = {Computing an exact solution in interior-point methods for linear programming}, BOOKTITLE = {African {A}mericans in mathematics, {II} ({H}ouston, {TX}, 1998)}, SERIES = {Contemp. Math.}, VOLUME = {252}, PAGES = {9--29}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {1999}, MRCLASS = {90C05 (65F30)}, MRNUMBER = {1747275 (2001a:90030)}, MRREVIEWER = {Shu Zhong Zhang}, } @article {MR1107559, AUTHOR = {Tapia, R.A. and Zhang, Y.}, TITLE = {An optimal-basis identification technique for interior-point linear programming algorithms}, NOTE = {Interior point methods for linear programming}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {152}, YEAR = {1991}, PAGES = {343--363}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {90C05 (65K05)}, MRNUMBER = {1107559 (92d:90044)}, MRREVIEWER = {Vera V. Kova{\u{c}}evi{\'c}-Vuj{\u{c}}i{\'c}}, DOI = {10.1016/0024-3795(91)90281-Z}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/0024-3795(91)90281-Z}, } @article {MR1398265, AUTHOR = {El-Bakry, A.S. and Tapia, R.A. and Zhang, Y.}, TITLE = {On the convergence rate of {N}ewton interior-point methods in the absence of strict complementarity}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {6}, YEAR = {1996}, NUMBER = {2}, PAGES = {157--167}, ISSN = {0926-6003}, CODEN = {CPPPEF}, MRCLASS = {90C30 (65K05 90C33)}, MRNUMBER = {1398265 (97c:90103)}, MRREVIEWER = {Florian Jarre}, DOI = {10.1007/BF00249644}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/BF00249644}, } @book {MR2686529, AUTHOR = {El-Bakry, A.S.}, TITLE = {On the role of indicators in identifying zero variables in linear programming}, NOTE = {Thesis (Ph.D.)--Rice University}, PUBLISHER = {ProQuest LLC, Ann Arbor, MI}, YEAR = {1991}, PAGES = {77}, MRCLASS = {Thesis}, MRNUMBER = {2686529}, URL = {http://gateway.proquest.com.proxy.lib.uwaterloo.ca/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:9136018}, } @article {par, AUTHOR = {van den Berg, E. and Friedlander, M.P.}, TITLE = {Probing the {P}areto frontier for basis pursuit solutions}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {31}, YEAR = {2008/09}, NUMBER = {2}, PAGES = {890--912}, ISSN = {1064-8275}, MRCLASS = {90C25 (65K10 90C06 90C52)}, MRNUMBER = {2466141 (2010b:90086)}, DOI = {10.1137/080714488}, URL = {http://dx.doi.org/10.1137/080714488}, } @article {lsqr_con, AUTHOR = {van den Berg, E. and Friedlander, M.P.}, TITLE = {Sparse optimization with least-squares constraints}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {21}, YEAR = {2011}, NUMBER = {4}, PAGES = {1201--1229}, ISSN = {1052-6234}, CODEN = {SJOPE8}, MRCLASS = {94A12 (15A83 49M29 65K10 90C06 90C25 94A08)}, MRNUMBER = {2854580 (2012i:94062)}, MRREVIEWER = {Junfeng Yang}, DOI = {10.1137/100785028}, URL = {http://dx.doi.org/10.1137/100785028}, } @article {spgl1:2007, AUTHOR ={E. van den Berg and M.P. Friedlander}, TITLE = {{SPGL1}: A solver for large-scale sparse reconstruction}, YEAR = {2007}, JOURNAL = {http://www.cs.ubc.ca/labs/scl/spgl1}, } @misc{davis2019stochastic, title={Stochastic algorithms with geometric step decay converge linearly on sharp functions}, author={D. Davis and D. Drusvyatskiy and V. Charisopoulos}, year={2019}, eprint={1907.09547}, archivePrefix={arXiv}, primaryClass={math.OC} } @techreport{paquette:2020, title={Halting Time is Predictable for Large Models: A Universality Property and Average-case Analysis}, author={C. Paquette and B. van Merrienboer and F. Pedregosa}, year={2020}, eprint={2006.04299}, archivePrefix={arXiv}, primaryClass={math.OC} } @article {MR3869491, AUTHOR = {Davis, D. and Drusvyatskiy, D. and MacPhee, K.J. and Paquette, C.}, TITLE = {Subgradient methods for sharp weakly convex functions}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {179}, YEAR = {2018}, NUMBER = {3}, PAGES = {962--982}, ISSN = {0022-3239}, MRCLASS = {65K05 (65K10 90C25 90C56)}, MRNUMBER = {3869491}, MRREVIEWER = {Chee-Khian Sim}, DOI = {10.1007/s10957-018-1372-8}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10957-018-1372-8}, } @article {MR3756929, AUTHOR = {Drusvyatskiy, D. and Paquette, C.}, TITLE = {Variational analysis of spectral functions simplified}, JOURNAL = {J. Convex Anal.}, FJOURNAL = {Journal of Convex Analysis}, VOLUME = {25}, YEAR = {2018}, NUMBER = {1}, PAGES = {119--134}, ISSN = {0944-6532}, MRCLASS = {49J52 (26B05 46G05)}, MRNUMBER = {3756929}, MRREVIEWER = {Shawn Xianfu Wang}, } @article {DP2, AUTHOR = {Drusvyatskiy, D. and Paquette, C.}, TITLE = {Efficiency of minimizing compositions of convex functions and smooth maps}, JOURNAL = mprog, FJOURNAL = {Mathematical Programming}, VOLUME = {20}, YEAR = {2018}, NUMBER = {1}, PAGES = {1--56} } @InProceedings{pmlr-v84-paquette18a, title = {Catalyst for Gradient-based Nonconvex Optimization}, author = {C. Paquette and H. Lin and D. Drusvyatskiy and J. Mairal and Z. Harchaoui}, booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics}, pages = {613--622}, year = {2018}, editor = {Amos Storkey and Fernando Perez-Cruz}, volume = {84}, series = {Proceedings of Machine Learning Research}, address = {Playa Blanca, Lanzarote, Canary Islands}, month = {09--11 Apr}, publisher = {PMLR}, } @misc{paquette2017catalyst, title={Catalyst Acceleration for Gradient-Based Non-Convex Optimization}, author={C. Paquette and H. Lin and D. Drusvyatskiy and J. Mairal and Z. Harchaoui}, year={2017}, eprint={1703.10993}, archivePrefix={arXiv}, primaryClass={stat.ML} } @article {DFR, AUTHOR = {Drusvyatskiy, D. and Fazel, M. and Roy, S.}, TITLE = {An optimal first order method based on optimal quadratic averaging}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {28}, YEAR = {2018}, NUMBER = {1}, PAGES = {251--271}, ISSN = {1052-6234}, MRCLASS = {65K05 (90C06 90C25)}, MRNUMBER = {3757113}, MRREVIEWER = {Nicolas Gillis}, DOI = {10.1137/16M1072528}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/16M1072528}, } @article {flippy, Author = {S. Aravkin and J. Burke and D. Drusvyatskiy and M.P. Friedlander and S. Roy}, TITLE = {Level-set methods for convex optimization}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming}, VOLUME = {174}, YEAR = {2019}, NUMBER = {1-2, Ser. B}, PAGES = {359--390}, ISSN = {0025-5610}, MRCLASS = {90C25 (49M29 65K10 90C22)}, MRNUMBER = {3935084}, MRREVIEWER = {Yekini Shehu}, DOI = {10.1007/s10107-018-1351-8}, URL = {https://doi.org/10.1007/s10107-018-1351-8}, } @article{ArBuFr:13, AUTHOR = {A.Y. Aravkin, J.V. Burke, M.P. Friedlander}, title = "Variational Properties of Value Functions", journal = siopt, volume = "23", number = "3", pages = "1689?1717", year = "2013" } @article {MR95b:90047, AUTHOR = {El-Bakry, A.S. and Tapia, R.A. and Zhang, Y.}, TITLE = {A study of indicators for identifying zero variables in interior-point methods}, JOURNAL = {SIAM Rev.}, FJOURNAL = {SIAM Review. A Publication of the Society for Industrial and Applied Mathematics}, VOLUME = {36}, YEAR = {1994}, NUMBER = {1}, PAGES = {45--72}, ISSN = {0036-1445}, CODEN = {SIREAD}, MRCLASS = {90C05}, MRNUMBER = {95b:90047}, } @ARTICLE {Ar:66, author = "L. Armijo", title = "Minimization of functions having {L}ipschitz-continuous first partial derivatives", journal = "Pacific J. Math.", year = "1966", volume = "16", pages = "1-3"} @article {MR1850791, AUTHOR = {Artzner, P. and Delbaen, F. and Eber, J.-M. and Heath, D.}, TITLE = {Coherent measures of risk}, JOURNAL = {Math. Finance}, FJOURNAL = {Mathematical Finance. An International Journal of Mathematics, Statistics and Financial Economics}, VOLUME = {9}, YEAR = {1999}, NUMBER = {3}, PAGES = {203--228}, ISSN = {0960-1627}, MRCLASS = {91B30 (91B28)}, MRNUMBER = {1850791}, MRREVIEWER = {Yanhong Wu}, DOI = {10.1111/1467-9965.00068}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1111/1467-9965.00068}, } @book {AsterBorchersThurber:03, AUTHOR = {R. ASTER and B. BORCHERS and C. THURBER}, TITLE = {Parameter Estimation and Inverse Problems}, PUBLISHER = {Academic Press}, ADDRESS = {}, YEAR = {2004}, PAGES = {to appear}, MRCLASS = {}, MRNUMBER = {}, } @book {MR34:4027, AUTHOR = {Athans, Michael and Falb, Peter L.}, TITLE = {Optimal control. {A}n introduction to the theory and its applications}, PUBLISHER = {McGraw-Hill Book Co.}, ADDRESS = {New York}, YEAR = {1966}, PAGES = {xiv+879}, MRCLASS = {93.00}, MRNUMBER = {34 \#4027}, MRREVIEWER = {G. P. Szeg{\"o}}, } @ARTICLE {Au:86, author = "G. AUCHMUTY", title = "Dual variational principles for eigenvalue problems", journal = "Proceedings of Symposia in Pure Mathematics", year = "1986", volume = "45", pages = "55-71"} @TECHREPORT{Au:88, author = "G. AUCHMUTY", title = "Unconstrained variational principles for eigenvalues of real symmetric matrices", institution = "University of Houston", year = "1988", number = "Research Report UH/MD/-23"} @ARTICLE {Aus:77, author = "A. Auslender", title = "Minimisation sans constraintes de fonctions localement {L}ipschitziennes", journal = "Comptes Reud. Adac. So., Paris", year = "1977", volume = "284", pages = "959-961"} @INCOLLECTION {Aus:78, author = "A. Auslender", title = "Minimisation de fonctions localement {L}ipschitziennes: Applications \`{a} le programmation mi-convex, mi-differentiable", booktitle = "Nonlinear Programming 3", publisher = "Academic Press", year = "1978", editor = "O.L. Mangasarian and R.R. Meyer and S.M. Robinson", pages = "429-459", address = "New York, NY"} @ARTICLE {AuJo:83, author = "N.H. AUSTRIA and G.W. Johnson", title = "A quasi-{N}ewton method employing direct secant updates of matrix factorizations", journal = "SIAM J. Numer. Anal.", year = "1983", volume = "20", pages = "315-325"} @BOOK {Av:76, author = "M. AVRIEL", title = "Nonlinear Programming: Analysis and Methods", publisher = "Prentice-Hall", year = "1976", address = "Englewood Cliffs, NJ"} @INCOLLECTION {Ax:80a, author = "O. AXELSSON", title = "A generalized conjugate direction method and its application on a singular perturbation problem", booktitle = "Lecture Notes in Mathematics \#773, Numerical Analysis, Proceedings of the 8th Biennial Numerical Analysis Conference, Dundee, Scotland, June 26-29, 1979", publisher = "Springer-Verlag", year = "1980", editor = "G.A. Watson", address = "Berlin"} @book {MR95f:65005, AUTHOR = {AXELSSON, O.}, TITLE = {Iterative solution methods}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {1994}, PAGES = {xiv+654}, ISBN = {0-521-44524-8}, MRCLASS = {65-02 (65F10)}, MRNUMBER = {95f:65005}, MRREVIEWER = {Joaqu{\'{\i}}m J. J{\'u}dice}, } @ARTICLE {Ax:80b, author = "O. AXELSSON", title = "Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations", journal = laa, year = "1980", volume = "29", pages = "1-16"} @article {MR1831936, AUTHOR = {AXELSSON, O. and KAPORIN, I.}, TITLE = {Error norm estimation and stopping criteria in preconditioned conjugate gradient iterations}, JOURNAL = {Numer. Linear Algebra Appl.}, FJOURNAL = {Numerical Linear Algebra with Applications}, VOLUME = {8}, YEAR = {2001}, NUMBER = {4}, PAGES = {265--286}, ISSN = {1070-5325}, CODEN = {NLAAEM}, MRCLASS = {}, MRNUMBER = {1 831 936}, } @incollection{Aybat-book-2016, title = {Algorithms for Stable PCA}, booktitle = {Handbook of Robust Low Rank and Sparse Matrix Decomposition: Applications in Image and Video Processing}, publisher = {CRC Press, Taylor and Francis Group}, year = {2016}, author = {N.S. Aybat}, editor = {T. Bouwmans and N. S. Aybat and E. Zahzah}, } @article{Ma-Aybat-ieee-2018, author = {S. Ma and N.S. Aybat}, title = {Efficient Optimization Algorithms for Robust Principal Component Analysis and Its Variants}, journal = {Proceedings of the IEEE}, volume = "106", number = "8", pages = "1411-1426", year = {2018}, } %BBBBBBBB @article {MR815257, AUTHOR = {Bapat, R.B. and Sunder, V.S.}, TITLE = {On majorization and {S}chur products}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {72}, YEAR = {1985}, PAGES = {107--117}, ISSN = {0024-3795}, MRCLASS = {15A18 (15A57)}, MRNUMBER = {815257}, MRREVIEWER = {George P. Barker}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1016/0024-3795(85)90147-8}, } @book {BattBrun:17, author = "R. Battiti and M. Brunato", title = "The {LION} way. {M}achine {L}earning {\em plus} {I}ntelligent {O}ptimization", publisher = "LIONlab, University of Trento, Italy", year = "2017", url = "http://intelligent-optimization.org/LIONbook/" } @techreport{BabDongetal:07, AUTHOR = {M. BABOULIN and J. DONGARRA and S. GRATTON and J. LANGOU}, title = "Computing the Conditioning of the Components of a Linear Least Squares Solution", institution = "CERFACS and University of Tennessee", address = "Tennessee", number="arXiv:0710.0829v1", year = "2007", } @article {MR0084194, AUTHOR = {Douglas, Jr.J. and Rachford, Jr.H.H.}, TITLE = {On the numerical solution of heat conduction problems in two and three space variables}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {82}, YEAR = {1956}, PAGES = {421--439}, ISSN = {0002-9947}, MRCLASS = {65.3X}, MRNUMBER = {0084194 (18,827f)}, MRREVIEWER = {C. Saltzer}, } @ARTICLE{2008JSMTE..10..008B, author = {{Blondel}, V.~D. and {Guillaume}, J.-L. and {Lambiotte}, R. and {Lefebvre}, E.}, title = "{Fast unfolding of communities in large networks}", journal = {Journal of Statistical Mechanics: Theory and Experiment}, archivePrefix = "arXiv", eprint = {0803.0476}, primaryClass = "physics.soc-ph", year = 2008, month = oct, volume = 10, pages = {10008}, doi = {10.1088/1742-5468/2008/10/P10008}, adsurl = {http://adsabs.harvard.edu/abs/2008JSMTE..10..008B}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } @incollection {MR1183260, AUTHOR = {Goh, C.J. and Boland, N.L. and Mees, A.I.}, TITLE = {An algorithm for solving quadratic cost network flow optimization problems}, BOOKTITLE = {Optimization, {V}ol. 1, 2 ({S}ingapore, 1992)}, PAGES = {284--293}, PUBLISHER = {World Sci. Publ., River Edge, NJ}, YEAR = {1992}, MRCLASS = {90C35}, MRNUMBER = {1183260}, } @article {MR459599, AUTHOR = {Bland, R.G.}, TITLE = {New finite pivoting rules for the simplex method}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {2}, YEAR = {1977}, NUMBER = {2}, PAGES = {103--107}, ISSN = {0364-765X}, MRCLASS = {90C05}, MRNUMBER = {459599}, MRREVIEWER = {Jacques Dubois}, DOI = {10.1287/moor.2.2.103}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1287/moor.2.2.103}, } @article {MR1117772, AUTHOR = {Boland, N.L. and Goh, C.J. and Mees, A.I.}, TITLE = {An algorithm for solving quadratic network flow problems}, JOURNAL = {Appl. Math. Lett.}, FJOURNAL = {Applied Mathematics Letters. An International Journal of Rapid Publication}, VOLUME = {4}, YEAR = {1991}, NUMBER = {4}, PAGES = {61--64}, ISSN = {0893-9659}, MRCLASS = {90C35}, MRNUMBER = {1117772}, DOI = {10.1016/0893-9659(91)90056-2}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1016/0893-9659(91)90056-2}, } @article {MR1336787, AUTHOR = {Boukari, D. and Fiacco, A.V.}, TITLE = {Survey of penalty, exact-penalty and multiplier methods from 1968 to 1993}, JOURNAL = {Optimization}, FJOURNAL = {Optimization. A Journal of Mathematical Programming and Operations Research}, VOLUME = {32}, YEAR = {1995}, NUMBER = {4}, PAGES = {301--334}, ISSN = {0233-1934}, MRCLASS = {90C30 (90-02)}, MRNUMBER = {1336787}, DOI = {10.1080/02331939508844053}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1080/02331939508844053}, } @article {MR0434441, AUTHOR = {Borwein, J.M.}, TITLE = {Proper efficient points for maximizations with respect to cones}, JOURNAL = {SIAM J. Control Optimization}, FJOURNAL = {SIAM Journal on Control and Optimization}, VOLUME = {15}, YEAR = {1977}, NUMBER = {1}, PAGES = {57--63}, ISSN = {0363-0129}, MRCLASS = {90C30 (65K05 49B99)}, MRNUMBER = {0434441}, MRREVIEWER = {M. Rossler}, } @techreport{ArtachoBoTaDouglasRach:13, AUTHOR = {F.J.A. Artacho and J.M. Borwein and M.K. Tam}, TITLE = "Douglas-{R}achford Feasibility Methods for Matrix Completion Problems", TYPE = "Technical Report", NUMBER = "math.OC/01.308.4234v1 at arxiv.org", INSTITUTION = "CARMA, University of Newcastle", ADDRESS = "Callaghan, Australia", URL = "http://arxiv.org/abs/1308.4243", YEAR = "2013", } @article {ArtachoBoTa:13, AUTHOR = {F.J.A. Artacho and J.M. Borwein and M.K. Tam}, TITLE = {Recent results on {D}ouglas-{R}achford methods}, JOURNAL = {Serdica Mathematical Journal}, VOLUME = {39}, YEAR = {2013}, PAGES = {313--330}, } @article {MR3149115, AUTHOR = {Borwein, J.M. and Tam, M.K.}, TITLE = {A {C}yclic {D}ouglas--{R}achford {I}teration {S}cheme}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {160}, YEAR = {2014}, NUMBER = {1}, PAGES = {1--29}, ISSN = {0022-3239}, MRCLASS = {47-XX (90C25 90C48)}, MRNUMBER = {3149115}, DOI = {10.1007/s10957-013-0381-x}, URL = {http://dx.doi.org/10.1007/s10957-013-0381-x}, } @article {MR2140093, AUTHOR = {BAILEY, D.H. and Borwein, J.M.}, TITLE = {Experimental mathematics: examples, methods and implications}, JOURNAL = {Notices Amer. Math. Soc.}, FJOURNAL = {Notices of the American Mathematical Society}, VOLUME = {52}, YEAR = {2005}, NUMBER = {5}, PAGES = {502--514}, ISSN = {0002-9920}, CODEN = {AMNOAN}, MRCLASS = {00A35}, MRNUMBER = {MR2140093}, } @incollection {MR1852153, AUTHOR = {BAILEY, D.H. and Borwein, J.M.}, TITLE = {Experimental mathematics: recent developments and future outlook}, BOOKTITLE = {Mathematics unlimited---2001 and beyond}, PAGES = {51--66}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {2001}, note = {URL: users.cs.dal.ca/\~{ }jborwein/math-future.pdf}, url = {http://users.cs.dal.ca/~jborwein/math-future.pdf}, MRCLASS = {00A99}, MRNUMBER = {MR1852153}, } @incollection {MR2389624, AUTHOR = {Hachez, Y. and Woerdeman, H.J.}, TITLE = {The {F}ischer-{F}robenius transformation and outer factorization}, BOOKTITLE = {Operator theory, structured matrices, and dilations}, SERIES = {Theta Ser. Adv. Math.}, VOLUME = {7}, PAGES = {181--203}, PUBLISHER = {Theta, Bucharest}, YEAR = {2007}, MRCLASS = {47A68 (15A48 47B35 90C22)}, MRNUMBER = {2389624}, MRREVIEWER = {A. B\"ottcher}, } @article {MR2151933, AUTHOR = {Hachez, Y. and Woerdeman, H.J.}, TITLE = {Approximating sums of squares with a single square}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {399}, YEAR = {2005}, PAGES = {187--201}, ISSN = {0024-3795}, MRCLASS = {41A50 (42A10 90C22 93E11)}, MRNUMBER = {2151933}, MRREVIEWER = {Mihail Voicu}, DOI = {10.1016/j.laa.2004.10.005}, URL = {https://doi.org/10.1016/j.laa.2004.10.005}, } @incollection {MR1246810, AUTHOR = {Bakonyi, M. and Woerdeman, H.J.}, TITLE = {The central method for positive semi-definite, contractive and strong {P}arrott type completion problems}, BOOKTITLE = {Operator theory and complex analysis ({S}apporo, 1991)}, SERIES = {Oper. Theory Adv. Appl.}, VOLUME = {59}, PAGES = {78--95}, PUBLISHER = {Birkh\"auser, Basel}, YEAR = {1992}, MRCLASS = {47A57 (47A20)}, MRNUMBER = {1246810}, MRREVIEWER = {Aurelian Gheondea}, } @article {MR1321785, AUTHOR = {Bakonyi, M. and Woerdeman, H.J.}, TITLE = {Maximum entropy elements in the intersection of an affine space and the cone of positive definite matrices}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {16}, YEAR = {1995}, NUMBER = {2}, PAGES = {369--376}, ISSN = {0895-4798}, MRCLASS = {15A15 (15A48 62F99)}, MRNUMBER = {1321785}, MRREVIEWER = {Jacques Dubois}, DOI = {10.1137/S0895479893243542}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/S0895479893243542}, } @book {MR2807419, AUTHOR = {Bakonyi, M. and Woerdeman, H.J.}, TITLE = {Matrix completions, moments, and sums of {H}ermitian squares}, PUBLISHER = {Princeton University Press, Princeton, NJ}, YEAR = {2011}, PAGES = {xii+518}, ISBN = {978-0-691-12889-4}, MRCLASS = {47A05 (15A83 47A20 47A57)}, MRNUMBER = {2807419}, MRREVIEWER = {Andr{\'e} C. M. Ran}, DOI = {10.1515/9781400840595}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1515/9781400840595}, } @TECHREPORT {BaWo:91, author = "M. BAKONYI and H.J. WOERDEMAN", title = "Maximum entropy elements in the intersection of an affine space and the cone of positive definite matrices", institution = "Department of Mathematics, College of William and Mary", year = "1991", address = "Williamsburg, Virginia" } @article {BaTaTsZh:93, author = "A.S. EL-BAKRY and R.A. Tapia and T. TSUCHIYA and Y. ZHANG", title = "On the formulation and theory of the {N}ewton interior-point method for nonlinear programming", journal = jota, institution = "Department of Mathematical Sciences, Rice University", year = "1996", volume = "89", pages = "507-541", address = "Houston, TX"} @ARTICLE {BaJuRe:89, author = "F. BARAHONA, M. J{\"{U}}NGER and G. REINELT", title = "Experiments in quadratic 0-1 programming", journal = mprog, year = "1989", volume = "44", pages = "127-137"} @BOOK {Ba:70, author = "Y. BARD", title = "Nonlinear Parameter Estimation", publisher = "Academic Press", year = "1970", address = "New York, NY"} @TECHREPORT {Barlow:91, author = "J.L. BARLOW", title = " Error Analysis of update methods for the symmetric eigenvalue problem", institution = "Department of Computer Science, Penn State", year = "1991", number = "CS-91-09", address = "Univ. Park, PA 16802", note = "To appear in SIMAX"} @ARTICLE {Ba:65, author = "J. BARNES", title = "An algorithm for solving nonlinear equations based on the secant method", journal = "Comput. J.", year = "1965", volume = "8", pages = "66-72"} \@ARTICLE {Ba:82, author = "E.R. BARNES", title = "An algorithm for partitioning the nodes of a graph", journal = "SIAM J. Algebraic and Discrete Mathematics", year = "1982 ", volume = "3", pages = "541-550"} @article{int:Barnes1, author = "E. R. BARNES", title = "A variation on {K}armarkar's algorithm for solving linear programming problems", journal = mprog, volume = "36", year = "1986", pages = "174--182" } @inproceedings {int:Barnes91, author = "E. R. BARNES", title = "On the convergence of the affine algorithm", booktitle = "Proceedings of Symposium on Mathematical Developments Arising From Linear Programming", publisher= "AMS", volume = "114", year = "1991", pages = "131-139" } \@INCOLLECTION {BaHo:84, author = "E.R. BARNES and A.J. Hoffman", title = "Paritioning, spectra, and linear programming", booktitle = "Progress in Combinatorial Optimization", publisher = "Academic Press", year = "1984 ", editor = "W.E. Pulleyblank", pages = "13-25"} \@ARTICLE {BaVaWa:88, author = "E.R. BARNES and A. VANNELLI and J.Q.WALKER", title = "A new heuristic for partitioning the nodes of a graph", journal = "SIAM J. Discrete Mathematics", year = "1988 ", volume = "1", pages = "299-305"} @BOOK {BaBo:83, author = "R.E. BARNHILL and W. BOEHM (eds.)", title = "Surfaces in Computer Aided Geometric Design", publisher = "North-Holland", year = "1983", address = "Amsterdam"} @BOOK {BaRi:75, author = "R.E. BARNHILL and R.F. RIESENFELD", title = "Computer Aided Geometric Design", publisher = "Academic Press", year = "1975", address = "New York, NY"} @MISC {BaDe:79, author = "P. BARRERA and J.E. {Dennis Jr.}", title = "When to stop making quasi-{N}ewton updates", note = "Presented at the 10th. International Simposium on Mathematical Programming, 1979"} @article {MR2398876, AUTHOR = {Demmel, J.W. and Marques, O.A. and Parlett, B.N. and V{\"o}mel, C.}, TITLE = {Performance and accuracy of {LAPACK}'s symmetric tridiagonal eigensolvers}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {30}, YEAR = {2008}, NUMBER = {3}, PAGES = {1508--1526}, ISSN = {1064-8275}, CODEN = {SJOCE3}, MRCLASS = {65F15 (65Y20)}, MRNUMBER = {2398876 (2008m:65116)}, MRREVIEWER = {Ross A. Lippert}, DOI = {10.1137/070688778}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/070688778}, } @article{Demmel:1993:GSD:152613.152616, author = {Demmel, J. and K{\aa}gstr\"{o}m, B.}, title = {The generalized {S}chur decomposition of an arbitrary pencil ${A}-\lambda {B}$; robust software with error bounds and applications. Part {II}: software and applications}, journal = {ACM Trans. Math. Softw.}, issue_date = {June 1993}, volume = {19}, number = {2}, month = jun, year = {1993}, issn = {0098-3500}, pages = {175--201}, numpages = {27}, url = {http://doi.acm.org/10.1145/152613.152616}, doi = {10.1145/152613.152616}, acmid = {152616}, publisher = {ACM}, address = {New York, NY, USA}, keywords = {Kronecker canonical form, Schur decomposition, controllable subspace, generalized eigenvalues, ill-posed problem, matrix pencils, reducing subspaces, uncontrollable modes}, } @article {MR1236734, AUTHOR = {Barrett, W. and Johnson, C.R. and Tarazaga, P.}, TITLE = {The real positive definite completion problem for a simple cycle}, NOTE = {Computational linear algebra in algebraic and related problems (Essen, 1992)}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {192}, YEAR = {1993}, PAGES = {3--31}, ISSN = {0024-3795}, MRCLASS = {15A99 (05C50)}, MRNUMBER = {1236734}, DOI = {10.1016/0024-3795(93)90234-F}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/0024-3795(93)90234-F}, } @BOOK{templates, author = {R. BARRETT and M. BERRY and T. CHAN and J.W. DEMMEL and J. DONATO and J. DONGARRA and V. EIJKHOUT and R. POZO and C. ROMINE and H. van der VORST}, title = {Templates for the solution of linear systems}, year = 1994, publisher = {SIAM}, url = {http://www.netlib.org/templates/templates.ps} } @article {BaJoLo:93, author = "W.W. BARRETT and C.R. Johnson and R. LOEWY", title = "The real positive definite completion problem: cycle completability", journal = "Memoirs of the American Mathematical Society", year = "1996", pages = "71pp" } @article {MR88f:15049, AUTHOR = {Loewy, Raphael}, TITLE = {Diagonal similarity of matrices}, NOTE = {Linear algebra and its applications (Coimbra, 1984)}, JOURNAL = {Portugal. Math.}, FJOURNAL = {Portugaliae Mathematica}, VOLUME = {43}, YEAR = {1985/86}, NUMBER = {1}, PAGES = {55--59}, ISSN = {0032-5155}, CODEN = {POMAAJ}, MRCLASS = {15A99}, MRNUMBER = {88f:15049}, MRREVR = {M. Pearl}, } @ARTICLE {BaJoLu:89, author = "W.W. BARRETT and C.R. Johnson and M. LUNDQUIST", title = "Determinantal formulae for matrix completions associated with chordal graphs", journal = laa, year = "1989", volume = "121", pages = "265-289"} @incollection {MR1320296, AUTHOR = {Blair, J.R.S. and Peyton, B.}, TITLE = {An introduction to chordal graphs and clique trees}, BOOKTITLE = {Graph theory and sparse matrix computation}, SERIES = {IMA Vol. Math. Appl.}, VOLUME = {56}, PAGES = {1--29}, PUBLISHER = {Springer, New York}, YEAR = {1993}, MRCLASS = {05C75 (05C85 68Q25)}, MRNUMBER = {1320296}, MRREVIEWER = {Alexander Barg}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/978-1-4613-8369-7_1}, } @INCOLLECTION {BaCo:81, author = "R. Bartels and A. Conn", title = "An approach to nonlinear $l_{1}$ data fitting", booktitle = "Lecture Notes in Mathematics, Numerical Analysis, Proceedings of the Third IIMAS Workshop held at Cocoyoc, Mexico, January 1981", publisher = "Springer-Verlag", year = "1981", editor = "J.P. Hennart", pages = "48-58", address = "Berlin"} @ARTICLE {BaPl:88, author = "J.J. Bartholdi III and L.K. Platzman", title = "Heuristics based on spacefilling curves for combinatorial problems in {E}uclidean space", journal = "Management Science", year = "1988", volume = "34", pages = "291-305"} @INCOLLECTION {BaBi:80, author = "M.C. BARTHOLOMEW-BIGGS", title = "Recursive quadratic programming based on penalty functions for constrained minimization", booktitle = "Nonlinear Optimization, Theory and Algorithms", publisher = "Birkhauser", year = "1980", editor = "L.C.W. Dixon and E. Spedicato and G.P. Szego"} @INCOLLECTION {BaBi:82, author = "M.C. BARTHOLOMEW-BIGGS", title = "Recursive quadratic programming methods for nonlinear constraints", booktitle = "Nonlinear Optimization 1981", publisher = "Academic Press", year = "1982", editor = "M.J.D. Powell", address = "London"} @phdthesis{JimitM:21, author = "J. Majmudar", year = 2021, title = "Recovery Guarantees for Graph Clustering Problems", school = "Department of Combinatorics and Optimization, University of Waterloo" } @techreport{majmudar2021robust, title={Robust Correlation Clustering with Asymmetric Noise}, author={Jimit Majmudar and Stephen Vavasis}, year={2021}, institution = "Department of Combinatorics and Optimization, University of Waterloo", eprint={2110.08385}, archivePrefix={arXiv}, primaryClass={cs.SI} } @techreport{majmudar2020provable, title={Provable Overlapping Community Detection in Weighted Graphs}, author={Jimit Majmudar and Stephen Vavasis}, year={2020}, institution = "Department of Combinatorics and Optimization, University of Waterloo", eprint={2004.07150}, archivePrefix={arXiv}, primaryClass={cs.SI} } @ARTICLE {BaBo:88, author = "J. Barzilai and J.M. Borwein", title = "Two point step size gradient methods", journal = imajna, year = "1988", volume = "8", pages = "141-148"} @incollection {BaCoGa:92, author = "J. BARZILAI and W.D. COOK and B. GOLANY", title = "The analytic hierarchy process: structure of the problem and its solutions", booktitle = "Systems and Management Science by Extremal Methods", editor = "F.Y. Phillips and J.J. Rousseau", year = "1992", publisher = "Kluwer Academic Publishers", pages = "361-371"} @article{Birk:46, author = "Birkoff, G.", title = "Tres observaciones sobre el algebra lineal", journal = "Univ. Nac. Tucuman Rev.", volume = "Ser. A", pages = "147--151", year = "1946" } Article{bate:1983, journal = "Technometrics", volume = "25", pages = "373--376", keywords = "D-optimality; Sequential design", author = "Douglas Bates", title = "The Derivative of the Determinant of {X}'{X} and Its Uses", year = "1983", } @Article{bate:watt:1984, journal = "Communications in Stat., Part B--Simulation and Comp.", volume = "13", pages = "705--715", keywords = "Computer program; Nonlinear least squares", author = "Douglas M. Bates and Donald G. Watts", title = "A Multi-response {G}auss-{N}ewton Algorithm", year = "1984", } @Article{bate:watt:1985, journal = "Technometrics", volume = "27", pages = "329--360", keywords = "Gradient; Hessian; Convergence", author = "Douglas M. Bates and Donald G. Watts", title = "Multiresponse Estimation With Special Application to Linear Systems of Differential Equations", year = "1985", } @Article{bate:watt:1987, journal = "SIAM J. on Scientific and Stat'l. Computing", volume = "8", pages = "49--55", keywords = "Nonlinear optimization", author = "Douglas M. Bates and Donald G. Watts", title = "A Generalized {G}auss-{N}ewton Procedure for Multi-response Parameter Estimation", year = "1987", } @Article{lind:bate:1988, journal = JASA, volume = "83", pages = "1014--1022", keywords = "Growth curve; Longitudinal data", author = "Mary J. Lindstrom and Douglas M. Bates", title = "{N}ewton-{R}aphson and {E}{M} Algorithms for Linear Mixed-effects Models for Repeated-measures Data", year = "1988", } @Book{bate:watt:1988, publisher = "Wiley", address = "New York", pages = "365", author = "Douglas M. Bates and Donald G. Watts", title = "Nonlinear Regression Analysis and Its Applications", year = "1988", } @ARTICLE {BaEnSt:81, author = "K.J. BATHE and M.S. ENGELMAN and G. STRANG", title = "The application of quasi-{N}ewton methods in fluid mechanics", journal = "Internat. J. Numer. Methods Engrg.", year = "1981", volume = "17", pages = "707-718"} @ARTICLE {BaWa:80, author = "D.M. BATES and D.G. WATTS", title = "Relative curvature measures of nonlinearity", journal = "J. Roy. Statist. Soc. Ser. B", year = "1980", volume = "42", pages = "1-25"} @ARTICLE {BaiDemMck:89, author = "Z. BAI and J.W. DEMMEL and A. MCKENNEY", title = "On the conditioning of the nonsymmetric eigenproblem: Theory and software", journal = "Preprint CS-89-86, Courant Institute", year = "1989"} @book {MR889048, AUTHOR = {BAUMEISTER, J.}, TITLE = {Stable solution of inverse problems}, SERIES = {Advanced Lectures in Mathematics}, PUBLISHER = {Friedr. Vieweg \& Sohn}, ADDRESS = {Braunschweig}, YEAR = {1987}, PAGES = {viii+254}, ISBN = {3-528-08961-X}, MRCLASS = {65-02 (35R30 45-02 47-02 47A50 65J10)}, MRNUMBER = {MR889048 (89a:65004)}, MRREVIEWER = {Charles W. Groetsch}, } @article {MR3175442, AUTHOR = {Jiang, B. and Dai, Y.-H.}, TITLE = {Feasible {B}arzilai-{B}orwein-like methods for extreme symmetric eigenvalue problems}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods \& Software}, VOLUME = {28}, YEAR = {2013}, NUMBER = {4}, PAGES = {756--784}, ISSN = {1055-6788}, MRCLASS = {90C20}, MRNUMBER = {3175442}, MRREVIEWER = {Laura Martein}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1080/10556788.2012.656115}, } @INCOLLECTION {Be:67, author = "E.M.L. BEALE", title = "Numerical Methods", booktitle = "Nonlinear Programming", publisher = "North-Holland", year = "1967", editor = "J. Abadie", address = "Amsterdam"} @INCOLLECTION {Bea:77, author = "E.M.L. BEALE", title = "Integer programming", booktitle = "The State of the Art in Numerical Analysis", publisher = "Academic Press", year = "1977", editor = "D. Jacobs", pages = "409-448", address = "London"} @article {Bertsimas10, AUTHOR = {Bertsimas, D. and Doan, X.V. and Natarajan, K. and Teo, C.-P.}, TITLE = {Models for minimax stochastic linear optimization problems with risk aversion}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {35}, YEAR = {2010}, NUMBER = {3}, PAGES = {580--602}, ISSN = {0364-765X}, MRCLASS = {90C47 (90C15 90C22)}, MRNUMBER = {2724065}, MRREVIEWER = {Huifu Xu}, DOI = {10.1287/moor.1100.0445}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1287/moor.1100.0445}, } @article{Bouwmans-survey-cviu-2014, author = {T. Bouwmans and E.H. Zahzah}, title = {Robust PCA via Principal Component Pursuit: A review for a comparative evaluation in video surveillance}, journal = {Computer Vision and Image Understanding}, year = {2014}, volume = {122}, pages = {22-34}, } @article {MR1324058, AUTHOR = {Chan, R.H. and Wong, C.K.}, TITLE = {Best-conditioned circulant preconditioners}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {218}, YEAR = {1995}, PAGES = {205--211}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {65F35}, MRNUMBER = {MR1324058 (95m:65081)}, } @TECHREPORT {ChMeBeSh:98, author = "T.-J. CHANG and N. MEADE and J.E. BEASLEY and Y.M. SHARAIHA", title = "Heuristics for cardinality constrained portfolio optimisation", institution = "The Management School", year = "1998", address = "Imperial College, London"} @ARTICLE {BeTu:74, author = "A.E. BEATON and J.W. TUKEY", title = "The fitting of power series, meaning polynomials, illustrated on hand-spectroscopic data", journal = "Technometrics", year = "1974", volume = "16", pages = "147-192"} @article{Beck05, AUTHOR = {Beck, A. and Eldar, Y.C.}, title = "Strong duality in nonconvex quadratic optimization with two quadratic constraints", journal = siopt, volume = "17", number = "3", pages = "844-860", year = "2006" } @article {MR2520357, AUTHOR = {Beck, A.}, TITLE = {Convexity properties associated with nonconvex quadratic matrix functions and applications to quadratic programming}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {142}, YEAR = {2009}, NUMBER = {1}, PAGES = {1--29}, ISSN = {0022-3239}, CODEN = {JOTABN}, MRCLASS = {90C20}, MRNUMBER = {MR2520357}, DOI = {10.1007/s10957-009-9539-y}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s10957-009-9539-y}, } @article {MR2488072, AUTHOR = {Beck, A. and Ben-Tal, A.}, TITLE = {Duality in robust optimization: primal worst equals dual best}, JOURNAL = {Oper. Res. Lett.}, FJOURNAL = {Operations Research Letters}, VOLUME = {37}, YEAR = {2009}, NUMBER = {1}, PAGES = {1--6}, ISSN = {0167-6377}, CODEN = {ORLED5}, MRCLASS = {90C25 (90C31)}, MRNUMBER = {MR2488072 (2009k:90082)}, MRREVIEWER = {Henry Wolkowicz}, DOI = {10.1016/j.orl.2008.09.010}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/j.orl.2008.09.010}, } @article {MR2399588, AUTHOR = {Beck, A. and BEN-TAL, A. and KANZOW, C.}, TITLE = {A fast method for finding the global solution of the regularized structured total least squares problem for image deblurring}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {30}, YEAR = {2008}, NUMBER = {1}, PAGES = {419--443}, ISSN = {0895-4798}, MRCLASS = {90C26 (15A29 94A08)}, MRNUMBER = {MR2399588 (2009a:90080)}, MRREVIEWER = {Jinhai Chen}, DOI = {10.1137/070709013}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/070709013}, } @article {MR2329128, AUTHOR = {Beck, A.}, TITLE = {On the convexity of a class of quadratic mappings and its application to the problem of finding the smallest ball enclosing a given intersection of balls}, JOURNAL = {J. Global Optim.}, FJOURNAL = {Journal of Global Optimization. An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering}, VOLUME = {39}, YEAR = {2007}, NUMBER = {1}, PAGES = {113--126}, ISSN = {0925-5001}, CODEN = {JGOPEO}, MRCLASS = {90C26}, MRNUMBER = {MR2329128 (2008j:90095)}, DOI = {10.1007/s10898-006-9127-8}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s10898-006-9127-8}, } @article {MR2255337, AUTHOR = {Beck, A. and BEN-TAL, A. and TEBOULLE, M.}, TITLE = {Finding a global optimal solution for a quadratically constrained fractional quadratic problem with applications to the regularized total least squares}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {28}, YEAR = {2006}, NUMBER = {2}, PAGES = {425--445 (electronic)}, ISSN = {0895-4798}, MRCLASS = {90C20 (65K10 90C32)}, MRNUMBER = {MR2255337 (2007h:90042)}, MRREVIEWER = {Michael Patriksson}, DOI = {10.1137/040616851}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/040616851}, } @article {MR1771780, AUTHOR = {Beckermann, B.}, TITLE = {The condition number of real {V}andermonde, {K}rylov and positive definite {H}ankel matrices}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {85}, YEAR = {2000}, NUMBER = {4}, PAGES = {553--577}, ISSN = {0029-599X}, CODEN = {NUMMA7}, MRCLASS = {65F35 (15A12 65F20)}, MRNUMBER = {MR1771780 (2001e:65075)}, MRREVIEWER = {Jin Xi Zhao}, } @article {Bellare, AUTHOR = "M. BELLARE and P. ROGAWAY", TITLE = {The complexity of approximating a nonlinear program}, JOURNAL = mprog, FJOURNAL = {Mathematical Programming}, VOLUME = {69}, YEAR = {1995}, PAGES = {429--442}, } @incollection {FanBell:63, AUTHOR = {Bellman, Richard and Fan, Ky}, TITLE = {On systems of linear inequalities in {H}ermitian matrix variables}, BOOKTITLE = {Convexity, Proc. Sympos. Pure Math., Vol. VII}, Editor = {V.L. Klee}, PAGES = {1--11}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, R.I.}, YEAR = {1963}, MRCLASS = {15.50}, MRNUMBER = {MR0154876 (27 \#4820)}, MRREVIEWER = {B. J. Stone}, } @techreport{BensShanVander:00, AUTHOR = {BENSON, H.Y. and SHANNO, D.F. and Vanderbei, R.J.}, title = "Interior-Point Methods for Nonconvex Nonlinear Programming: Jamming and Comparative Numerical Testing", institution = "Statistics and Operations Research, Princeton University", address = "Princeton, NJ", keywords = "interior-point, NLP", year = "2000" } @article {BenTal09b, AUTHOR = {Ben-Tal, A. and Nemirovski, A.}, TITLE = {On safe tractable approximations of chance-constrained linear matrix inequalities}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {34}, YEAR = {2009}, NUMBER = {1}, PAGES = {1--25}, ISSN = {0364-765X}, MRCLASS = {90C15 (90C22)}, MRNUMBER = {2542986 (2010j:90089)}, MRREVIEWER = {Roland Hildebrand}, DOI = {10.1287/moor.1080.0352}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1287/moor.1080.0352}, } @incollection {MR1748769, AUTHOR = {Ben-Tal, A. and Margalit, T. and Nemirovski, A.}, TITLE = {Robust modeling of multi-stage portfolio problems}, BOOKTITLE = {High performance optimization}, SERIES = {Appl. Optim.}, VOLUME = {33}, PAGES = {303--328}, PUBLISHER = {Kluwer Acad. Publ., Dordrecht}, YEAR = {2000}, MRCLASS = {90C15 (91B28)}, MRNUMBER = {1748769}, MRREVIEWER = {K. Zimmermann}, DOI = {10.1007/978-1-4757-3216-0_12}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/978-1-4757-3216-0_12}, } @article {MR95b:90079, AUTHOR = {Ben-Tal, A. and Eiger, G. and Gershovitz, V.}, TITLE = {Global minimization by reducing the duality gap}, JOURNAL = mprog, FJOURNAL = {Mathematical Programming}, VOLUME = {63}, YEAR = {1994}, NUMBER = {2, Ser. A}, PAGES = {193--212}, ISSN = {0025-5610}, CODEN = {MHPGA4}, } @article {MR669724, AUTHOR = {Ben-Israel, A. and Ben-Tal, A. and Zlobec, S.}, TITLE = {Optimality in convex programming: a feasible directions approach}, NOTE = {Optimality and stability in mathematical programming}, JOURNAL = {Math. Programming Stud.}, FJOURNAL = {Mathematical Programming Study}, NUMBER = {19}, YEAR = {1982}, PAGES = {16--38}, ISSN = {0303-3929}, CODEN = {MPSTDF}, MRCLASS = {90C25 (65K05)}, MRNUMBER = {MR669724 (83m:90070)}, MRREVIEWER = {Bruce D. Craven}, } @book {MR607673, AUTHOR = {Ben-Israel, A. and Ben-Tal, A. and Zlobec, S.}, TITLE = {Optimality in nonlinear programming: a feasible directions approach}, NOTE = {A Wiley-Interscience Publication}, PUBLISHER = {John Wiley \& Sons, Inc., New York}, YEAR = {1981}, PAGES = {xii+144}, ISBN = {0-471-08057-8}, MRCLASS = {90C30 (49D37)}, MRNUMBER = {607673}, MRREVIEWER = {J. Abrham}, } @preamble{ "\def\cprime{$'$} " } @incollection {MR580462, AUTHOR = {Ben-Israel, A. and Ben-Tal, A. and Zlobec, S.}, TITLE = {Optimality conditions in convex programming}, BOOKTITLE = {Survey of mathematical programming (Proc. Ninth Internat. Math. Programming Sympos., Budapest, 1976), Vol. 1}, PAGES = {153--169}, PUBLISHER = {North-Holland}, ADDRESS = {Amsterdam}, YEAR = {1979}, MRCLASS = {90C25}, MRNUMBER = {MR580462 (82c:90071)}, MRREVIEWER = {N. N. Astaf{\cprime}ev}, } @article {MR539539, AUTHOR = {Ben-Israel, A. and Ben-Tal, A. and Zlobec, S.}, TITLE = {Characterizations of optimality in convex programming: the nondifferentiable case}, JOURNAL = {Applicable Anal.}, FJOURNAL = {Applicable Analysis. An International Journal}, VOLUME = {9}, YEAR = {1979}, NUMBER = {2}, PAGES = {137--156}, ISSN = {0003-6811}, CODEN = {APANCC}, MRCLASS = {90C25}, MRNUMBER = {MR539539 (80i:90074)}, MRREVIEWER = {J. Parida}, } @article {MR0439190, AUTHOR = {Ben-Israel, A. and Ben-Tal, A. and Zlobec, S.}, TITLE = {Characterization of optimality in convex programming without a constraint qualification}, JOURNAL = {J. Optimization Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {20}, YEAR = {1976}, NUMBER = {4}, PAGES = {417--437}, ISSN = {0022-3239}, MRCLASS = {90C25}, MRNUMBER = {MR0439190 (55 \#12087)}, MRREVIEWER = {Jean-Baptiste Hiriart-Urruty}, } @book {BBZ:81, AUTHOR = {Ben-Israel, A. and Ben-Tal, A. and Zlobec, S.}, TITLE = {Optimality in nonlinear programming: a feasible directions approach}, NOTE = {A Wiley-Interscience Publication}, PUBLISHER = {John Wiley \&\ Sons Inc.}, ADDRESS = {New York}, YEAR = {1981}, PAGES = {xii+144}, ISBN = {0-471-08057-8}, } @ARTICLE {BeNe:94, author = "A. BEN-TAL and A.S. Nemirovski", title = "Potential reduction polynomial time method for truss topology design", journal = siopt, year = "1994", volume = "4", pages = "596-612"} @article {MR2280215, AUTHOR = {Teboulle, M.}, TITLE = {A unified continuous optimization framework for center-based clustering methods}, JOURNAL = {J. Mach. Learn. Res.}, FJOURNAL = {Journal of Machine Learning Research (JMLR)}, VOLUME = {8}, YEAR = {2007}, PAGES = {65--102}, ISSN = {1532-4435}, MRCLASS = {62H30 (90C90)}, MRNUMBER = {2280215}, } @article {BeTe:93, AUTHOR = {Ben-Tal, A. and Teboulle, M.}, TITLE = {Hidden convexity in some nonconvex quadratically constrained quadratic programming}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {72}, YEAR = {1996}, NUMBER = {1, Ser. A}, PAGES = {51--63}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C26 (90C20)}, MRNUMBER = {97a:90047}, MRREVIEWER = {Stefan Mititelu}, } @article {MR84d:90090, AUTHOR = {BEN-TAL, A. and ZOWE, J.}, TITLE = {A unified theory of first and second order conditions for extremum problems in topological vector spaces}, JOURNAL = {Math. Programming Stud.}, FJOURNAL = {Mathematical Programming Study}, volume = {19}, YEAR = {1982}, PAGES = {39--76}, ISSN = {0303-3929}, CODEN = {MPSTDF}, } @article {MR2168342, AUTHOR = {Benzi, M. and Golub, G.H. and LIESEN, J.}, TITLE = {Numerical solution of saddle point problems}, JOURNAL = {Acta Numer.}, FJOURNAL = {Acta Numerica}, VOLUME = {14}, YEAR = {2005}, PAGES = {1--137}, ISSN = {0962-4929}, MRCLASS = {65F10 (76D07 90C47)}, MRNUMBER = {MR2168342 (2006m:65059)}, MRREVIEWER = {Timothy Nigel Phillips}, DOI = {10.1017/S0962492904000212}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1017/S0962492904000212}, } @article {MR2112850, AUTHOR = {Benzi, Michele and Golub, Gene H.}, TITLE = {A preconditioner for generalized saddle point problems}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {26}, YEAR = {2004}, NUMBER = {1}, PAGES = {20--41 (electronic)}, ISSN = {0895-4798}, MRCLASS = {65F10}, MRNUMBER = {MR2112850 (2005j:65026)}, MRREVIEWER = {Judith M. Ford}, DOI = {10.1137/S0895479802417106}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/S0895479802417106}, } @article {MR2058873, AUTHOR = {Benzi, Michele and Gander, Martin J. and Golub, Gene H.}, TITLE = {Optimization of the {H}ermitian and skew-{H}ermitian splitting iteration for saddle-point problems}, JOURNAL = {BIT}, FJOURNAL = {BIT. Numerical Mathematics}, VOLUME = {43}, YEAR = {2003}, NUMBER = {suppl.}, PAGES = {881--900}, ISSN = {0006-3835}, MRCLASS = {65F10 (65N22)}, MRNUMBER = {MR2058873 (2005e:65032)}, MRREVIEWER = {Zden{\v{e}}k Dost{\'a}l}, DOI = {10.1023/B:BITN.0000014548.26616.65}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1023/B:BITN.0000014548.26616.65}, } @article {MR1708693, AUTHOR = {Benzi, Michele and Golub, Gene H.}, TITLE = {Bounds for the entries of matrix functions with applications to preconditioning}, JOURNAL = {BIT}, FJOURNAL = {BIT. Numerical Mathematics}, VOLUME = {39}, YEAR = {1999}, NUMBER = {3}, PAGES = {417--438}, ISSN = {0006-3835}, MRCLASS = {65F10 (15A12 65F30)}, MRNUMBER = {MR1708693 (2000h:65047)}, MRREVIEWER = {George D. Poole}, DOI = {10.1023/A:1022362401426}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1023/A:1022362401426}, } @ARTICLE {Beck:48, author = "E.F. BECKENBACH", title = "Convex functions", journal = "Bull. Amer. Math. Soc.", year = "1948", volume = "54", pages = "439-460"} @BOOK {BeBe, AUTHOR = {BECKENBACH, E. F. and BELLMAN, R.}, TITLE = {Inequalities}, NOTE = {Second revised printing. Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge, Band 30}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York, Inc.}, YEAR = {1965}, PAGES = {xi+198}, MRCLASS = {26.70 (26.00)}, MRNUMBER = {33 #236}, MRREVR = {J. Acz{\'e}l}, } @BOOK {Bell:57, author = "R. BELLMAN", title = "Dynamic Programming", publisher = "Princeton University Press", year = "1957", address = "Princeton, NJ"} @BOOK {Bell:60, author = "R. BELLMAN", title = "Introduction to Matrix Analysis", publisher = "McGraw Hill", year = "1957", address = "New York"} @article {MR40:5260, AUTHOR = {Beltrami, E. J.}, TITLE = {A constructive proof of the {K}uhn-{T}ucker multiplier rule}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {26}, YEAR = {1969}, PAGES = {297--306}, } @article {MR0252035, AUTHOR = {Beltrami, E. J.}, TITLE = {A constructive proof of the {K}uhn-{T}ucker multiplier rule}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {26}, YEAR = {1969}, PAGES = {297--306}, ISSN = {0022-247x}, MRCLASS = {90.58}, MRNUMBER = {0252035 (40 \#5260)}, MRREVIEWER = {G. Reklaitis}, } @BOOK {Berg:66, author = "C. BERGE", title = "Espaces topoligiques. Fonctions multivoques", publisher = "Dunod", year = "1966", address = "Paris"} @ARTICLE {Be:90, author = "M. Berger", title = "Convexity", journal = "American Mathematical Monthly", year = "1990", volume = "97", pages = "650-678"} @TECHREPORT {BeJaRoTe:96, author = "A.B. Berkelaar and B. Jansen and K. Roos and T. Terlaky", title = "Sensitivity analysis in (degenerate) quadratic programming", institution = "Tinbergen Institute Rotterdam", year = "1996", keywords = "sensitivity analysis, quadratic programming" } @article {MR2072530, AUTHOR = {BERGAMASCHI, L. and Gondzio, J. and ZILLI, G.}, TITLE = {Preconditioning indefinite systems in interior point methods for optimization}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {28}, YEAR = {2004}, NUMBER = {2}, PAGES = {149--171}, ISSN = {0926-6003}, CODEN = {CPPPEF}, MRCLASS = {90C51 (65F10 90C20 90C30)}, MRNUMBER = {MR2072530 (2005f:90154)}, MRREVIEWER = {Ji-Ming Peng}, } @book {MR1464690, AUTHOR = {Berge, C.}, TITLE = {Topological spaces}, NOTE = {Including a treatment of multi-valued functions, vector spaces and convexity, Translated from the French original by E. M. Patterson, Reprint of the 1963 translation}, PUBLISHER = {Dover Publications, Inc., Mineola, NY}, YEAR = {1997}, PAGES = {xiv+270}, ISBN = {0-486-69653-7}, MRCLASS = {54-01 (04-01)}, MRNUMBER = {1464690}, } @book {MR1260009, TITLE = {Degeneracy in optimization problems}, EDITOR = {Gal, T.}, NOTE = {Ann. Oper. Res. {{\bf{4}}6/47} (1993), no. 1-4}, PUBLISHER = {Baltzer Science Publishers BV, Bussum}, YEAR = {1993}, PAGES = {i--vi and 1--560}, ISSN = {0254-5330}, MRCLASS = {90-06 (90C27 90C31)}, MRNUMBER = {1260009}, } @article {MR1260019, AUTHOR = {Terlaky, T. and Zhang, S.Z.}, TITLE = {Pivot rules for linear programming: a survey on recent theoretical developments}, NOTE = {Degeneracy in optimization problems}, JOURNAL = {Ann. Oper. Res.}, FJOURNAL = {Annals of Operations Research}, VOLUME = {46/47}, YEAR = {1993}, NUMBER = {1-4}, PAGES = {203--233}, ISSN = {0254-5330}, MRCLASS = {90C05 (90-02)}, MRNUMBER = {1260019}, DOI = {10.1007/BF02096264}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/BF02096264}, } @incollection {MR1482240, AUTHOR = {Berkelaar, A.B. and Roos, K. and Terlaky, T.}, TITLE = {The optimal set and optimal partition approach to linear and quadratic programming}, BOOKTITLE = {Advances in sensitivity analysis and parametric programming}, SERIES = {Internat. Ser. Oper. Res. Management Sci.}, VOLUME = {6}, PAGES = {6.1--6.44}, PUBLISHER = {Kluwer Acad. Publ., Boston, MA}, YEAR = {1997}, MRCLASS = {90C05 (90C20 90C31)}, MRNUMBER = {1482240}, MRREVIEWER = {S. Zlobec}, } @article {MR1725231, author = "A.B. Berkelaar and B. Jansen and K. Roos and T. Terlaky", TITLE = {Basis- and partition identification for quadratic programming and linear complementarity problems}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {86}, YEAR = {1999}, NUMBER = {2, Ser. A}, PAGES = {261--282}, ISSN = {0025-5610}, MRCLASS = {90Cxx}, MRNUMBER = {1 725 231}, } @incollection {MR98j:90035, author = "A.B. BERKELAAR and K. ROOS and T. Terlaky", TITLE = {The optimal set and optimal partition approach to linear and quadratic programming}, BOOKTITLE = {Advances in sensitivity analysis and parametric programming}, PAGES = {6.1--6.44}, PUBLISHER = {Kluwer Acad. Publ.}, ADDRESS = {Boston, MA}, YEAR = {1997}, MRCLASS = {90C05 (90C20 90C31)}, MRNUMBER = {98j:90035}, MRREVR = {S. Zlobec}, } @BOOK {BerPle:79, author = "A. BERMAN and R. PLEMMONS", title = "Nonnegative matrices in the mathematical sciences", publisher = "Academic Press", year = "1979", address = "New York, NY"} @article {MR87b:65048, AUTHOR = {Berry, M. W. and Heath, M. T. and Kaneko, I. and Lawo, M. and Plemmons, R.J. and Ward, R. C.}, TITLE = {An algorithm to compute a sparse basis of the null space}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {47}, YEAR = {1985}, NUMBER = {4}, PAGES = {483--504}, ISSN = {0029-599X}, CODEN = {NUMMA7}, } @ARTICLE {Bert:76, author = "D.P. Bertsekas", title = "On penalty and multiplier methods for constrained optimization", journal = "SIAM J. Control Optim.", year = "1976", volume = "14", pages = "216-235"} @article{Bert:75, title={Necessary and sufficient conditions for a penalty method to be exact}, author={Bertsekas, Dimitri P}, journal={Mathematical programming}, volume={9}, number={1}, pages={87--99}, year={1975}, publisher={Springer} } @BOOK {Bert:82, author = "D.P. Bertsekas", title = "Constrained optimization and Lagrange multipliers", publisher = "Academic Press", year = "1982", address = "New York, NY"} @BOOK {Bert:95, author = "D.P. Bertsekas", title = "Nonlinear Programming", publisher = "Athena Scientific", year = "1995", Note = "2nd edition 1999", address = "Belmont, MA"} @BOOK {Ber, author = "D.P. Bertsekas", title = "Nonlinear Optimization", publisher = "Athena Scientific", year = "1999", address = "Belmont, MA"} @book {MR2184037, AUTHOR = {Bertsekas, D.P.}, TITLE = {Convex analysis and optimization}, NOTE = {With Angelia Nedi\'c and Asuman E. Ozdaglar}, PUBLISHER = {Athena Scientific, Belmont, MA}, YEAR = {2003}, PAGES = {xvi+534}, ISBN = {1-886529-45-0}, MRCLASS = {90-01 (49-01)}, MRNUMBER = {MR2184037 (2006j:90001)}, MRREVIEWER = {Serge G. Kruk}, } @article {MR2313781, AUTHOR = {Bertsekas, D.P. and Tseng, P.}, TITLE = {Set intersection theorems and existence of optimal solutions}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {110}, YEAR = {2007}, NUMBER = {2, Ser. A}, PAGES = {287--314}, ISSN = {0025-5610}, MRCLASS = {90C26 (90C47)}, MRNUMBER = {MR2313781 (2008c:90046)}, MRREVIEWER = {Jean-Pierre Crouzeix}, } @proceedings {MR97h:65005, TITLE = {Computational differentiation}, BOOKTITLE = {Proceedings of the 2nd International Workshop held in Santa Fe, NM, February 12--14, 1996}, EDITOR = {BERZ, M. and BISCHOF, C. and CORLISS, G.}, NOTE = {Techniques, applications, and tools}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {1996}, PAGES = {xvi+421}, ISBN = {0-89871-385-4}, MRCLASS = {65-06 (65D25)}, MRNUMBER = {97h:65005}, } @ARTICLE {Bett:76, author = "J.T. BETTS", title = "Solving the nonlinear least squares problem: {A}pplication of general method", journal = "J. Optim. Theory Appl.", year = "1976", volume = "18", pages = "469-484"} @ARTICLE {Bi:46, AUTHOR = {Birkhoff, G.}, TITLE = {Three observations on linear algebra}, JOURNAL = {Univ. Nac. Tucum\'an. Revista A.}, VOLUME = {5}, YEAR = {1946}, PAGES = {147--151}, MRCLASS = {09.1X}, MRNUMBER = {0020547}, MRREVIEWER = {J. L. Dorroh}, } @article {MR0020547, author = "G. BIRKHOFF", title = "Tres observaciones sobre el algebra lineal", journal = "Univ. Nac. Tucuman Rev. Ser. A", year = "1946", volume = "5", pages = "147-151"} @article {MR2991475, AUTHOR = {Bixby, R.E.}, TITLE = {A brief history of linear and mixed-integer programming computation}, JOURNAL = {Doc. Math.}, FJOURNAL = {Documenta Mathematica}, YEAR = {2012}, NUMBER = {Extra vol.: Optimization stories}, PAGES = {107--121}, ISSN = {1431-0635}, MRCLASS = {90-03 (01A60 90C05 90C11)}, MRNUMBER = {2991475}, MRREVIEWER = {Mechthild Opperud}, } @article {MR1885204, AUTHOR = {Bixby, R.E.}, TITLE = {Solving real-world linear programs: a decade and more of progress}, NOTE = {50th anniversary issue of Operations Research}, JOURNAL = {Oper. Res.}, FJOURNAL = {Operations Research}, VOLUME = {50}, YEAR = {2002}, NUMBER = {1}, PAGES = {3--15}, ISSN = {0030-364X}, CODEN = {OPREAI}, MRCLASS = {90C05 (90-03)}, MRNUMBER = {MR1885204}, } @article {MR1189064, AUTHOR = {BIXBY, R.E. and GREGORY, J.W. and LUSTIG, I.J. and MARSTEN, R.E. and SHANNO, D.F.}, TITLE = {Very large-scale linear programming: a case study in combining interior point and simplex methods}, JOURNAL = {Oper. Res.}, FJOURNAL = {Operations Research. The Journal of the Operations Research Society of America}, VOLUME = {40}, YEAR = {1992}, NUMBER = {5}, PAGES = {885--897}, ISSN = {0030-364X}, CODEN = {OPREAI}, } @incollection {MR2001e:90047, AUTHOR = {Bixby, R.E. and Fenelon, Mary and Gu, Zonghao and Rothberg, Ed and Wunderling, Roland}, TITLE = {M{I}{P}: theory and practice---closing the gap}, BOOKTITLE = {System modelling and optimization (Cambridge, 1999)}, PAGES = {19--49}, PUBLISHER = {Kluwer Acad. Publ.}, ADDRESS = {Boston, MA}, YEAR = {2000}, MRCLASS = {90C11 (90-02)}, MRNUMBER = {2001e:90047}, } @BOOK {Bjorck:90, author = "A. BJORCK", title = "Numerical Methods for Least Squares Problems", publisher = "SIAM", year = "1996", address = " Philadelphia", isbn = "0-89871360-9"} @article {MR1611183, AUTHOR = {BJ{\"O}RCK, {\AA}. and ELFVING, T. and STRAKO{\u{S}}, Z.}, TITLE = {Stability of conjugate gradient and {L}anczos methods for linear least squares problems}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {19}, YEAR = {1998}, NUMBER = {3}, PAGES = {720--736 (electronic)}, ISSN = {1095-7162}, MRCLASS = {65F20}, MRNUMBER = {MR1611183 (99a:65051)}, } @ARTICLE {BjEl:79, author = "A. BJORCK and T. ELFVING", title = "Accelerated projection methods for computing pseudoinverse solutions of systems of linear equations", journal = "BIT", year = "1979", volume = "19", pages = "145-163"} @article {MR3436116, AUTHOR = {Blanchard, J.D. and Tanner, J. and Wei, K.}, TITLE = {C{GIHT}: conjugate gradient iterative hard thresholding for compressed sensing and matrix completion}, JOURNAL = {Inf. Inference}, FJOURNAL = {Information and Inference. A Journal of the IMA}, VOLUME = {4}, YEAR = {2015}, NUMBER = {4}, PAGES = {289--327}, ISSN = {2049-8764}, MRCLASS = {94A12}, MRNUMBER = {3436116}, DOI = {10.1093/imaiai/iav011}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1093/imaiai/iav011}, } @article {MR3440180, AUTHOR = {Tanner, J. and Wei, K.}, TITLE = {Low rank matrix completion by alternating steepest descent methods}, JOURNAL = {Appl. Comput. Harmon. Anal.}, FJOURNAL = {Applied and Computational Harmonic Analysis. Time-Frequency and Time-Scale Analysis, Wavelets, Numerical Algorithms, and Applications}, VOLUME = {40}, YEAR = {2016}, NUMBER = {2}, PAGES = {417--429}, ISSN = {1063-5203}, MRCLASS = {65F99 (15A83 68W40 90C26 94A12)}, MRNUMBER = {3440180}, DOI = {10.1016/j.acha.2015.08.003}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/j.acha.2015.08.003}, } @article {MR3313258, AUTHOR = {Blanchard, Jeffrey D. and Tanner, Jared}, TITLE = {Performance comparisons of greedy algorithms in compressed sensing}, JOURNAL = {Numer. Linear Algebra Appl.}, FJOURNAL = {Numerical Linear Algebra with Applications}, VOLUME = {22}, YEAR = {2015}, NUMBER = {2}, PAGES = {254--282}, ISSN = {1070-5325}, MRCLASS = {94A12 (65Y10 90C90)}, MRNUMBER = {3313258}, DOI = {10.1002/nla.1948}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1002/nla.1948}, } @article {MR3299481, AUTHOR = {Blanchard, Jeffrey D. and Tanner, Jared and Wei, Ke}, TITLE = {Conjugate gradient iterative hard thresholding: observed noise stability for compressed sensing}, JOURNAL = {IEEE Trans. Signal Process.}, FJOURNAL = {IEEE Transactions on Signal Processing}, VOLUME = {63}, YEAR = {2015}, NUMBER = {2}, PAGES = {528--537}, ISSN = {1053-587X}, MRCLASS = {94A12}, MRNUMBER = {3299481}, DOI = {10.1109/TSP.2014.2379665}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1109/TSP.2014.2379665}, } @article {MR3134338, AUTHOR = {Bah, Bubacarr and Tanner, Jared}, TITLE = {Bounds of restricted isometry constants in extreme asymptotics: formulae for {G}aussian matrices}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {441}, YEAR = {2014}, PAGES = {88--109}, ISSN = {0024-3795}, MRCLASS = {15B52 (60F10 94A12 94A20)}, MRNUMBER = {3134338}, MRREVIEWER = {Alireza Nematollahi}, DOI = {10.1016/j.laa.2012.11.024}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/j.laa.2012.11.024}, } @article {MR3124656, AUTHOR = {Bah, Bubacarr and Tanner, Jared}, TITLE = {Vanishingly sparse matrices and expander graphs, with application to compressed sensing}, JOURNAL = {IEEE Trans. Inform. Theory}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Information Theory}, VOLUME = {59}, YEAR = {2013}, NUMBER = {11}, PAGES = {7491--7508}, ISSN = {0018-9448}, MRCLASS = {94A12 (05C50 15B52 94A20)}, MRNUMBER = {3124656}, MRREVIEWER = {Jing Liu}, DOI = {10.1109/TIT.2013.2274267}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1109/TIT.2013.2274267}, } @article {MR3120763, AUTHOR = {Tanner, Jared and Wei, Ke}, TITLE = {Normalized iterative hard thresholding for matrix completion}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {35}, YEAR = {2013}, NUMBER = {5}, PAGES = {S104--S125}, ISSN = {1064-8275}, MRCLASS = {65F30 (15A83 68Q25 90C90)}, MRNUMBER = {3120763}, MRREVIEWER = {Suvrit Sra}, DOI = {10.1137/120876459}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/120876459}, } \@INPROCEEDINGS {Bo:87, author = "R.B. BOPPANA", title = "Eigenvalues and graph bisection: An average case analysis", booktitle = "Proceedings of the 28th Annual Symposium on Foundations of Computer Science", year = "1987", pages = "280-285", address = "Los Angeles, California", publisher = "IEEE" } @ARTICLE {BoRiStTi:82, author = "C.G.E. BOENDER and A.H.G. {RINNOOY KAN} and L. STOUGIE and G.T. TIMMER", title = "A stochastic method for global optimization", journal = "Math. Prog.", year = "1982", volume = "22", pages = "125-140"} @article {MR97a:90034, AUTHOR = {BOGGS, P. T. and DOMICH, P. D. and ROGERS, J. E.}, TITLE = {An interior point method for general large-scale quadratic programming problems}, NOTE = {Interior point methods in mathematical programming}, JOURNAL = {Ann. Oper. Res.}, FJOURNAL = {Annals of Operations Research}, VOLUME = {62}, YEAR = {1996}, PAGES = {419--437}, ISSN = {0254-5330}, } @ARTICLE {BoBySchn:87a, author = "P.T. BOGGS and R.H. Byrd and R.B. Schnabel", title = "A stable and efficient algorithm for nonlinear orthogonal distance regression", journal = "SIAM J. Sci. Statist. Comput.", year = "1987", volume = "8", pages = "1052-1078"} @INPROCEEDINGS {BoBySchn:87b, author = "P.T. BOGGS and R.H. Byrd and R.B. Schnabel", title = "An efficient algorithm for orthogonal distance data fitting", booktitle = "Computer Science and Statistics: Proceedings of the 18th Symposium on the Interface", year = "1987", editor = "T.J. Boardman", pages = "285-293", publisher = "American Statistical Association", address = "Washington, D.C."} @article {MR902565, AUTHOR = {BOSCH, A. J.}, TITLE = {Note on the factorization of a square matrix into two {H}ermitian or symmetric matrices}, JOURNAL = {SIAM Rev.}, FJOURNAL = {SIAM Review. A Publication of the Society for Industrial and Applied Mathematics}, VOLUME = {29}, YEAR = {1987}, NUMBER = {3}, PAGES = {463--468}, ISSN = {0036-1445}, CODEN = {SIREAD}, MRCLASS = {15A23}, MRNUMBER = {MR902565 (88f:15018)}, MRREVIEWER = {Shao Kuan Li}, DOI = {10.1137/1029077}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/1029077}, } @article {MR843191, AUTHOR = {BOSCH, A. J.}, TITLE = {The factorization of a square matrix into two symmetric matrices}, JOURNAL = {Amer. Math. Monthly}, FJOURNAL = {The American Mathematical Monthly}, VOLUME = {93}, YEAR = {1986}, NUMBER = {6}, PAGES = {462--464}, ISSN = {0002-9890}, CODEN = {AMMYAE}, MRCLASS = {15A21 (15A23)}, MRNUMBER = {MR843191 (87g:15012)}, MRREVIEWER = {Lajos L{\'a}szl{\'o}}, DOI = {10.2307/2323471}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.2307/2323471}, } @TECHREPORT {BoByDoSchn:87, author = "P.T. BOGGS and R.H. Byrd and J.R. DONALDSON and R.B. Schnabel", title = "{ODRPACK - S}oftware for weighted orthogonal distance regression", institution = "Department of Computer Science, University of Colorado", year = "1987", number = "CU-CS-360-87", address = "Boulder, CO", note = "To appear in ACM Transactions on Mathematical Software"} @ARTICLE {BoDe:76, author = "P.T. BOGGS and J.E. {Dennis Jr.}", title = "A stability analysis for perturbed nonlinear iterative methods", journal = "Math. Comp.", year = "1976", volume = "30", pages = "1-17"} @ARTICLE {BoDoSchnSpie:88, author = "P.T. BOGGS and J.R. DONALDSON and R.B. Schnabel and C.H. SPIEGELMAN", title = "A computational examination of orthogonal distance regression", journal = "J. Econometrics", year = "1988", volume = "38", pages = "169-201"} @ARTICLE {BoTo:80, author = "P.T. BOGGS and J.W. TOLLE", title = "Augmented {L}agrangians that are quadratic in the multiplier", journal = "J. Optim. Theory Appl.", year = "1980", volume = "3", pages = "17-26"} @ARTICLE {BoTo:84, author = "P.T. BOGGS and J.W. TOLLE", title = "A family of descent functions for constrained optimization", journal = "SIAM J. Num. Anal.", year = "1984", volume = "21", pages = "1146-1161"} @TECHREPORT {BoTo:81, author = "P.T. BOGGS and J.W. TOLLE", title = "An implementation of a quasi-{N}ewton method for constrained optimization", institution = "Dept. of Mathematics and Curriculum in Operations Research and Systems Analysis, University of North Carolina", year = "1981", number = "81-3", address = "Chapel Hill, NC"} @ARTICLE {BoToWa:82, author = "P.T. BOGGS and J.W. TOLLE and P. WANG", title = "On the local convergence of quasi-{N}ewton methods for constrained optimization", journal = "SIAM J. Control Optim.", year = "1982", volume = "20", pages = "161-171"} @ARTICLE {BoTo:95, AUTHOR = {Boggs, P.T. and Tolle, J.W.}, TITLE = {Sequential quadratic programming}, BOOKTITLE = {Acta numerica, 1995}, SERIES = {Acta Numer.}, PAGES = {1--51}, PUBLISHER = {Cambridge Univ. Press, Cambridge}, YEAR = {1995}, MRCLASS = {90C30 (65K05)}, MRNUMBER = {1352470 (96f:90097)}, MRREVIEWER = {K. Schittkowski}, } @article {MR98i:90060, AUTHOR = {BOMZE, I. M.}, TITLE = {Global escape strategies for maximizing quadratic forms over a simplex}, JOURNAL = {J. Global Optim.}, FJOURNAL = {Journal of Global Optimization. An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering}, VOLUME = {11}, YEAR = {1997}, NUMBER = {3}, PAGES = {325--338}, ISSN = {0925-5001}, CODEN = {JGOPEO}, } @article {MR97i:90092, AUTHOR = {BOMZE, I. M.}, TITLE = {Block pivoting and shortcut strategies for detecting copositivity}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {248}, YEAR = {1996}, PAGES = {161--184}, ISSN = {0024-3795}, CODEN = {LAAPAW}, } @article {MR3080997, AUTHOR = {Al-Mohy, A.H. and Higham, N.J. and Relton, S.D.}, TITLE = {Computing the {F}r\'{e}chet derivative of the matrix logarithm and estimating the condition number}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {35}, YEAR = {2013}, NUMBER = {4}, PAGES = {C394--C410}, ISSN = {1064-8275}, MRCLASS = {65F60 (65F35)}, MRNUMBER = {3080997}, MRREVIEWER = {A. Bultheel}, DOI = {10.1137/120885991}, URL = {https://doi.org/10.1137/120885991}, } @misc{chen2011projection, title={Projection Onto A Simplex}, author={Y. Chen and X. Ye}, year={2011}, eprint={1101.6081}, archivePrefix={arXiv}, primaryClass={math.OC} } @article{Chen2011ProjectionOA, title={Projection onto a simplex}, author={Chen, Y. and Ye, X.}, journal={arXiv preprint arXiv:1101.6081}, year={2011} } @article {MR1825853, AUTHOR = {Cheng, S.H. and Higham, N.J. and Kenney, C.S. and Laub, A.J.}, TITLE = {Approximating the logarithm of a matrix to specified accuracy}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {22}, YEAR = {2001}, NUMBER = {4}, PAGES = {1112--1125}, ISSN = {0895-4798}, MRCLASS = {65F30}, MRNUMBER = {1825853}, MRREVIEWER = {Jin Yun Yuan}, DOI = {10.1137/S0895479899364015}, URL = {https://doi.org/10.1137/S0895479899364015}, } @article {MR2026712, AUTHOR = {BOJANCZYK, A. and Higham, N.J. and PATEL, H.}, TITLE = {The equality constrained indefinite least squares problem: theory and algorithms}, JOURNAL = {BIT}, FJOURNAL = {BIT. Numerical Mathematics}, VOLUME = {43}, YEAR = {2003}, NUMBER = {3}, PAGES = {505--517}, ISSN = {0006-3835}, MRCLASS = {65F20}, MRNUMBER = {MR2026712 (2004m:65049)}, } @article {MR1740875, AUTHOR = {Bomze, Immanuel M.}, TITLE = {Linear-time copositivity detection for tridiagonal matrices and extension to block-tridiagonality}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {21}, YEAR = {2000}, NUMBER = {3}, PAGES = {840--848 (electronic)}, ISSN = {1095-7162}, MRCLASS = {65F30 (15A57)}, MRNUMBER = {1 740 875}, } @techreport{BouwSobrJavJungZah:16, AUTHOR = "T. Bouwmans and A. Sobral and S. Javed and S.K. Jung and E.-H. Zahzah", TITLE = "Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset Model", TYPE = "Technical Report", NUMBER = "1511.01245v3 at arxiv.org", INSTITUTION = "Princeton University", ADDRESS = "Univ. La Rochelle, France", URL = "https://arxiv.org/pdf/1511.01245.pdf", YEAR = "2016", } @article {MR93j:90079, AUTHOR = {Danninger, G.}, TITLE = {Role of copositivity in optimality criteria for nonconvex optimization problems}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {75}, YEAR = {1992}, NUMBER = {3}, PAGES = {535--558}, ISSN = {0022-3239}, CODEN = {JOTABN}, MRCLASS = {90C26 (90C30)}, MRNUMBER = {93j:90079}, MRREVR = {K. G. Murty}, } @incollection {MR91i:15022, AUTHOR = {Danninger, G.}, TITLE = {A recursive algorithm for determining (strict) copositivity of a symmetric matrix}, BOOKTITLE = {XIV Symposium on Operations Research (Ulm, 1989)}, PAGES = {45--52}, PUBLISHER = {Athen\"aum/Hain/Hanstein}, ADDRESS = {K\"onigstein}, YEAR = {1990}, MRCLASS = {15A48 (90C30)}, MRNUMBER = {91i:15022}, MRREVR = {R. A. Horn}, } @incollection {MR91g:90141, AUTHOR = {Bomze, Immanuel M.}, TITLE = {Copositivity and optimization}, BOOKTITLE = {XII Symposium on Operations Research (Passau, 1987)}, PAGES = {27--35}, PUBLISHER = {Athen\"aum/Hain/Hanstein}, ADDRESS = {K\"onigstein}, YEAR = {1989}, MRCLASS = {90C30}, MRNUMBER = {91g:90141}, } @article {MR89b:90159, AUTHOR = {Bomze, Immanuel M.}, TITLE = {Remarks on the recursive structure of copositivity}, JOURNAL = {J. Inform. Optim. Sci.}, FJOURNAL = {Journal of Information \& Optimization Sciences}, VOLUME = {8}, YEAR = {1987}, NUMBER = {3}, PAGES = {243--260}, ISSN = {0252-2667}, CODEN = {JIOSDC}, MRCLASS = {90C20}, MRNUMBER = {89b:90159}, MRREVR = {K. G. Murty}, } @article {MR1165996, AUTHOR = {K{\'e}ri, G.}, TITLE = {Methods of nonconvex quadratic optimization based on the matrix copositivity investigation}, JOURNAL = {Alkalmaz. Mat. Lapok}, FJOURNAL = {Alkalmazott Matematikai Lapok}, VOLUME = {15}, YEAR = {1990/91}, NUMBER = {1-2}, PAGES = {115--132 (1992)}, ISSN = {0133-3399}, CODEN = {AMLAD8}, MRCLASS = {90C25 (90C26)}, MRNUMBER = {1 165 996}, } @article {MR95b:90068, AUTHOR = {BOMZE, I. M. and DANNINGER, G.}, TITLE = {A finite algorithm for solving general quadratic problems}, JOURNAL = {J. Global Optim.}, FJOURNAL = {Journal of Global Optimization. An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering}, VOLUME = {4}, YEAR = {1994}, NUMBER = {1}, PAGES = {1--16}, ISSN = {0925-5001}, CODEN = {JGOPEO}, } @article {MR95a:90054, AUTHOR = {BOMZE, I. M. and DANNINGER, G.}, TITLE = {A global optimization algorithm for concave quadratic programming problems}, JOURNAL = siopt, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {3}, YEAR = {1993}, NUMBER = {4}, PAGES = {826--842}, ISSN = {1052-6234}, CODEN = {SJOPE8}, } @article {MR94j:90061, AUTHOR = {DANNINGER, G. and BOMZE, I. M.}, TITLE = {Using copositivity for global optimality criteria in concave quadratic programming problems}, JOURNAL = mprog, FJOURNAL = {Mathematical Programming}, VOLUME = {62}, YEAR = {1993}, NUMBER = {3, Ser. A}, PAGES = {575--580}, ISSN = {0025-5610}, CODEN = {MHPGA4}, } @article{BongConnGoulToin95, author = {I. Bongartz and A. R. Conn and N.I.M. Gould and Ph.L. Toint}, title = {{\sf CUTE}: Constrained and Unconstrained Testing Environment}, journal = TOMS, volume = 21, number = 1, pages = {123--160}, year = 1995} @TECHREPORT {Boon:82, author = "P.G.M. BOONEKAMP", title = "{SELPE}: a model of the {D}utch {E}nergy {S}ystem", institution = "Energy Study Center", year = "1982", number = "ECS-17", address = "Petten"} @article {MR1438095, AUTHOR = {Bouaricha, A. and Mor{\'e}, J.J.}, TITLE = {Impact of partial separability on large-scale optimization}, NOTE = {Computational issues in high performance software for nonlinear optimization (Capri, 1995)}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {7}, YEAR = {1997}, NUMBER = {1}, PAGES = {27--40}, ISSN = {0926-6003}, CODEN = {CPPPEF}, MRCLASS = {90C06 (65K05 90C30)}, MRNUMBER = {MR1438095 (97m:90058)}, } @ARTICLE {Boo:62, author = "J.C.G. BOOT", title = "On trivial and binding constraints in programming problems", journal = "Management Sci.", year = "1962", volume = "8", pages = "419"} \@TECHREPORT {BoMi:95, author = "B. BORCHERS and J. E. MITCHELL", title = "An improved branch and bound algorithm for mixed integer nonlinear programs", year = "1995", institution = "New Mexico Tech", address = "Socorro, NM", keywords = "branch and bound, mixed integer programming" } @ARTICLE {BoCrHa:90, author = "E. BOROS and Y. CRAMA and P.L. HAMMER", title = "Upper bounds for quadratic $0-1$ maximization", journal = " Operations Research Letters", year = "1990 ", volume = "9", pages = "73-79"} @ARTICLE {BoCrHa:92, author = "E. BOROS and Y. CRAMA and P.L. HAMMER", title = "Chv\'{a}tal cuts and odd cycle inequalities in quadratic $0-1$ optimization", journal = " SIAM Journal on Discrete Mathematics", year = "1992 ", volume = "5", pages = "163-177"} @ARTICLE {BoCrHa:91, author = "E. BOROS and P.L. HAMMER", title = "The Max-Cut problem and Quadratic $0-1$ Optimization, Polyhedral Aspects, Relaxations and Bounds", journal = " Annals of Operations Research", year = "1991 ", volume = "33", pages = "151-180"} @ARTICLE {BoCrHa:93, author = "E. BOROS and P.L. HAMMER", title = "Cut-Polytopes, {B}oolean Quadric Polytopes and Nonnegative Quadratic Pseudo-{B}oolean Functions", journal = mor, year = "1993 ", volume = "18", pages = "245-253"} @ARTICLE {BoCrHa:89, author = "E. BOROS and A. PR\'{E}KOPA", title = "Probabilistic bounds and algorithms for the maximum satisfiability problem", journal = " Annals of Operations Research", year = "1989 ", volume = "21", pages = "109-126"} @incollection {MR2858834, AUTHOR = {Borwein, J.M. and Sims, B.}, TITLE = {The {D}ouglas-{R}achford algorithm in the absence of convexity}, BOOKTITLE = {Fixed-point algorithms for inverse problems in science and engineering}, SERIES = {Springer Optim. Appl.}, VOLUME = {49}, PAGES = {93--109}, PUBLISHER = {Springer, New York}, YEAR = {2011}, MRCLASS = {47N10 (47H10 47J25 65J15 90C26)}, MRNUMBER = {2858834 (2012i:47098)}, MRREVIEWER = {A. G. Kartsatos}, DOI = {10.1007/978-1-4419-9569-8\_6}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/978-1-4419-9569-8\_6}, } @article {MR85j:15012, AUTHOR = {Borwein, J.M. and Richmond, B.}, TITLE = {How many matrices have roots?}, JOURNAL = {Canad. J. Math.}, FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques}, VOLUME = {36}, YEAR = {1984}, NUMBER = {2}, PAGES = {286--299}, ISSN = {0008-414X}, CODEN = {CJMAAB}, MRCLASS = {15A23}, MRNUMBER = {85j:15012}, MRREVIEWER = {J. L. Brenner}, } @article {springerlink:10.1007/BF00046618, author = {Borgwardt, K. H.}, title = {Probabilistic analysis of optimization algorithms-some aspects from a practical point of view}, journal = {Acta Applicandae Mathematicae}, publisher = {Springer Netherlands}, issn = {0167-8019}, keyword = {Physics and Astronomy}, pages = {171-210}, volume = {10}, issue = {2}, url = {http://dx.doi.org/10.1007/BF00046618}, note = {10.1007/BF00046618}, year = {1987} } @book {MR2144010, AUTHOR = {Borwein, J.M. and ZHU, Q.J.}, TITLE = {Techniques of variational analysis}, SERIES = {CMS Books in Mathematics/Ouvrages de Math\'ematiques de la SMC, 20}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {2005}, PAGES = {vi+362}, ISBN = {0-387-24298-8}, MRCLASS = {49-02 (49J52 49J53 90-02)}, MRNUMBER = {MR2144010 (2006h:49002)}, MRREVIEWER = {Richard B. Vinter}, } @inproceedings{borwein1145780:06, author = {J.M. Borwein and C.H. HAMILTON}, title = {Symbolic computation of multidimensional Fenchel conjugates}, booktitle = {ISSAC '06: Proceedings of the 2006 international symposium on Symbolic and algebraic computation}, year = {2006}, isbn = {1-59593-276-3}, pages = {23--30}, location = {Genoa, Italy}, doi = {http://doi.acm.org/10.1145/1145768.1145780}, publisher = {ACM Press}, address = {New York, NY, USA}, } @ARTICLE {Bo:76, author = "J.M. Borwein", title = "Fractional programming without differentiability", journal = mprog, year = "1976", volume = "11", pages = "283-290"} @INPROCEEDINGS {Borwein:87, author = "J.M. Borwein", title = "Cones, minimality notions and consequences", booktitle = "Recent Advances and Historic Development of Vector Optimization", publisher = "Springer-Verlag", pages = "62-85", year = "1987"} @ARTICLE {Bo:83, author = "J.M. Borwein", title = "On the existence of {P}areto efficient points", journal = mor, year = "1983", volume = "8", pages = "64-73"} @ARTICLE {Bor:93, author = "J.M. Borwein", title = "On the failure of maximum entropy reconstruction for {F}redholm equations and other infinite systems", journal = mprog, year = "1993", volume = "61", pages = "251-261"} @ARTICLE {BoLe1:92, author = "J.M. Borwein and A.S. Lewis", title = "Partially finite convex programming, Part {I}, Duality theory", journal = mprog, year = "1992", volume = "57", pages = "15-48"} @ARTICLE {BoLe2:92, author = "J.M. Borwein and A.S. Lewis", title = "Partially finite convex programming, Part {II}, Explicit lattice models", journal = mprog, year = "1992", volume = "57", pages = "49-84"} @book {BoLe:00, author = "J.M. Borwein and A.S. Lewis", TITLE = {Convex analysis and nonlinear optimization}, NOTE = {Theory and examples}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {2000}, PAGES = {x+273}, ISBN = {0-387-98940-4}, MRCLASS = {49-01 (46N10 47N10 49-02 49J53 90-01)}, MRNUMBER = {2001h:49001}, MRREVIEWER = {John R. Giles}, } @book {MR2184742, AUTHOR = {Borwein, J.M. and Lewis, A.S.}, TITLE = {Convex analysis and nonlinear optimization}, SERIES = {CMS Books in Mathematics/Ouvrages de Math\'ematiques de la SMC, 3}, EDITION = {Second}, NOTE = {Theory and examples}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {2006}, PAGES = {xii+310}, ISBN = {978-0387-29570-1; 0-387-29570-4}, MRCLASS = {49-01 (46N10 47N10 49-02 49J53 90-01)}, MRNUMBER = {MR2184742 (2006f:49001)}, } @article {MR2421271, AUTHOR = {Borwein, Jonathan M. and Hamilton, Chris H.}, TITLE = {Symbolic {F}enchel conjugation}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {116}, YEAR = {2009}, NUMBER = {1-2, Ser. B}, PAGES = {17--35}, ISSN = {0025-5610}, MRCLASS = {90-04 (44A15 49J52 65K10 90C25 90C46)}, MRNUMBER = {MR2421271 (2009h:90003)}, DOI = {10.1007/s10107-007-0134-4}, URL = {http://dx.doi.org/10.1007/s10107-007-0134-4}, } @incollection {MR2427663, AUTHOR = {Bailey, David H. and Borwein, Jonathan M.}, TITLE = {Computer-assisted discovery and proof}, BOOKTITLE = {Tapas in experimental mathematics}, SERIES = {Contemp. Math.}, VOLUME = {457}, PAGES = {21--52}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {2008}, MRCLASS = {11Y99 (68T15 68U35 68W30)}, MRNUMBER = {MR2427663 (2010d:11154)}, MRREVIEWER = {Jeffrey O. Shallit}, } @incollection {MR3060439, AUTHOR = {Boomsma, W. and Frellsen, J. and Hamelryck, T.}, TITLE = {Probabilistic models of local biomolecular structure and their applications}, BOOKTITLE = {Bayesian methods in structural bioinformatics}, SERIES = {Stat. Biol. Health}, PAGES = {233--254}, PUBLISHER = {Springer, Heidelberg}, YEAR = {2012}, MRCLASS = {62P10 (92D20 92E10)}, MRNUMBER = {3060439}, DOI = {10.1007/978-3-642-27225-7_10}, URL = {http://dx.doi.org/10.1007/978-3-642-27225-7_10}, } @article {BH05, AUTHOR = {Boomsma, W. and Hamelryck, T.}, TITLE = {Full cycle coordinate descent: solving the protein loop closure problem in {C}$\alpha$ space}, journal = {BMC Bioinformatics}, PAGES = {}, YEAR = {Open access:}, URL = {http: //www.biomedcentral.com/1471-2105/6/159}, } @article {BK05, author = {Buss, S.R. and Kim, J.-S.}, title = {Selectively damped least squares for inverse kinematics}, journal = {Journal of Graphics Tools}, volume = {10}, year = {2005}, pages = {37-49}, URL = {http://math.ucsd.edu/~sbus/ResearchWeb/ikmethods/} } @article {LKN13, author = {M. Lundgren and A. Krokhotin and A. Niemi}, title = {Topology and structural self-organization in folded proteins}, journal = {Physical Review E}, volume = {88}, year = {2013}, pages = {1-15}, } @incollection {MR2289097, AUTHOR = {Borwein, Jonathan M. and Hamilton, Chris H.}, TITLE = {Symbolic computation of multidimensional {F}enchel conjugates}, BOOKTITLE = {I{SSAC} 2006}, PAGES = {23--30}, PUBLISHER = {ACM}, ADDRESS = {New York}, YEAR = {2006}, MRCLASS = {68W30 (65K10)}, MRNUMBER = {MR2289097}, DOI = {10.1145/1145768.1145780}, URL = {http://dx.doi.org/10.1145/1145768.1145780}, } @ARTICLE{BD86, AUTHOR="J.P. Boyle and R.L. Dykstra", TITLE="A method of finding projections onto the intersection convex sets in {H}ilbert space", JOURNAL="Lecture Notes in Statistics", YEAR="1986", VOLUME="37", NUMBER=" ", PAGES="28--47" } @ARTICLE {BoxG:57, author = "G.E.P. BOX", title = "Evolutionary operation: a method for increasing industrial productivity", journal = "Appl. Statist.", year = "1957", volume = "6", number = "2", pages = "81-101", note = "Presented at the International Conference on Statistical Quality Control, Paris, July 1955"} @ARTICLE {BoxM:66, author = "M.J. BOX", title = "A comparison of several current optimization methods, and the use of transformations in constrained problems", journal = "The Computer Journal", year = "1966", volume = "9", number = "1", pages = "67-77"} @INCOLLECTION {BoxDaSwa:69, author = "M.J. BOX and D. DAVIES and W.H. SWANN", title = "Non-linear {O}ptimization {T}echniques", booktitle = "ICI Monograph \# 5", publisher = "Oliver \& Boyd", year = "1969", address = "Edinburgh"} @ARTICLE{Douglas1956421, author={Douglas, J. and Rachford, H.H.}, title={On the numerical solution of heat conduction problems in two and three space variables}, journal={Transactions of the American Mathematical Society}, year={1956}, volume={82}, number={2}, pages={421-439}, doi={10.1090/s0002-9947-1956-0084194-4}, note={cited By 747}, url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-84967782959&doi=10.1090%2fs0002-9947-1956-0084194-4&partnerID=40&md5=47cf7f85db757d61e0b149c2bcb48703}, document_type={Article}, source={Scopus}, } @article{FG85, title = {Fortin, M. / Glowinski, R., Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems. Amsterdam-New York, North-Holland Publ. Co. 1983. XX, 340 S., US \$ 59.50. Dfl. 140.00. ISBN 0-444-86 680-9 (Studies in Mathematics and its Applications 15) ��?Translation from the French}, journal = {ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik}, volume = {65}, number = {12}, pages = {622-622}, doi = {10.1002/zamm.19850651211}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/zamm.19850651211}, eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/zamm.19850651211}, year = {1985} } @ARTICLE{Arrow1958, author={Arrow, K.J. and Hurwicz, L. and Uzawa, H.}, journal={Studies in Linear and Non-Linear Programming}, year={1958}, note={cited By 359}, document_type={Article}, source={Scopus}, } @ARTICLE{Zhang201120, author={Zhang, X. and Burger, M. and Osher, S.}, title={A unified primal-dual algorithm framework based on Bregman iteration}, journal={Journal of Scientific Computing}, year={2011}, volume={46}, number={1}, pages={20-46}, doi={10.1007/s10915-010-9408-8}, note={cited By 202}, url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-78651419159&doi=10.1007%2fs10915-010-9408-8&partnerID=40&md5=865e0c8f6fbd9c31ade47ad34ab0b5f8}, document_type={Article}, source={Scopus}, } @ARTICLE{Esser20101015, author={Esser, E. and Zhang, X. and Chan, T.F.}, title={A general framework for a class of first order primal-dual algorithms for convex optimization in imaging science}, journal={SIAM J. Imaging Sci.}, year={2010}, volume={3}, number={4}, pages={1015-1046}, note={cited By 278}, document_type={Article}, source={Scopus}, } @ARTICLE{Chambolle2011120, author={Chambolle, A. and Pock, T.}, title={A first-order primal-dual algorithm for convex problems with applications to imaging}, journal={Journal of Mathematical Imaging and Vision}, year={2011}, volume={40}, number={1}, pages={120-145}, doi={10.1007/s10851-010-0251-1}, note={cited By 1666}, url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-79953201848&doi=10.1007%2fs10851-010-0251-1&partnerID=40&md5=8f748034cf972376d2e2659981524f56}, document_type={Article}, source={Scopus}, } @ARTICLE{Gabay1983299, author={Gabay, D.}, title={Chapter IX Applications of the Method of Multipliers to Variational Inequalities}, journal={Studies in Mathematics and its Applications}, year={1983}, volume={15}, number={C}, pages={299-331}, doi={10.1016/S0168-2024(08)70034-1}, note={cited By 308}, url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-77957064934&doi=10.1016%2fS0168-2024%2808%2970034-1&partnerID=40&md5=dd327551d3a04fdd8da6923f1a54f984}, document_type={Article}, source={Scopus}, } @ARTICLE{Glowinski197541, author={Glowinski, R. and Marroco, A.}, title={Approximation by Finite Elements of Order One and Solution by Penalization-Duality of a Class of Nonlinear Dirichlet Problems. [SUR L'APPROXIMATION, PAR ELEMENTS FINIS D'ORDRE UN, ET LA RESOLUTION, PAR PENALISATION-DUALITE, D'UNE CLASSE DE PROBLEMES DE DIRICHLET NON LINEAIRES.]}, journal={Rev Fr Autom Inf Rech Oper}, year={1975}, volume={9}, number={R-2}, pages={41-76}, note={cited By 649}, url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-0016536442&partnerID=40&md5=5cc6aa2d89f3dee643c04806c774ecb1}, document_type={Article}, source={Scopus}, } @book{chan1978finite, title={Finite element approximation and iterative solution of a class of mildly non-linear elliptic equations}, author={Chan, Tony Fan C and Glowinski, Roland}, year={1978}, publisher={Computer Science Department, Stanford University Stanford} } @ARTICLE{Gabay197617, author={Gabay, D. and Mercier, B.}, title={A dual algorithm for the solution of nonlinear variational problems via finite element approximation}, journal={Computers and Mathematics with Applications}, year={1976}, volume={2}, number={1}, pages={17-40}, doi={10.1016/0898-1221(76)90003-1}, note={cited By 1056}, url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-0002211517&doi=10.1016%2f0898-1221%2876%2990003-1&partnerID=40&md5=df840062c32a6f534c3aa1867c1f1758}, document_type={Article}, source={Scopus}, } @ARTICLE{Eckstein1992293, author={Eckstein, J. and Bertsekas, D.P.}, title={On the {D}ouglas-{R}achford splitting method and the proximal point algorithm for maximal monotone operators}, journal={Mathematical Programming}, year={1992}, volume={55}, number={1-3}, pages={293-318}, doi={10.1007/BF01581204}, note={cited By 701}, url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-34249837486&doi=10.1007%2fBF01581204&partnerID=40&md5=e11749476e527312b07cb8b4e5500350}, document_type={Article}, source={Scopus}, } @ARTICLE{Eckstein0000, author={Eckstein, J. and Yao, W.}, title={Augmented Lagrangian and alternating direction methods for convex optimization: A tutorial and some illustrative computational results}, journal={Pac. J. Optim}, year={0000}, note={cited By 1}, document_type={Article}, source={Scopus}, } @ARTICLE{Eckstein:2020, author={Eckstein, J.}, title={Deriving solution value bounds from the {ADMM}}, journal={Optimization Letters}, year={2020}, volume = {}, pages = {}, doi = {https://doi.org/10.1007/s11590-020-01584-1}, } @ARTICLE{Glowinski201459, author={Glowinski, R.}, title={On alternating direction methods of multipliers: A historical perspective}, journal={Computational Methods in Applied Sciences}, year={2014}, volume={34}, pages={59-82}, doi={10.1007/978-94-017-9054-3_4}, note={cited By 42}, url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-85006789785&doi=10.1007%2f978-94-017-9054-3_4&partnerID=40&md5=3d4c0e99b78cdbe3f3f0bbc812737fdb}, document_type={Book Chapter}, source={Scopus}, } @ARTICLE{HY12, author={He, B. and Yuan, X.}, title={On the O(1/N) convergence rate of the {D}ouglas-{R}achford alternating direction method}, journal={SIAM Journal on Numerical Analysis}, year={2012}, volume={50}, number={2}, pages={700-709}, doi={10.1137/110836936}, note={cited By 351}, url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-84861398963&doi=10.1137%2f110836936&partnerID=40&md5=39116ad03c9e34153b338bc2445ec348}, document_type={Review}, source={Scopus}, } @ARTICLE{HY15, author={He, B. and Yuan, X.}, title={On non-ergodic convergence rate of {D}ouglas-{R}achford alternating direction method of multipliers}, journal={Numerische Mathematik}, year={2015}, volume={130}, number={3}, pages={567-577}, doi={10.1007/s00211-014-0673-6}, note={cited By 84}, url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-84912569509&doi=10.1007%2fs00211-014-0673-6&partnerID=40&md5=35847a928102455895875c9ca4e76cc1}, document_type={Article}, source={Scopus}, } @article {BoydParikhChuPeleatoEckstein:11, author = "S. Boyd and N. Parikh and E. Chu and B. Peleato and J. Eckstein", title = "Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers", JOURNAL = "Found. Trends Machine Learning", VOLUME = "3", YEAR = "2011", NUMBER = "1", PAGES = "1--122" } @article{Boyd:92, AUTHOR = "S. Boyd and L.\ {EL GHAOUI}", TITLE = "Method of Centers for Minimizing Generalized Eigenvalues", JOURNAL = " Linear Algebra Appl.", VOLUME = "188", YEAR = "1993", PAGES = "63--111", } @BOOK {Bradhaxmagn:77, author = "Bradley, S.P. and Hax, A.C. and Magnanti, T.L.", title = "Applied Mathematical Programming", publisher = "Addison-Wesley", year = "1977", address = "Reading, MA"} @ARTICLE {Braun:62, author = "C.C. BRAUNSCHWEIGER and CLARK, H.E.", TITLE = {An {E}xtension of the {F}arkas {T}heorem}, JOURNAL = {Amer. Math. Monthly}, FJOURNAL = {The American Mathematical Monthly}, VOLUME = {69}, YEAR = {1962}, NUMBER = {4}, PAGES = {272--277}, ISSN = {0002-9890}, CODEN = {AMMYAE}, MRCLASS = {Contributed Item}, MRNUMBER = {MR1531625}, } @article {MR0398498, AUTHOR = {Brearley, A.L. and Mitra, G. and Williams, H.P.}, TITLE = {Analysis of mathematical programming problems prior to applying the simplex algorithm}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {8}, YEAR = {1975}, PAGES = {54--83}, ISSN = {0025-5610}, MRCLASS = {90C05}, MRNUMBER = {0398498 (53 \#2349)}, MRREVIEWER = {Tomas Gal}, } @BOOK {Bre:73, author = "R.P. BRENT", title = "Algorithms For Minimization Without Derivatives", publisher = "Prentice-Hall", year = "1973", address = "Englewood Cliffs, NJ"} @article {MR80a:93055b, AUTHOR = {BREWER, J.W.}, TITLE = {Correction to: ``{K}ronecker products and matrix calculus in system theory'' ({IEEE} {T}rans. {C}ircuits and {S}ystems {\bf 25} (1978), no. 9, 772--781)}, JOURNAL = {IEEE Trans. Circuits and Systems}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Circuits and Systems}, VOLUME = {26}, YEAR = {1979}, NUMBER = {5}, PAGES = {360}, ISSN = {0098-4094}, CODEN = {ICSYBT}, MRCLASS = {93B30}, MRNUMBER = {80a:93055b}, } @article {MR80a:93055a, AUTHOR = {BREWER, J.W.}, TITLE = {Kronecker products and matrix calculus in system theory}, NOTE = {Special issue on the mathematical foundations of system theory}, JOURNAL = {IEEE Trans. Circuits and Systems}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Circuits and Systems}, VOLUME = {25}, YEAR = {1978}, NUMBER = {9}, PAGES = {772--781}, ISSN = {0098-4094}, CODEN = {ICSYBT}, MRCLASS = {93B30}, MRNUMBER = {80a:93055a}, } @ARTICLE {BriSpeWil:79, author = "G.F. BRISSEY and R.B. SPENCER and C.L. WILKINS", title = "High-Speed algorithm for simplex optimization calculations", journal = "Anal. Chem.", year = "1979", volume = "51", number = "13", pages = "2295-2297"} @INCOLLECTION {Brod:77, author = "K.W. BRODLIE", title = "Unconstrained minimization", booktitle = "The State of the Art in Numerical Analysis", publisher = "Academic Press", year = "1977", editor = "D.Jacobs", pages = "229-268", address = "London"} @BOOK {Bron:83, author = "A. BRONDSTED", title = "An Introduction to Convex Polytopes", publisher = "Springer Verlag", year = "1983", address = "Berlin"} @ARTICLE {BrooMi:61, author = "S.H. BROOKS and M.R. MICKEY", title = "Optimum estimation of gradient direction in steepest ascent experiments", journal = "Biometrics", year = "1961", volume = "17", pages = "48-56"} @ARTICLE {Broy:65, author = "C.G. BROYDEN", title = "A class of methods for solving nonlinear simultaneous equations", journal = "Math. Comp.", year = "1965", volume = "19", pages = "577-593"} @ARTICLE {Broy:69, author = "C.G. BROYDEN", title = "A new double-rank minimization algorithm", journal = "Notices Amer. Math. Soc.", year = "1969", volume = "16", pages = "670"} @ARTICLE {Broy:70a, author = "C.G. BROYDEN", title = "The convergence of a class of double-rank minimization algorithms, {P}art {I}", journal = "IMA J. Appl. Math.", year = "1970", volume = "6", pages = "76-90"} @ARTICLE {Broy:70b, author = "C.G. BROYDEN", title = "The convergence of a class of double-rank minimization algorithms, {P}art {II}", journal = "IMA J. Appl. Math.", year = "1970", volume = "6", pages = "222-236"} @ARTICLE {Broy:71, author = "C.G. BROYDEN", title = "The convergence of an algorithm for solving sparse nonlinear systems", journal = "Math. Comp.", year = "1971", volume = "25", pages = "285-294"} @ARTICLE {BrDeMo:73, author = "C.G. BROYDEN and J.E. {Dennis Jr.} and J.J. Mor\'{e}", title = "On the local and superlinear convergence of quasi-{N}ewton methods", journal = "IMA J. Appl. Math.", year = "1973", volume = "12", pages = "223-246"} @BOOK {Brual:92, author = "R.A. Brualdi", title = "Introductory Combinatorics", publisher = "North-Holland", year = "1992", address = "New York"} @article {MR3291396, AUTHOR = {Girard, M.W. and Gour, G. and Friedland, S.}, TITLE = {On convex optimization problems in quantum information theory}, JOURNAL = {J. Phys. A}, FJOURNAL = {Journal of Physics. A. Mathematical and Theoretical}, VOLUME = {47}, YEAR = {2014}, NUMBER = {50}, PAGES = {505302, 25}, ISSN = {1751-8113}, MRCLASS = {94A15 (81P45 90C25 90C90)}, MRNUMBER = {3291396}, MRREVIEWER = {Koichiro Matsuno}, DOI = {10.1088/1751-8113/47/50/505302}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1088/1751-8113/47/50/505302}, } @article{Friedlandetal:11, author = {Friedland, S. and Li,C.-K. and Poon, Y.-T. and Sze, N.-S.}, title = {The automorphism group of separable states in quantum information theory}, journal = {Journal of Mathematical Physics}, volume = {52}, number = {4}, pages = {042203}, year = {2011}, doi = {10.1063/1.3578015}, URL = {https://doi.org/10.1063/1.3578015}, eprint = {https://doi.org/10.1063/1.3578015} } @article {MR95i:65070, AUTHOR = {Brualdi, Richard A. and Friedland, S. and Pothen, Alex}, TITLE = {The sparse basis problem and multilinear algebra}, JOURNAL = simax, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {16}, YEAR = {1995}, NUMBER = {1}, PAGES = {1--20}, ISSN = {0895-4798}, CODEN = {SJMAEL}, } @BOOK {BrualRys:91, place={Cambridge}, series={Encyclopedia of Mathematics and its Applications}, title={Combinatorial Matrix Theory}, DOI={10.1017/CBO9781107325708}, publisher={Cambridge University Press}, author={Brualdi, R.A. and Ryser, H.J.}, year={1991}, collection={Encyclopedia of Mathematics and its Applications}} @article{brualdi1988some, title={Some applications of doubly stochastic matrices}, author={Brualdi, R.A.}, journal={Linear Algebra and its Applications}, volume={107}, pages={77--100}, year={1988}, publisher={Elsevier} } @ARTICLE {BCR:94, author = "L. BRUNETTA and M. CONFORTI and G. RINALDI", title = "A Branch-and-cut algorithm for the equicut problem", journal = mprog, volume = "78", year = "1997", pages = "243-263"} @ARTICLE {Bry:68, author = "C.A. BRYAN", title = "Approximate solutions to nonlinear integral equations", journal = "SIAM J. Numer. Anal.", year = "1968", volume = "5", pages = "151-155"} @ARTICLE{2015arXiv150608187B, author = {{Bubeck}, S. and {Tat Lee}, Y. and {Singh}, M.}, title = "{A geometric alternative to Nesterov's accelerated gradient descent}", journal = {ArXiv e-prints}, archivePrefix = "arXiv", eprint = {1506.08187}, primaryClass = "math.OC", keywords = {Mathematics - Optimization and Control, Computer Science - Data Structures and Algorithms, Computer Science - Learning, Computer Science - Numerical Analysis}, year = 2015, month = jun, adsurl = {http://adsabs.harvard.edu/abs/2015arXiv150608187B}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } @ARTICLE {BuckLe:83, author = "A.G. BUCKLEY and A. LENIR", title = "Q{N}-like variable storage conjugate gradients", journal = "Math. Prog.", year = "1983", volume = "27", pages = "155-175"} @ARTICLE {Buck:78a, author = "A.G. BUCKLEY", title = "A combined conjugate gradient quasi-{N}ewton minimization algorithm", journal = "Math. Prog.", year = "1978", volume = "15", pages = "200-210"} @ARTICLE {Buck:78b, author = "A.G. BUCKLEY", title = "Extending the relationship between the conjugate gradient and {BFGS} algorithms", journal = "Math. Prog.", year = "1978", volume = "15", pages = "343-348"} @INPROCEEDINGS {BuJo:93, author = "T.N. BUI and C. JONES", title = "A heuristic for reducing fill-in in sparse matrix factorization", booktitle = "Proceedings of the 6th SIAM Conference on Parallel Processing", year = "1993"} @INPROCEEDINGS {BuMo:93, author = "T.N. BUI and B.R. MOON", title = "Hyperplane synthesis for genetic algorithms", booktitle = "Proceedings of the 5th International Conference on Genetic Algorithms", year = "1993"} @ARTICLE {BuPa:71, author = "J.R. BUNCH and B.N. PARLETT", title = "Direct methods for solving symmetric indefinite systems of linear equations", journal = "SIAM J. Numer. Anal.", year = "1971", volume = "8", pages = "639-655"} @BOOK {BuDoMoSt:79, author = "J.R. BUNCH and J.J. DONGARRA and C.B. MOLER and G.B. Stewart", title = "LINPACK User's Guide", publisher = "SIAM Publications", year = "1979", address = "Philadelphia"} @article {MR3780460, AUTHOR = {Xu, G. and Burer, S.}, TITLE = {A copositive approach for two-stage adjustable robust optimization with uncertain right-hand sides}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {70}, YEAR = {2018}, NUMBER = {1}, PAGES = {33--59}, ISSN = {0926-6003}, MRCLASS = {90C20 (90C22 90C26 90C59)}, MRNUMBER = {3780460}, MRREVIEWER = {Riccardo Cambini}, DOI = {10.1007/s10589-017-9974-x}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10589-017-9974-x}, } @article {MR3347551, AUTHOR = {Burer, S.}, TITLE = {A gentle, geometric introduction to copositive optimization}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming}, VOLUME = {151}, YEAR = {2015}, NUMBER = {1, Ser. B}, PAGES = {89--116}, ISSN = {0025-5610}, MRCLASS = {90C20 (90C22 90C25 90C30)}, MRNUMBER = {3347551}, MRREVIEWER = {Janez Povh}, DOI = {10.1007/s10107-015-0888-z}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10107-015-0888-z}, } @article {MR2913613, AUTHOR = {Burer, S. and Dong, H.}, TITLE = {Representing quadratically constrained quadratic programs as generalized copositive programs}, JOURNAL = {Oper. Res. Lett.}, FJOURNAL = {Operations Research Letters}, VOLUME = {40}, YEAR = {2012}, NUMBER = {3}, PAGES = {203--206}, ISSN = {0167-6377}, MRCLASS = {90C20 (90C26)}, MRNUMBER = {2913613}, MRREVIEWER = {Mirjam D\"{u}r}, DOI = {10.1016/j.orl.2012.02.001}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1016/j.orl.2012.02.001}, } @incollection {MR2894696, AUTHOR = {Burer, S.}, TITLE = {Copositive programming}, BOOKTITLE = {Handbook on semidefinite, conic and polynomial optimization}, SERIES = {Internat. Ser. Oper. Res. Management Sci.}, VOLUME = {166}, PAGES = {201--218}, PUBLISHER = {Springer, New York}, YEAR = {2012}, MRCLASS = {90C20 (90C26)}, MRNUMBER = {2894696}, MRREVIEWER = {Mirjam D\"{u}r}, DOI = {10.1007/978-1-4614-0769-0_8}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/978-1-4614-0769-0_8}, } @article {MR2505747, AUTHOR = {Burer, S.}, TITLE = {On the copositive representation of binary and continuous nonconvex quadratic programs}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {120}, YEAR = {2009}, NUMBER = {2, Ser. A}, PAGES = {479--495}, ISSN = {0025-5610}, MRCLASS = {90C25 (90C20 90C26)}, MRNUMBER = {2505747}, DOI = {10.1007/s10107-008-0223-z}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10107-008-0223-z}, } @article {MR2192210, AUTHOR = {Anstreicher, K.M. and Burer, S.}, TITLE = {D.{C}. versus copositive bounds for standard {QP}}, JOURNAL = {J. Global Optim.}, FJOURNAL = {Journal of Global Optimization. An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering}, VOLUME = {33}, YEAR = {2005}, NUMBER = {2}, PAGES = {299--312}, ISSN = {0925-5001}, MRCLASS = {90C20 (90C22)}, MRNUMBER = {2192210}, DOI = {10.1007/s10898-004-4312-0}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10898-004-4312-0}, } @INCOLLECTION{Burkarddupl:91, AUTHOR = "R.E. Burkard ", TITLE = " Locations with spatial interactions: the quadratic assignment problem", booktitle = " Discrete Location Theory", publisher = "John Wiley", editor = "P.B.\ Mirchandani and R.L.\ Francis", YEAR = 1991, } @ARTICLE {BuKaRe:91, author = "R.E. Burkard and S. Karisch and F. Rendl", title = "A quadratic assignment problem library", journal = "European Journal of Operations Research", year = "1991", volume = "55", note = "http://fmatbhp1.tu-graz.ac.at/~karisch/rep287.ps for updates", pages = "151-119"} @techreport{LewisOvertonBFGSexactlin:08, AUTHOR = {Lewis, A.S. and Overton, M.L.}, TITLE = "BEHAVIOR OF {BFGS} WITH AN EXACT LINE SEARCH ONNONSMOOTH EXAMPLES", TYPE = "Report", INSTITUTION = "Cornell University", YEAR = "2008", } @article {MR2002c:49031, AUTHOR = {Burke, J. V. and Lewis, A.S. and Overton, M.L.}, TITLE = {Optimal stability and eigenvalue multiplicity}, JOURNAL = {Found. Comput. Math.}, FJOURNAL = {Foundations of Computational Mathematics. The Journal of the Society for the Foundations of Computational Mathematics}, VOLUME = {1}, YEAR = {2001}, NUMBER = {2}, PAGES = {205--225}, ISSN = {1615-3375}, MRCLASS = {49J53 (49J52 65F15 90C31)}, MRNUMBER = {2002c:49031}, MRREVIEWER = {Marcos Raydan}, } @article{burke:265, author = {J.V. Burke and P. Tseng}, collaboration = {}, title = {A Unified Analysis of Hoffman's Bound via Fenchel Duality}, publisher = {SIAM}, year = {1996}, journal = {SIAM Journal on Optimization}, volume = {6}, number = {2}, pages = {265-282}, keywords = {Fenchel duality; error bound; linear system; positively homogeneous convex function; convex cone; semidefinite programming}, url = {http://link.aip.org/link/?SJE/6/265/1}, doi = {10.1137/0806015} } @article {MR91e:90082, AUTHOR = {Burke, J.}, TITLE = {On the identification of active constraints. {II}.\ {T}he nonconvex case}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {27}, YEAR = {1990}, NUMBER = {4}, PAGES = {1081--1103}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {90C26}, MRNUMBER = {91e:90082}, MRREVIEWER = {Pierre Loridan}, } @article {MR95d:49026, AUTHOR = {Burke, J.V. and Mor\'{e}, J.J.}, TITLE = {Exposing constraints}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {4}, YEAR = {1994}, NUMBER = {3}, PAGES = {573--595}, ISSN = {1052-6234}, CODEN = {SJOPE8}, MRCLASS = {49J52 (90C30)}, MRNUMBER = {95d:49026}, MRREVIEWER = {Paul H. Calamai}, } @article {MR89i:90068, AUTHOR = {Burke, J.V. and Mor{\'e}, J.J.}, TITLE = {On the identification of active constraints}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {25}, YEAR = {1988}, NUMBER = {5}, PAGES = {1197--1211}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {90C30 (65K05)}, MRNUMBER = {89i:90068}, MRREVIEWER = {Pierre Loridan}, } @ARTICLE {BuNi:87, author = "K.W.C. BURTON and G. NICKLESS", title = "Optimization via {S}implex, part {I}. {B}ackground, definitions and a simple application", journal = "Chemometrics and Intelligent Laboratory Systems", year = "1987", volume = "1", pages = "135-149"} @ARTICLE {BuPa:84, author = "W.R. BUSING and M. MATSUI", title = "The application of external forces to computational models of crystals", journal = "Acta Cryst. Sect. A", year = "1984", volume = "40", pages = "532"} @PHDTHESIS {Buy:72, author = "J.D. BUYS", title = "Dual algorithms for constrained optimization problems", school = "University of Leiden", year = "1972", address = "Netherlands"} @ARTICLE {BuyHaa:70, author = "J.D. BUYS and P.C. HAARHOFF", title = "A new method for the optimization of a nonlinear function subject to nonlinear constraints", journal = "Comput. J.", year = "1970", volume = "13", pages = "178-184"} @TECHREPORT {Byr:84, author = "R.H. Byrd", title = "On the convergence of constrained optimization methods with accurate {H}essian information on a subspace", institution = "Department of Computer Science, University of Colorado", year = "1984", number = "CU-CS-270-84", address = "Boulder, CO"} @ARTICLE {Byr:85, author = "R.H. Byrd", title = "An example of irregular convegence in some constrained optimization methods that use projected {H}essian", journal = "Math. Prog.", year = "1985", volume = "32", pages = "232-237"} @UNPUBLISHED {Byr:89, author = "R.H. Byrd", title = "A multiobjective characterization of the {B}royden class", note = "In preparation. Presented at ORSA/TIMS, New York, Sept. 1990."} @TECHREPORT {ByrDeRiSchn:86, author = "R.H. Byrd and C.L. DERT and A.H.G. {RINNOOY KAN} and R.B. Schnabel", title = "Concurrent stochastic methods for global optimization", institution = "Department of Computer Science, University of Colorado", year = "1986", number = "CU-CS-338-86", address = "Boulder, CO"} @INPROCEEDINGS {ByrDeRiSchn:87, author = "R.H. Byrd and C.L. DERT and A.H.G. {RINNOOY KAN} and R.B. Schnabel", title = "Concurrent global optimization on a network of computers", booktitle = "Proceedings of ARO Workshop on Parallel Processing and Medium-Scale Multiprocessing", publisher = "SIAM", year = "1987", editor = "A. Wouk", address = "Philadelphia"} @ARTICLE {ByrNoc:89, author = "R.H. Byrd and R.H. Nocedal", title = "A tool for the analysis of quasi-{N}ewton methods with application to unconstrained minimization", journal = "SIAM J. Numer. Anal.", year = "1989", volume = "26", pages = "727-739"} @ARTICLE{ByrLiuNoc:92, author = "R.H. Byrd and D.C. Liu and R.H. Nocedal", title = "On the behaviour of {B}royden's class of quasi-{N}ewton methods", journal = siopt, year = "1992", volume = "2"} @TECHREPORT {ByrLiuNoc:98, author = "R.H. Byrd and D.C. Liu and R.H. Nocedal", title = "On the Local Behavior of an Interior Point Method for Nonlinear Programming", institution = "Optimization Technology Center, Northwestern University", number = "Report OTC 98/02", year = "1998", address = "Evanston Il 60208"} @TECHREPORT {ByrGilNoc:96, author = "R.H. Byrd and J.C. GILBERT and R.H. Nocedal", title = "A Trust Region Method Based on Interior Point Techniques for Nonlinear Programming", institution = "Optimization Technology Center, Northwestern University", number = "Report OTC 96/02", year = "1996", address = "Evanston Il 60208"} @ARTICLE {ByrNocYua:87, author = "R.H. Byrd and R.H. Nocedal and Y.YUAN", title = "Global convergence of a class of quasi-{N}ewton methods on convex problems", journal = "SIAM J. Numer. Anal.", year = "1987", volume = "24", pages = "1171-1191"} @ARTICLE {ByrSchnSchu:85, author = "R.H. Byrd and R.B. Schnabel and G.A. SCHULTZ", title = "A family of trust-region-based algorithms for unconstrained minimization with strong global convergence properties", journal = "SIAM J. Numer. Anal.", year = "1985", volume = "22", pages = "47-67", note = "Also available as Technical Report CU-CS-216-82, Department of Computer Science, University of Colorado, Boulder, CO"} @ARTICLE {ByrSchn:86, author = "R.H. Byrd and R.B. Schnabel", title = "Continuity of the null space basis and constrained optimization", journal = "Math. Prog.", year = "1986", volume = "35", pages = "32-41"} @ARTICLE {ByrSchnSchu:87, author = "R.H. Byrd and R.B. Schnabel and G.A. SCHULTZ", title = "A trust region algorithm for nonlinearly constrained optimization", journal = "SIAM J. Numer. Anal.", year = "1987", volume = "24", pages = "1152-1170", note = "Also available as Technical Report CU-CS-313-85, Department of Computer Science, University of Colorado, Boulder, CO"} @ARTICLE {ByrSchnSchu:88a, author = "R.H. Byrd and R.B. Schnabel and G.A. SCHULTZ", title = "Approximate solution of the trust region problem by minimization over two-dimensional subspaces", journal = "Math. Prog.", year = "1988", volume = "40", pages = "247-263"} @ARTICLE {ByrSchnSchu:88b, author = "R.H. Byrd and R.B. Schnabel and G.A. SCHULTZ", title = "Using parallel function evaluations to improve {H}essian approximations for unconstrained optimization", journal = "Annals of Operations Research", year = "1988", volume = "14", pages = "167-193", note = "Also available as Technical Report CU-CS-361-87, Department of Computer Science, University of Colorado, Boulder, CO"} @ARTICLE {ByrSchnSchu:88c, author = "R.H. Byrd and R.B. Schnabel and G.A. SCHULTZ", title = "Parallel quasi-{N}ewton methods for unconstrained optimization", journal = "Math. Prog.", year = "1988", volume = "42", pages = "273-306", note = "Also available as Technical Report CU-CS-396-88, Department of Computer Science, University of Colorado, Boulder, CO"} @MISC {ByrSchnZhan:88, author = "R.H. Byrd and R.B. Schnabel and X. ZHANG", title = "Parallel methods for block bordered nonlinear problems", note = "To appear in Proceedings of the Sixth Army Conference on Applied Mathematics and Computing, June 1988"} @MISC {ByrSchnZhan:89, author = "R.H. Byrd and R.B. Schnabel and X. ZHANG", title = "Solving nonlinear block bordered circuit equations on a hypercube multiprocessor", note = "To appear in Proceedings of the Fourth Conference on Hypercubes, Concurrent Computers and Applications, Monterey, CA, Mar. 1989"} %CCCCCCC @ARTICLE{2018arXiv180609222C, author = {{Carmon}, Y. and {Duchi}, J.~C.}, title = "{Analysis of Krylov Subspace Solutions of Regularized Nonconvex Quadratic Problems}", journal = {ArXiv e-prints}, archivePrefix = "arXiv", eprint = {1806.09222}, primaryClass = "math.OC", keywords = {Mathematics - Optimization and Control}, year = 2018, month = jun, adsurl = {http://adsabs.harvard.edu/abs/2018arXiv180609222C}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } @book {LiesenStrakos:12, AUTHOR = {Liesen, J. and Strakos, Z.}, TITLE = {Krylov Subspace Methods: Principles and Analysis}, SERIES = {A Series of Books in the Mathematical Sciences}, PUBLISHER = {W. H. Freeman and Company, New York}, YEAR = {2012}, PAGES = {}, ISBN = {13: 9780199655410}, DOI = {10.1093/acprof:oso/9780199655410.001.0001} } @article {MR488703, AUTHOR = {Abbott, J.P.}, TITLE = {An efficient algorithm for the determination of certain bifurcation points}, JOURNAL = {J. Comput. Appl. Math.}, FJOURNAL = {Journal of Computational and Applied Mathematics}, VOLUME = {4}, YEAR = {1978}, NUMBER = {1}, PAGES = {19--27}, ISSN = {0377-0427}, MRCLASS = {65H10}, MRNUMBER = {488703}, MRREVIEWER = {Colin M. Campbell}, DOI = {10.1016/0771-050X(78)90015-3}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1016/0771-050X(78)90015-3}, } @article{Carlson2002447, author = "H.A. Carlson", title = "Protein flexibility and drug design: how to hit a moving target ", journal = "Current Opinion in Chemical Biology ", volume = "6", number = "4", pages = "447 - 452", year = "2002", note = "", issn = "1367-5931", doi = "10.1016/S1367-5931(02)00341-1", url = "http://www.sciencedirect.com/science/article/pii/S1367593102003411" } @article {MR2098608, AUTHOR = {CATRAL, M. and HAN, L. and NEUMANN, M. and PLEMMONS, R.J.}, TITLE = {On reduced rank nonnegative matrix factorization for symmetric nonnegative matrices}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {393}, YEAR = {2004}, PAGES = {107--126}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A48 (15A23)}, MRNUMBER = {MR2098608 (2005i:15034)}, MRREVIEWER = {Jianhong Xu}, } @ARTICLE {Calabi:49, author = "E. CALABI", TITLE = {Linear systems of real quadratic forms}, JOURNAL = {Proc. Amer. Math. Soc.}, VOLUME = {15}, YEAR = {1964}, PAGES = {844--846}, MRCLASS = {15.70 (10.16)}, MRNUMBER = {29 \#3480}, MRREVIEWER = {W. Klingenberg}, } @ARTICLE {CalMor:87, author = "P.H. CALAMAI and J. J. Mor\'{e}", title = "Quasi-{N}ewton updates with bounds", journal = "SIAM J. Numer. Anal.", year = "1987", volume = "24", pages = "1434-1441"} @ARTICLE {Cauchy:47, author = "A. Cauchy", title = "Methode generale pour la resolution des systemes d'equations simultanees", journal = "Comp. Rend. Acad. Sci. Paris", year = "1847", volume = "25", pages = "536-538"} @article {MR2589670, TITLE = {2008 {IEEE} {I}nformation {T}heory {S}ociety {P}aper {A}ward}, author = {Unknown}, JOURNAL = {IEEE Trans. Inform. Theory}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Information Theory}, VOLUME = {55}, YEAR = {2009}, NUMBER = {1}, PAGES = {1--2}, ISSN = {0018-9448}, CODEN = {IETTAW}, MRCLASS = {01A70}, MRNUMBER = {MR2589670}, DOI = {10.1109/TIT.2008.2011351}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1109/TIT.2008.2011351}, } @article {donoho:06, author = {D. Donoho}, TITLE = {Compressed Sensing}, JOURNAL = {IEEE Trans. Inform. Theory}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Information Theory}, VOLUME = {52}, YEAR = {2006}, NUMBER = {4}, PAGES = {1289--1306} } @article {MR2565240, AUTHOR = {Cand{\`e}s, E.J. and Recht, B.}, TITLE = {Exact matrix completion via convex optimization}, JOURNAL = {Found. Comput. Math.}, FJOURNAL = {Foundations of Computational Mathematics. The Journal of the Society for the Foundations of Computational Mathematics}, VOLUME = {9}, YEAR = {2009}, NUMBER = {6}, PAGES = {717--772}, ISSN = {1615-3375}, MRCLASS = {90C25 (15A83 90C22)}, MRNUMBER = {2565240}, MRREVIEWER = {Gunter Semmler}, DOI = {10.1007/s10208-009-9045-5}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s10208-009-9045-5}, } @article {MR2300700, AUTHOR = {Candes, E.J. and Tao, T.}, TITLE = {Near-optimal signal recovery from random projections: universal encoding strategies?}, JOURNAL = {IEEE Trans. Inform. Theory}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Information Theory}, VOLUME = {52}, YEAR = {2006}, NUMBER = {12}, PAGES = {5406--5425}, ISSN = {0018-9448}, CODEN = {IETTAW}, MRCLASS = {94A12 (41A25 94A13)}, MRNUMBER = {MR2300700 (2008c:94009)}, MRREVIEWER = {L. L. Campbell}, DOI = {10.1109/TIT.2006.885507}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1109/TIT.2006.885507}, } @inproceedings{Candesetal2005, author = "Candes, E. and Rudelson, M. and Tao, T. and Vershynin, R.", year = "2005", title = "Error correction via linear programming", booktitle ="Proceedings of hte 2005 46th Annual EIII Symposium on Foundations of Computer Science, (FOCS'o5)", publisher = "IEEE", pages = "1-14"} AUTHOR = {Candes, E.J. and Tao, T.}, TITLE = {Near-optimal signal recovery from random projections: universal encoding strategies?}, JOURNAL = {IEEE Trans. Inform. Theory}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Information Theory}, VOLUME = {52}, YEAR = {2006}, NUMBER = {12}, PAGES = {5406--5425}, ISSN = {0018-9448}, CODEN = {IETTAW}, MRCLASS = {94A12 (41A25 94A13)}, MRNUMBER = {MR2300700 (2008c:94009)}, MRREVIEWER = {L. L. Campbell}, DOI = {10.1109/TIT.2006.885507}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1109/TIT.2006.885507}, } @article {MR2230846, AUTHOR = {Cand{\`e}s, E.J. and Romberg, J.K. and Tao, T.}, TITLE = {Stable signal recovery from incomplete and inaccurate measurements}, JOURNAL = {Comm. Pure Appl. Math.}, FJOURNAL = {Communications on Pure and Applied Mathematics}, VOLUME = {59}, YEAR = {2006}, NUMBER = {8}, PAGES = {1207--1223}, ISSN = {0010-3640}, CODEN = {CPAMA}, MRCLASS = {94A12}, MRNUMBER = {MR2230846 (2007f:94007)}, MRREVIEWER = {Brody Dylan Johnson}, DOI = {10.1002/cpa.20124}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1002/cpa.20124}, } @article {MR2723472, AUTHOR = {Cand{\`e}s, E.J. and Tao, T.}, TITLE = {The power of convex relaxation: near-optimal matrix completion}, JOURNAL = {IEEE Trans. Inform. Theory}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Information Theory}, VOLUME = {56}, YEAR = {2010}, NUMBER = {5}, PAGES = {2053--2080}, ISSN = {0018-9448}, CODEN = {IETTAW}, MRCLASS = {15A83 (60B20 90C22 90C46 94A12)}, MRNUMBER = {2723472}, MRREVIEWER = {Tian Zhou Xu}, DOI = {10.1109/TIT.2010.2044061}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1109/TIT.2010.2044061}, } @article {MR2243152, AUTHOR = {Candes, E.J. and Tao, T.}, TITLE = {Decoding by linear programming}, JOURNAL = {IEEE Trans. Inform. Theory}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Information Theory}, VOLUME = {51}, YEAR = {2005}, NUMBER = {12}, PAGES = {4203--4215}, ISSN = {0018-9448}, CODEN = {IETTAW}, MRCLASS = {94B35 (90C08)}, MRNUMBER = {MR2243152 (2007b:94313)}, MRREVIEWER = {Josep Rif{\`a}}, DOI = {10.1109/TIT.2005.858979}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1109/TIT.2005.858979}, } @ARTICLE {CandesWakin:08, author = "E. Candes and M. Wakin", title = "An Introduction to Compressive Sensing", journal = "IEEE Signal Processing Magazine", year = "2008", volume = "25", number = "2", pages = "21-30"} @ARTICLE {Cant:69, author = "J.W. CANTRELL", title = "Relation between the memory gradient method and the {F}letcher-{R}eeves method", journal = "J. Optim. Theory Appl.", year = "1969", volume = "4", pages = "67-71"} @ARTICLE {CantMie:69, author = "J.W. CANTRELL and A. MIELE", title = "Study on a memory gradient method for the minimization of functions", journal = "J. Optim. Theory Appl.", year = "1969", volume = "3", pages = "459-470"} @TECHREPORT {Carcione, author = "L. CARCIONE", title = "Test functions for separable nonlinear least squares problems", institution = "Departamento de Computaci\'{o}n, Facultad de Ciencias Exactas y Naturales", year = "1989", number = "2-89"} @ARTICLE {CaLuMuSh:93, author = "T.J. CARPENTER and I. J. LUSTIG and R.E. MARSTEN and D. F. SHANNO", title = "Higher-order predictor-corrector interior point methods with application to quadratic objectives", year = "1993", volume = "3", journal = siopt, number = "4", pages = "696-725"} @article {MR94h:90022, AUTHOR = {HALL, L.A. and Vanderbei, R.J.}, TITLE = {Two-thirds is sharp for affine scaling}, JOURNAL = {Oper. Res. Lett.}, FJOURNAL = {Operations Research Letters}, VOLUME = {13}, YEAR = {1993}, NUMBER = {4}, PAGES = {197--201}, ISSN = {0167-6377}, CODEN = {ORLED5}, MRCLASS = {90C05}, MRNUMBER = {94h:90022}, } @ARTICLE{VC91, author = "R.J. Vanderbei and T.J. CARPENTER", title = "Symmetric indefinite systems for interior-point methods", journal = mprog, year = "1993", volume = "58", pages = "1-32"} @TECHREPORT {Car:86, author = "R.G. CARTER", title = "Multi-model algorithms for optimization", institution = "Department of Mathematical Sciences, Rice University", year = "1986", number = "TR86-3", address = "Houston,TX"} @TECHREPORT {Car:87a, author = "R.G. CARTER", title = "Safeguarding {H}essian approximations in trust region algorithms", institution = "Department of Mathematical Sciences, Rice University", year = "1987", number = "TR87-12", address = "Houston, TX"} @TECHREPORT {Car:87b, author = "R.G. CARTER", title = "Global convergence theory for line search and trust region algorithms", institution = "Department of Mathematical Sciences, Rice University", year = "1987", number = "TR87-16", address = "Houston,TX"} @BOOK {Cea:71, author = "J. C\'{E}A", title = "Optimisation: th\'{e}orie et algorithmes", publisher = "Dunod", year = "1971", address = "Paris"} @INPROCEEDINGS {CeDeTa:84, author = "M.R. Celis and J.E. {Dennis Jr.} and R.A. Tapia", title = "A trust region strategy for nonlinear equality constrained optimization", booktitle = "Proceedings of the SIAM Conference on Numerical Optimization, Boulder, CO", year = "1984", note = "Also available as Technical Report TR84-1, Department of Mathematical Sciences, Rice University, Houston, TX"} @article {MR579552, AUTHOR = {Lent, A. and Censor, Y.}, TITLE = {Extensions of {H}ildreth's row-action method for quadratic programming}, JOURNAL = {SIAM J. Control Optim.}, FJOURNAL = {SIAM Journal on Control and Optimization}, VOLUME = {18}, YEAR = {1980}, NUMBER = {4}, PAGES = {444--454}, ISSN = {0363-0129}, MRCLASS = {90C20 (65K05)}, MRNUMBER = {579552}, MRREVIEWER = {Jacques A. Ferland}, DOI = {10.1137/0318033}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/0318033}, } @article {MR4261289, AUTHOR = {Censor, Y. and Levy, E.}, TITLE = {An analysis of the superiorization method via the principle of concentration of measure}, JOURNAL = {Appl. Math. Optim.}, FJOURNAL = {Applied Mathematics and Optimization}, VOLUME = {83}, YEAR = {2021}, NUMBER = {3}, PAGES = {2273--2301}, ISSN = {0095-4616}, MRCLASS = {90C25}, MRNUMBER = {4261289}, MRREVIEWER = {Wen Song}, DOI = {10.1007/s00245-019-09628-4}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s00245-019-09628-4}, } @article {MR3626828, AUTHOR = {Censor, Y.}, TITLE = {Can linear superiorization be useful for linear optimization problems?}, JOURNAL = {Inverse Problems}, FJOURNAL = {Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data}, VOLUME = {33}, YEAR = {2017}, NUMBER = {4}, PAGES = {044006, 22}, ISSN = {0266-5611}, MRCLASS = {90C05 (65K05 90C49)}, MRNUMBER = {3626828}, MRREVIEWER = {S. A. Edalatpanah}, DOI = {10.1088/1361-6420/33/4/044006}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1088/1361-6420/33/4/044006}, } @article {MR3626822, AUTHOR = {Censor, Y. and Herman, G.T. and Jiang, M.}, TITLE = {Superiorization: theory and applications [{P}reface]}, JOURNAL = {Inverse Problems}, FJOURNAL = {Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data}, VOLUME = {33}, YEAR = {2017}, NUMBER = {4}, PAGES = {040301, 2}, ISSN = {0266-5611}, MRCLASS = {65-06}, MRNUMBER = {3626822}, DOI = {10.1088/1361-6420/aa5deb}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1088/1361-6420/aa5deb}, } @incollection {MR3577726, AUTHOR = {Censor, Y. and Zur, Y.}, TITLE = {Linear superiorization for infeasible linear programming}, BOOKTITLE = {Discrete optimization and operations research}, SERIES = {Lecture Notes in Comput. Sci.}, VOLUME = {9869}, PAGES = {15--24}, PUBLISHER = {Springer, [Cham]}, YEAR = {2016}, MRCLASS = {90C05}, MRNUMBER = {3577726}, DOI = {10.1007/978-3-319-44914-2\_2}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/978-3-319-44914-2_2}, } @article {MR3374759, AUTHOR = {Censor, Y.}, TITLE = {Weak and strong superiorization: between feasibility-seeking and minimization}, JOURNAL = {An. \c{S}tiin\c{t}. Univ. ``Ovidius'' Constan\c{t}a Ser. Mat.}, FJOURNAL = {Analele \c{S}tiin\c{t}ifice ale Universit\u{a}\c{t}ii ``Ovidius'' Constan\c{t}a. Seria Matematic\u{a}. Mathematical Journal of the Ovidius University of Constantza}, VOLUME = {23}, YEAR = {2015}, NUMBER = {3}, PAGES = {41--54}, ISSN = {1224-1784}, MRCLASS = {90C25 (65K10)}, MRNUMBER = {3374759}, DOI = {10.1515/auom-2015-0046}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1515/auom-2015-0046}, } @article {MR3327420, AUTHOR = {Censor, Y. and Zaslavski, A.J.}, TITLE = {Strict {F}ej\'{e}r monotonicity by superiorization of feasibility-seeking projection methods}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {165}, YEAR = {2015}, NUMBER = {1}, PAGES = {172--187}, ISSN = {0022-3239}, MRCLASS = {90C30 (65K10 90C25)}, MRNUMBER = {3327420}, MRREVIEWER = {Massimo Pappalardo}, DOI = {10.1007/s10957-014-0591-x}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10957-014-0591-x}, } @incollection {MR3155361, AUTHOR = {Davidi, Rn and Censor, Y. and Schulte, R.W. and Geneser, S. and Xing, L.}, TITLE = {Feasibility-seeking and superiorization algorithms applied to inverse treatment planning in radiation therapy}, BOOKTITLE = {Infinite products of operators and their applications}, SERIES = {Contemp. Math.}, VOLUME = {636}, PAGES = {83--92}, PUBLISHER = {Amer. Math. Soc., Providence, RI}, YEAR = {2015}, MRCLASS = {65K05 (90C59 90C90 92C50)}, MRNUMBER = {3155361}, MRREVIEWER = {Julien Ugon}, DOI = {10.1090/conm/636/12729}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1090/conm/636/12729}, } @article {MR3180993, AUTHOR = {Censor, Y. and Davidi, R. and Herman, G.T. and Schulte, R.W. and Tetruashvili, L.}, TITLE = {Projected subgradient minimization versus superiorization}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {160}, YEAR = {2014}, NUMBER = {3}, PAGES = {730--747}, ISSN = {0022-3239}, MRCLASS = {90-08 (90C25 90C90)}, MRNUMBER = {3180993}, MRREVIEWER = {Chee-Khian Sim}, DOI = {10.1007/s10957-013-0408-3}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10957-013-0408-3}, } @article {MR2647162, AUTHOR = {Censor, Y. and Davidi, R. and Herman, G. T.}, TITLE = {Perturbation resilience and superiorization of iterative algorithms}, JOURNAL = {Inverse Problems}, FJOURNAL = {Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data}, VOLUME = {26}, YEAR = {2010}, NUMBER = {6}, PAGES = {065008, 12}, ISSN = {0266-5611}, MRCLASS = {65K10}, MRNUMBER = {2647162}, MRREVIEWER = {V. F. Dem\cprime yanov}, DOI = {10.1088/0266-5611/26/6/065008}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1088/0266-5611/26/6/065008}, } @TECHREPORT {Censor:01, author = " Y. CENSOR", title = "On sequential and parallel projection algorithms for feasibility and optimization", institution = "University of Haifa", year = "2001", address = "Haifa, Israel"} @inproceedings{ChengChenSacchi:15, author = "J. Cheng and K. Chen and M.D. Sacchi", title = "Application of Robust Principal Component Analysis {(RPCA)} to suppress erratic noise in seismic records", booktitle ="SEG Technical Program Expanded", editor= " ", publisher = "SEG", year = "2015", pages = "4646-4651" } @article {MR1288811, AUTHOR = {P.D. Chinh}, TITLE = {Bounds for the effective conductivity and elastic moduli of fully-disordered multicomponent materials}, JOURNAL = {Arch. Rational Mech. Anal.}, FJOURNAL = {Archive for Rational Mechanics and Analysis}, VOLUME = {127}, YEAR = {1994}, NUMBER = {2}, PAGES = {191--198}, ISSN = {0003-9527}, MRCLASS = {73B27 (73B35 73K20 80A20)}, MRNUMBER = {1288811}, MRREVIEWER = {Robert Lipton}, DOI = {10.1007/BF00377661}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/BF00377661}, } @inproceedings{NIPS20144d6e4749, author = {R.K. Vinayak and S. Oymak and B. Hassibi}, booktitle = {Advances in Neural Information Processing Systems}, editor = {Z. Ghahramani and M. Welling and C. Cortes and N. Lawrence and K. Q. Weinberger}, pages = {}, publisher = {Curran Associates, Inc.}, title = {Graph Clustering With Missing Data: Convex Algorithms and Analysis}, url = {https://proceedings.neurips.cc/paper/2014/file/4d6e4749289c4ec58c0063a90deb3964-Paper.pdf}, volume = {27}, year = {2014} } @book {MR717219, AUTHOR = {Chv\'atal, V.}, TITLE = {Linear programming}, SERIES = {A Series of Books in the Mathematical Sciences}, PUBLISHER = {W. H. Freeman and Company, New York}, YEAR = {1983}, PAGES = {xiii+478}, ISBN = {0-7167-1195-8; 0-7167-1587-2}, MRCLASS = {90C05}, MRNUMBER = {717219}, MRREVIEWER = {A. G. Azpeitia}, } @book {MR2294029, AUTHOR = {Cornuejols, G. and T\"ut\"unc\"u, R.}, TITLE = {Optimization methods in finance}, SERIES = {Mathematics, Finance and Risk}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {2007}, PAGES = {xii+345}, ISBN = {978-0-521-86170-0}, MRCLASS = {91-01 (90C90 91B28)}, MRNUMBER = {2294029}, } @TECHREPORT {CerCornPat:94a, author = "S. CERIA and G. CORNUEJOLS and G. PATAKI", title = "Polyhedral methods for the maximum clique problem", institution = "GSIA Carnegie Mellon University", keywords = "sdp;coneprog", year = "1994", address = "Pittsburgh, PA"} @article {ChGuSa:99, AUTHOR = {S. CHANDRASEKARAN and M. GU and A. H. SAYED}, TITLE = {The sparse basis problem and multilinear algebra}, JOURNAL = simax, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {20}, YEAR = {1999}, NUMBER = {2}, PAGES = {354--362}, } @PHDTHESIS {Cha:78, author = "R. CHANDRA", title = "Conjugate gradient methods for partial differential equations", school = "Department of Computer Science, Yale University", year = "1978", address = "New Haven, CT", note = "Also available as Research Report \#129"} @BOOK {ChanHai:83, author = "V. CHANKONG and Y.Y. HAIMES", title = "Multiobjective Decision Making: Theory and Methodology", publisher = "North-Holland", year = "1983", address = "New York, NY"} @ARTICLE {Chara:79, author = "C. CHARALAMBOUS", title = "On conditions for optimality of the nonlinear $l_{1}$ problem", journal = "Math. Prog.", year = "1979", volume = "17", pages = "123-135"} @article {MR0056264, AUTHOR = {Charnes, A.}, TITLE = {Optimality and degeneracy in linear programming}, JOURNAL = {Econometrica}, FJOURNAL = {Econometrica. Journal of the Econometric Society}, VOLUME = {20}, YEAR = {1952}, PAGES = {160--170}, ISSN = {0012-9682}, MRCLASS = {90.0X}, MRNUMBER = {MR0056264 (15,48d)}, MRREVIEWER = {D. Gale}, } @TECHREPORT {CharSoWo:84, author = "A. Charnes and T. SONG and M. WOLFE", title = "An explicit solution sequence and convergence of {K}armarkar's algorithm", institution = "Center for Cybernetic Studies, University of Texas at Austin", year = "1984", type = "Research Report", number = "CCS 501", address = "Austin, TX"} @ARTICLE {CheGraSal:86, author = "D.H. CHEN and Z. SALEEM and D.W. GRACE", title = "A new simplex procedure for function minimization", journal = "International Journal of Modelling \& Simulation", year = "1986", volume = "6", number = "3", pages = "81-85"} @ARTICLE {ChRao:93, author = "S. CHOPRA and M.R. RAO", title = "The partition problem", journal = mprog, volume = "49", year = "1993", pages = "87-115"} @TECHREPORT {ChowSchna:89, author = "T CHOW and R.B. Schnabel", title = "Tensor methods for unconstrained optimization", institution = "Department of Computer Science, University of Colorado", year = "1989", number = "CU-CS-439-89", address = "Boulder, CO"} @article{chaitoh:07, AUTHOR = "CHAI, J-S and TOH, K-C", TITLE = "Preconditioning and iterative solution of symmetric indefinite linear systems arising from interior point methods for linear programming", journal = coap, volume = "36", pages = "221--247", number = "2-3", YEAR = "2007", } @techreport{choipaigesaunders:10, AUTHOR = "S.T. Choi, C.C. Paige, M.A. Saunders", TITLE = "{MINRES-QLP}: a {K}rylov subspace method for indefinite or singular symmetric systems", TYPE = "Report", INSTITUTION = "Stanford University", YEAR = "2010", } @phdthesis{Choi:1994:NOA:920836, author = {Choi, G.}, title = {Nondifferentiable Optimization Algorithms with Application to Solving Lagrangian Dual Problems}, year = {1994}, note = {AAI9424877}, school = {Virginia Polytechnic Institute and State University}, } @ARTICLE {ChBr:76, author = "N. CHRISTOFIDES and P. BROOKER", title = "The optimal partitioning of graphs", journal = "SIAM J. Applied Mathematics", year = "1976 ", volume = "30", pages = "55-69"} @ARTICLE {Chu:89, author = "K.E. CHU", title = "Symmetric solutions of linear matrix equations by matrix decompositions", journal = laa, year = "1989", volume = "119", pages = "35-50"} @BOOK {Ch:83, author = "V. CHV\'{A}TAL", TITLE = {Linear programming}, SERIES = {A Series of Books in the Mathematical Sciences}, PUBLISHER = {W. H. Freeman and Company}, ADDRESS = {New York}, YEAR = {1983}, PAGES = {xiii+478}, ISBN = {0-7167-1195-8; 0-7167-1587-2}, MRCLASS = {90C05}, MRNUMBER = {MR717219 (86g:90062)}, MRREVIEWER = {A. G. Azpeitia}, } @article {MR1531192, AUTHOR = {Clark, F.E.}, TITLE = {Mathematical {N}otes: {R}emark on the {C}onstraint {S}ets in {L}inear {P}rogramming}, JOURNAL = {Amer. Math. Monthly}, FJOURNAL = {American Mathematical Monthly}, VOLUME = {68}, YEAR = {1961}, NUMBER = {4}, PAGES = {351--352}, ISSN = {0002-9890}, MRCLASS = {DML}, MRNUMBER = {1531192}, DOI = {10.2307/2311583}, URL = {http://dx.doi.org/10.2307/2311583}, } @ARTICLE {Clark:85, author = "D.I. CLARK", title = "The mathematical structure of {H}uber's {M}-estimator", journal = "SIAM J. Sci. Statist. Comput.", year = "1985", volume = "6", pages = "209"} @PHDTHESIS {Clarke:73, author = "F.H. Clarke", title = "Necessary conditions for nonsmooth problems in {O}ptimal {C}ontrol and {C}alculus of {V}ariations", school = "University of Washington", year = "1973"} @ARTICLE {Clarke:75, author = "F.H. Clarke", title = "Generalized gradients and applications", journal = "Trans Amer. Math. Soc.", year = "1975", volume = "205", pages = "247-262"} @ARTICLE {Clarke:76, author = "F.H. Clarke", title = "A new approach to {L}agrange multipliers", journal = "Math. Op. Res.", year = "1976", volume = "1", pages = "165-174"} @ARTICLE {Clarke:81, author = "F.H. Clarke", title = "Generalized gradients of {L}ipschitz functionals", journal = "Adv. Math.", year = "1981", volume = "40", pages = "52-67"} @BOOK {Clarke:83, author = "F.H. Clarke", title = "Optimization and Nonsmooth Analysis", publisher = "John Wiley \& Sons", year = "1983", series = "Canadian Math. Soc. Series of Monographs and Advanced Texts"} @BOOK {Clarke1990optimization, AUTHOR = {Clarke, F.H.}, TITLE = {Optimization and nonsmooth analysis}, SERIES = {Classics in Applied Mathematics}, VOLUME = {5}, EDITION = {Second}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA}, YEAR = {1990}, PAGES = {xii+308}, ISBN = {0-89871-256-4}, MRCLASS = {49-02 (01A75 49J52 58C20 90C48)}, MRNUMBER = {1058436}, DOI = {10.1137/1.9781611971309}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/1.9781611971309}, } @article {Clausing, AUTHOR = {CLAUSING, A.}, TITLE = {Kantorovich-type inequalities}, JOURNAL = {Amer. Math. Monthly}, FJOURNAL = {The American Mathematical Monthly}, VOLUME = {89}, YEAR = {1982}, NUMBER = {5}, PAGES = {314, 327--30}, ISSN = {0002-9890}, CODEN = {AMMYAE}, MRCLASS = {26D15}, MRNUMBER = {83g:26026}, MRREVR = {Peter Bullen}, } @ARTICLE {CliMoSte:79, author = "A.K. CLINE and C.B. MOLER and G.W. Stewart and J.H. WILKINSON", title = "An estimate for the condition number of a matrix", journal = "SIAM J. Numer. Anal.", year = "1979", volume = "16", pages = "368-375"} @ARTICLE {CoLeMiMo:72, author = "G.M. COGGINS and A.V. LEVY and A. MIELE and P.E. MOSELEY", title = "On the method of multipliers for mathematical programming problems", journal = "J. Optim. Theory Appl.", year = "1972", volume = "10", pages = "1-33"} @INCOLLECTION {Col:84, author = "T.F. COLEMAN", title = "Large {S}parse {N}umerical {O}ptimization", booktitle = "Lecture Notes in Computer Science \#165", publisher = "Springer-Verlag", year = "1984", address = "Berlin"} @incollection {Col:91, author = "T.F. COLEMAN", title = "Large-scale numerical optimization: {I}ntroduction and overview", booktitle = "Encylopedia of Computer Science and Technology", volume = "28, Supplement 13", institution = "Cornell Theory Center, Cornell University", year = "1993", publisher = "Marcel Decker", pages = "167-196"} @article {MR89i:65043, AUTHOR = {Coleman, Thomas F. and Pothen, Alex}, TITLE = {The null space problem. {I}{I}. {A}lgorithms}, JOURNAL = {SIAM J. Algebraic Discrete Methods}, FJOURNAL = {Society for Industrial and Applied Mathematics. Journal on Algebraic and Discrete Methods}, VOLUME = {8}, YEAR = {1987}, NUMBER = {4}, PAGES = {544--563}, ISSN = {0196-5212}, CODEN = {STAMDU}, } @TECHREPORT {ColCon:82, author = "T.F. COLEMAN and A.R. Conn", title = "On the local convergence of a quasi-{N}ewton method for the nonlinear programming problem", institution = "Department of Computer Science, Cornell University", year = "1982", number = "TR 82-509", address = "Ithaca, NY"} @MISC {ColFen:85, author = "T.F. COLEMAN and T. FENYES", title = "Partitioned updates for {SQP}", note = "Presentation at Joint National Meeting of ORSA/TIMS, Atlanta, Georgia, 1985"} @ARTICLE {Co:90, author = "T.F. COLEMAN and C. HEMPEL", title = "Computing a trust region step for a penalty function", journal = "SIAM J. Sci. STAT. Comput.", year = "1990", volume = "11", pages = "180-201"} @TECHREPORT {ColLi:87a, author = "T.F. COLEMAN and G. LI", title = "Solving systems of nonlinear equations on a message-passing multiprocessor", institution = "Faculty of Mathematics, University of Waterloo", year = "1987", number = "CORR 87-89"} @TECHREPORT {ColLi:87b, author = "T.F. COLEMAN and G. LI", title = "A new method for solving triangular systems on a distributed memory message-passing multiprocessor", institution = "Department of Computer Science, Cornell University", year = "1987", number = "CS-87-812", address = "Ithaca, NY"} @ARTICLE {ColLi:88, author = "T.F. COLEMAN and G. LI", title = "A parallel triangular solver for a distributed memory multiprocessor", journal = "SIAM J. Sci. Statist. Comput.", year = "1988", volume = "9", number = "3", pages = "485-502"} @article {MR1416528, AUTHOR = {Coleman, Thomas F. and Li, Yuying}, TITLE = {A reflective {N}ewton method for minimizing a quadratic function subject to bounds on some of the variables}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {6}, YEAR = {1996}, NUMBER = {4}, PAGES = {1040--1058}, ISSN = {1052-6234}, CODEN = {SJOPE8}, MRCLASS = {90C30 (65K05)}, MRNUMBER = {1416528 (97h:90060)}, MRREVIEWER = {J. Mockus}, DOI = {10.1137/S1052623494240456}, URL = {http://dx.doi.org/10.1137/S1052623494240456}, } @article {MR1387333, AUTHOR = {Coleman, Thomas F. and Li, Yuying}, TITLE = {An interior trust region approach for nonlinear minimization subject to bounds}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {6}, YEAR = {1996}, NUMBER = {2}, PAGES = {418--445}, ISSN = {1052-6234}, CODEN = {SJOPE8}, MRCLASS = {90C30 (65K05)}, MRNUMBER = {1387333 (97d:90084)}, MRREVIEWER = {Shinji Mizuno}, DOI = {10.1137/0806023}, URL = {http://dx.doi.org/10.1137/0806023}, } @article {MR1305566, AUTHOR = {Coleman, Thomas F. and Li, Yuying}, TITLE = {On the convergence of interior-reflective {N}ewton methods for nonlinear minimization subject to bounds}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {67}, YEAR = {1994}, NUMBER = {2, Ser. A}, PAGES = {189--224}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C30 (65K05)}, MRNUMBER = {1305566 (95j:90070)}, MRREVIEWER = {A. M. Galperin}, DOI = {10.1007/BF01582221}, URL = {http://dx.doi.org/10.1007/BF01582221}, } @TECHREPORT {ColLi:97, author = "T.F. COLEMAN and G. LI", title = "A Trust Region and Affine Scaling Interior Point Method for Nonconvex Minimization with Linear Inequality Constraints", institution = "Department of Computer Science, Cornell University", year = "1997", number = "TR97-1641", address = "Ithaca, NY"} @techreport{cl, AUTHOR = "T.F.\ COLEMAN and Y.Y.\ LI", TITLE = "A primal dual trust region algorithm for nonconvex programming using a $L_1$ penalty function", TYPE = "Report", INSTITUTION = "Dept.\ of Computer Science, Cornell University", YEAR = "1998", } @TECHREPORT {ColMor:82, author = "T.F. COLEMAN and J.J. Mor\'{e}", title = "Software for estimating sparse {J}acobian matrices", institution = "Department of Computer Science, Cornell University", year = "1982", number = "TR 82-502", address = "Ithaca, NY"} @ARTICLE {ColMor:83, author = "T.F. COLEMAN and J.J. Mor\'{e}", title = "Estimation of sparse {J}acobian matrices and graph coloring problems", journal = "SIAM J. Numer. Anal.", year = "1983", volume = "20", pages = "187-209"} @ARTICLE {CRS:90, author = "M. CONFORTI, M.R. RAO and A. SASSANO", title = "The Equipartition polytope I and II", journal = mprog, year = "1990", volume = "49", pages = "49-90"} @book {Cornu-Tutu, AUTHOR = {G.~CORNU\'{E}JOLS and R.~T{\"U}T{\"U}NC{\"U}}, TITLE = {Optimization methods in finance}, SERIES = {Mathematics, Finance and Risk}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {2007}, PAGES = {xii+345}, ISBN = {978-0-521-86170-0}, MRCLASS = {91-01 (90C90 91B28)}, MRNUMBER = {MR2294029 (2007j:91001)}, } @article {MR1769494, AUTHOR = {Andersen, K.D. and CHRISTIANSEN, E. and Conn, A.R. and Overton, M.L.}, TITLE = {An efficient primal-dual interior-point method for minimizing a sum of {E}uclidean norms}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {22}, YEAR = {2000}, NUMBER = {1}, PAGES = {243--262 (electronic)}, ISSN = {1064-8275}, MRCLASS = {90C25 (65K10)}, MRNUMBER = {MR1769494 (2001c:90053)}, MRREVIEWER = {Shu Zhong Zhang}, } @inproceedings{Conn:84, author = "A.R. Conn", year = "1984", title = "Nonlinear programming, exact penalty functions and projection techniques for non-smooth functions", booktitle ="Numerical Optimization 1984", editor="P.T. BOGGS AND R. Byrd AND R.B. Schnabel", publisher = " SIAM", pages = "3-25"} @Book{Cox96, author = "David A. Cox and John B. Little and Don O'Shea", title = "Ideals, Varieties, and Algorithms", publisher = "Springer-Verlag", year = "1996", edition = "2nd", OPTvolume = "", OPTseries = "", address = "NY", note = "536 pages.", annote = "An introduction to computational algebraic geometry and commutative algebra" } @article {GoRoTho10, AUTHOR = {Gould, N.I.M. and Robinson, Daniel P. and Thorne, H. Sue}, TITLE = {On solving trust-region and other regularised subproblems in optimization}, JOURNAL = {Math. Program. Comput.}, FJOURNAL = {Mathematical Programming Computation}, VOLUME = {2}, YEAR = {2010}, NUMBER = {1}, PAGES = {21--57}, ISSN = {1867-2949}, MRCLASS = {90C30 (65K10 90C26)}, MRNUMBER = {2601719 (2011c:90097)}, MRREVIEWER = {Warren L. Hare}, DOI = {10.1007/s12532-010-0011-7}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s12532-010-0011-7}, } @techreport {GouldToint:10, author = "N.I.M. Gould and Ph.L. Toint", title = "A quadratic programming bibliography", INSTITUTION = "Rutherford Appleton Laboratory", ADDRESS = "England", year = "2001", note = "www.optimization-online.org/DB\_HTML/2001/02/285.html" } @article {ConGouToi:91, author = "A.R. Conn and N.I.M. Gould and Ph.L. Toint", title = "Convergence of quasi-{N}ewton matrices generated by the symmetric rank one update", journal = "Math. Prog.", year = "1991", volume = "50", pages = "177-195"} @BOOK {ConGouToi:91b, author = "A.R. Conn and N.I.M. Gould and Ph.L. Toint", title ="LANCELOT: a Fortran package for large-scale nonlinear optimization (Release A), Springer Series in Computational Mathematics", publisher = "Springer Verlag", year = "1992", address = "Heidelberg, Berlin, New York"} @incollection{ConnGoulToin92a, author = {A. R. Conn and N.I.M. Gould and {Ph}.L. Toint}, title = {Large-Scale Nonlinear Constrained Optimization}, booktitle = {Proceedings of the Second International Conference on Industrial and Applied Mathematics}, editor = {R.E. O'Malley, Jr.}, publisher = {SIAM}, address = {Phildelphia}, pages = {51-70}, note = {(Also in M.S. Moonen, G.H. Golub and B.L.R DeMoor, editors, {\em Linear Algebra for Large-Scale and Real-Time Applications}, volume 232 of {\em NATO ASI Series E: Applied Sciences.} Kluwer Academic Publishers, 1993)}, year = 1992 } @article {MR2776701, AUTHOR = {Cartis, C. and Gould, N.I.M. and Toint, P.L.}, TITLE = {Adaptive cubic regularisation methods for unconstrained optimization. {P}art {I}: motivation, convergence and numerical results}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming}, VOLUME = {127}, YEAR = {2011}, NUMBER = {2, Ser. A}, PAGES = {245--295}, ISSN = {0025-5610}, MRCLASS = {90C30 (49M15 49M37 65K10)}, MRNUMBER = {2776701}, MRREVIEWER = {C. Ilioi}, DOI = {10.1007/s10107-009-0286-5}, URL = {http://dx.doi.org/10.1007/s10107-009-0286-5}, } @article {MR2608356, AUTHOR = {Bellavia, S. and Cartis, C. and Gould, N.I.M. and Morini, B. and Toint, Ph.L.}, TITLE = {Convergence of a regularized {E}uclidean residual algorithm for nonlinear least-squares}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {48}, YEAR = {2010}, NUMBER = {1}, PAGES = {1--29}, ISSN = {0036-1429}, MRCLASS = {65K10 (90C26)}, MRNUMBER = {2608356 (2011e:65095)}, DOI = {10.1137/080732432}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/080732432}, } @article {MR2112974, AUTHOR = {Gould, N.I.M. and Leyffer, Sven and Toint, Ph.L.}, TITLE = {A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {15}, YEAR = {2004}, NUMBER = {1}, PAGES = {17--38 (electronic)}, ISSN = {1052-6234}, MRCLASS = {90C30 (65H10 90C06)}, MRNUMBER = {2112974 (2005m:90117)}, MRREVIEWER = {Paul H. Calamai}, DOI = {10.1137/S1052623403422637}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/S1052623403422637}, } @techreport{cgt, AUTHOR = "Conn, A.R. and Gould, N.I.M. and Toint, Ph.L. ", TITLE = "A primal-dual algorithm for minimizing a nonconvex function subject to bounds and nonlinear constraints", TYPE = "Report", NUMBER = "RC 20639", INSTITUTION = "IBM T.J.\ Watson Center", ADDRESS = "Yorktown Heights, NY", YEAR = "1996", } @BOOK {ConGouToi:00, author = "A.R. Conn and N.I.M. Gould and Ph.L. Toint", TITLE = {Trust-{R}egion {M}ethods}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {2000}, PAGES = {xx+959}, ISBN = {0-89871-460-5}, MRCLASS = {90-02 (65-02 65K05 90C30)}, MRNUMBER = {1 774 899}, } @BOOK {CoBoo:80, author = "S. CONTE and C. {DE BOOR}", title = "Elementary Numerical Analysis", publisher = "McGraw-Hill", year = "1980", address = "New York, NY"} @book {MR3396730, AUTHOR = {Cottle, R.W. and Pang, J-S. and Stone, R.E.}, TITLE = {The linear complementarity problem}, SERIES = {Classics in Applied Mathematics}, VOLUME = {60}, NOTE = {Corrected reprint of the 1992 original [ MR1150683]}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA}, YEAR = {2009}, PAGES = {xxvii+761}, ISBN = {978-0-898716-86-3}, MRCLASS = {90-02 (01A75 65K05 90C33)}, MRNUMBER = {3396730}, DOI = {10.1137/1.9780898719000.ch1}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/1.9780898719000.ch1}, } @book {MR1150683, AUTHOR = {Cottle, R.W. and Pang, J-S. and Stone, R.E.}, TITLE = {The linear complementarity problem}, SERIES = {Computer Science and Scientific Computing}, PUBLISHER = {Academic Press, Inc., Boston, MA}, YEAR = {1992}, PAGES = {xxiv+762}, ISBN = {0-12-192350-9}, MRCLASS = {90-02 (65K05 90C33)}, MRNUMBER = {1150683}, MRREVIEWER = {Michael M. Kostreva}, } @BOOK {Cotpangston:92, author = "R. W. COTTLE and J. Pang and R.E. STONE", title = "The linear complementarity problem", publisher = "Academic Press, Inc.", year = "1992", address = "Boston, MA"} @ARTICLE {Cou:43, author = "R. COURANT", title = "Variational methods for the solution of problems of equilibrium and vibrations", journal = "Bull. Amer. Math. Soc.", year = "1943", volume = "49", pages = "1-23"} @BOOK {CourHilb:53, author = "R. COURANT and D. HILBERT", title = "Methods of Mathematical Physics, I", publisher = "Interscience", year = "1953", address = "New York, NY"} @ARTICLE {CrLe:69, author = "E.E. CRAGG and A.V. LEVY ", title = "Study on a supermemory gradient method for the minimization of functions", journal = "J. Optim. Theory Appl.", year = "1969", volume = "4", pages = "191-205"} @ARTICLE {CrIyLeMi:71, author = "E.E. CRAGG and R.R. IYER and A.V. LEVY and A. MIELE", title = "Use of the augmented penalty function in mathematical programming, part {I}", journal = "J. Optim. Theory Appl.", year = "1971", volume = "8", pages = "115-130"} @ARTICLE {CrLeMi:71, author = "E.E. CRAGG and A.V. LEVY and A. MIELE", title = "Use of the augmented penalty function in mathematical programming, part {II}", journal = "J. Optim. Theory Appl.", year = "1971", volume = "8", pages = "131-153"} @INCOLLECTION {CrMiMo:72, author = "E.E. CRAGG and A. MIELE and P.E. MOSELEY", title = "A modification of the method of multipliers for mathematical programming problems", booktitle = "Techniques of Optimization", publisher = "Academic Press", year = "1972", editor = "A.V. Balakrishnan", address = "New York, NY"} @ARTICLE {Cr:93, author = "Y. CRAMA", title = "Concave extensions for nonlinear 0-1 maximization problems", journal = mprog, year = "1993 ", volume = "61", number = "1", pages = "53-60"} @TECHREPORT {Cri:90, author = "F. CRITCHLEY", title = "On the minimization of a positive definite quadratic form under an arbitrary quadratic constraint", institution = "University of Warwick", year = "1990", address = "England"} @article {MR0099887, AUTHOR = {Croes, G.A.}, TITLE = {A method for solving traveling-salesman problems}, JOURNAL = {Operations Res.}, FJOURNAL = {Operations Research}, VOLUME = {6}, YEAR = {1958}, PAGES = {791--812}, ISSN = {0030-364X}, MRCLASS = {90.00}, MRNUMBER = {0099887}, MRREVIEWER = {M. M. Flood}, } @ARTICLE {CuDoWo:75, author = "J. Cullum and W.E. Donath and P. Wolfe", title = "The minimization of certain nondifferentiable sums of eigenvalues of symmetric matrices", journal = "Mathematical Programming Study", year = "1975 ", volume = "3", pages = "35-55"} @book{cook2012pursuit, title={In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation}, author={Cook, W.}, isbn={9780691152707}, lccn={2011030626}, url={https://books.google.ca/books?id=S3bxbr\_-qhYC}, year={2012}, publisher={Princeton University Press} } @book {MR1490579, AUTHOR = {Cook, W.J. and Cunningham, W.H. and Pulleyblank, W.R. and Schrijver, A.}, TITLE = {Combinatorial optimization}, SERIES = {Wiley-Interscience Series in Discrete Mathematics and Optimization}, NOTE = {A Wiley-Interscience Publication}, PUBLISHER = {John Wiley \& Sons Inc.}, ADDRESS = {New York}, YEAR = {1998}, PAGES = {x+355}, ISBN = {0-471-55894-X}, MRCLASS = {90C27 (90-02 90C35)}, MRNUMBER = {1490579 (99b:90098)}, MRREVIEWER = {Ulrich Faigle}, } @ARTICLE {CuPoRe:74, author = "A. CURTIS and M.J.D. Powell and J.K. REID", title = "On the estimation of sparse {J}acobian matrices", journal = "IMA J. Appl. Math.", year = "1974", volume = "13", pages = "117-120"} @BOOK {CDS:79, author = "D.M. CVETKOVIC and M. DOOB and H. SACHS", title = "Spectra of Graphs - Theory and Applications", publisher = "Academic Press", year = "1979", address = "New York, NY"} %DDDDDDDDDDDDD @article {MR3685266, AUTHOR = {Davis, D. and Yin, W.}, TITLE = {Faster convergence rates of relaxed {P}eaceman-{R}achford and {ADMM} under regularity assumptions}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {42}, YEAR = {2017}, NUMBER = {3}, PAGES = {783--805}, ISSN = {0364-765X}, MRCLASS = {90C48 (65K05 90C25)}, MRNUMBER = {3685266}, MRREVIEWER = {Liusheng Hou}, DOI = {10.1287/moor.2016.0827}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1287/moor.2016.0827}, } @ARTICLE {Dam:70, author = "A.P. DAMBROWSKI", title = "Variable-step simplex optimization procedures", journal = "Tdch. Kibern.", year = "1970", volume = "1", pages = "33"} @BOOK {Dani:71, author = "J.W. DANIEL", title = "The Approximate Minimization of Functionals", publisher = "Prentice-Hall", year = "1971", address = "Englewood Cliffs, NJ"} @article{doi:10.1137/0114053, author = {J.M. Danskin}, title = {The Theory of Max-Min, with Applications}, journal = {SIAM Journal on Applied Mathematics}, volume = {14}, number = {4}, pages = {641-664}, year = {1966}, doi = {10.1137/0114053}, URL = {https://doi.org/10.1137/0114053}, eprint = {https://doi.org/10.1137/0114053} } @BOOK {Dans:67, author = "J.M. Danskin", TITLE = {The theory of max-min and its application to weapons allocation problems}, SERIES = {Econometrics and Operations Research, Vol. V}, PUBLISHER = {Springer-Verlag New York, Inc., New York}, YEAR = {1967}, PAGES = {ix+126}, MRCLASS = {90.70}, MRNUMBER = {MR0228260 (37 \#3843)}, MRREVIEWER = {K. O. Kortanek}, } @BOOK {Dant:63, author = "G.B. Dantzig", title = "Linear Programming and Extensions", publisher = "Princeton University Press", year = "1963", address = "Princeton, New Jersey"} @incollection {MR1068537, AUTHOR = {Dantzig, G.B.}, TITLE = {Impact of linear programming on computer development}, BOOKTITLE = {Computers in mathematics ({S}tanford, {CA}, 1986)}, SERIES = {Lecture Notes in Pure and Appl. Math.}, VOLUME = {125}, PAGES = {233--240}, PUBLISHER = {Dekker, New York}, YEAR = {1990}, MRCLASS = {01A60 (68-03)}, MRNUMBER = {1068537}, } @INCOLLECTION {Dant:90, author = "G.B. Dantzig", booktitle = "History of Mathematical Programming: A Collection of Personal Reminiscences", title = "Linear programming", publisher = "CWI North-Holland", year = "1991", address = "Amsterdam"} @incollection {MR1203105, AUTHOR = {Dantzig, G.B.}, TITLE = {Origins of the simplex method}, BOOKTITLE = {A history of scientific computing ({P}rinceton, {NJ}, 1987)}, SERIES = {ACM Press Hist. Ser.}, PAGES = {141--151}, PUBLISHER = {ACM}, ADDRESS = {New York}, YEAR = {1990}, MRCLASS = {01A60 (65-03 90-03)}, MRNUMBER = {1203105}, } @ARTICLE {Dan:82, author = "G. Dantzig", title = "Reminiscences about the origins of linear programming", journal = "Operations Research Letters", year = "1982", volume = "1", pages = "43-48"} @article {MR2594606, AUTHOR = {D'Apuzzo, M. and De Simone, V. and di Serafino, D.}, TITLE = {On mutual impact of numerical linear algebra and large-scale optimization with focus on interior point methods}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {45}, YEAR = {2010}, NUMBER = {2}, PAGES = {283--310}, ISSN = {0926-6003}, MRCLASS = {90C30 (65F08 65K10 90C06 90C51 90C55)}, MRNUMBER = {2594606 (2011c:90094)}, MRREVIEWER = {Marcos Raydan}, DOI = {10.1007/s10589-008-9226-1}, URL = {http://dx.doi.org/10.1007/s10589-008-9226-1}, } @article {MR1426640, AUTHOR = {Infanger, Gerd and Morton, David P.}, TITLE = {Cut sharing for multistage stochastic linear programs with interstage dependency}, NOTE = {Approximation and computation in stochastic programming}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {75}, YEAR = {1996}, NUMBER = {2, Ser. B}, PAGES = {241--256}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C15 (65C05)}, MRNUMBER = {1426640 (97k:90068)}, MRREVIEWER = {V. V. Kolbin}, DOI = {10.1016/S0025-5610(96)00014-7}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/S0025-5610(96)00014-7}, } @article {MR1254506, AUTHOR = {Dantzig, George B. and Infanger, Gerd}, TITLE = {Multi-stage stochastic linear programs for portfolio optimization}, JOURNAL = {Ann. Oper. Res.}, FJOURNAL = {Annals of Operations Research}, VOLUME = {45}, YEAR = {1993}, NUMBER = {1-4}, PAGES = {59--76}, ISSN = {0254-5330}, MRCLASS = {90C15 (90A09 90C90)}, MRNUMBER = {1254506 (95a:90046)}, MRREVIEWER = {C. Bergthaller}, DOI = {10.1007/BF02282041}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/BF02282041}, } @ARTICLE {DanFolSha:67, author = "G. Dantzig and J. FOLKMAN and N. SHAPIRO", title = "On the continuity of the minimum set of a continuous function", journal = "Journal Math. Anal. Appl.", year = "1967", volume = "17", pages = "519-548"} @ARTICLE {DFS, author = "G. Dantzig and J. FOLKMAN and N. SHAPIRO", title = "On the continuity of the minimum set of a continuous function", journal = "Journal Math. Anal. Appl.", year = "1967", volume = "17", pages = "519-548"} @article {MR0069584, AUTHOR = {Dantzig, G.B. and Orden, A. and Wolfe, P.}, TITLE = {The generalized simplex method for minimizing a linear form under linear inequality restraints}, JOURNAL = {Pacific J. Math.}, FJOURNAL = {Pacific Journal of Mathematics}, VOLUME = {5}, YEAR = {1955}, PAGES = {183--195}, ISSN = {0030-8730}, MRCLASS = {65.0X}, MRNUMBER = {MR0069584 (16,1054i)}, MRREVIEWER = {A. J. Hoffman}, } @TECHREPORT {Dav:59, author = "W.C. Davidon", title = "Variable metric methods for minimization", institution = "Argonne National Labs", year = "1959", number = "ANL-5990", address = "Argonne, IL"} @ARTICLE {Dav:75, author = "W.C. Davidon", title = "Optimally conditioned optimization algorithms without line searches", journal = "Math. Prog.", year = "1975", volume = "9", pages = "1-30"} @ARTICLE {Dav:80, author = "W.C. Davidon", title = "Conic approximations and collinear scalings for optimizers", journal = "SIAM J. Numer. Anal.", year = "1980", volume = "17", number = "2", pages = "268-281"} @phdthesis{delsarte:73, AUTHOR= "Delsarte, P.", year = "1973", title = "An Algebraic Approach to the Association Schemes of Coding Theory", school = "Universite Catholique de Louvain", address = "Louvain, France", } @article {changhan:07, author = "CHANG, X-W. and HAN Q.", TITLE = {Solving box-constrained integer least squares problems}, JOURNAL = {IEEE Trans. Wireless Communic.}, FJOURNAL = {IEEE Transactions of Wireless Communications}, VOLUME = {6}, YEAR = {2007}, NUMBER = {12}, PAGES = {1--11}, } @article {MR1912435, author = "MA, W-K. and DAVIDSON T.N. and WONG K.M. and LUO Z-Q. and CHING P-C.", TITLE = {Quasi-maximum-likelihood multiuser detection using semi-definite relaxation with application to synchronous {CDMA}}, JOURNAL = {IEEE Trans. Signal Process.}, FJOURNAL = {IEEE Transactions on Signal Processing}, VOLUME = {50}, YEAR = {2002}, NUMBER = {4}, PAGES = {912--922}, ISSN = {1053-587X}, CODEN = {ITPRED}, MRCLASS = {94A05}, MRNUMBER = {MR1912435}, } @book {MR1743598, AUTHOR = {Diestel, R.}, TITLE = {Graph theory}, SERIES = {Graduate Texts in Mathematics}, VOLUME = {173}, EDITION = {Second}, PUBLISHER = {Springer-Verlag, New York}, YEAR = {2000}, PAGES = {xiv+313}, ISBN = {0-387-95014-1}, MRCLASS = {05-01}, MRNUMBER = {1743598}, DOI = {10.1007/b100033}, URL = {http://dx.doi.org/10.1007/b100033}, } @incollection {MR1466704, AUTHOR = {BRUSS, F.T. and Ferguson, T.S.}, TITLE = {Half-prophets and {R}obbins' problem of minimizing the expected rank}, BOOKTITLE = {Athens Conference on Applied Probability and Time Series Analysis, Vol.\ I (1995)}, SERIES = {Lecture Notes in Statist.}, VOLUME = {114}, PAGES = {1--17}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {1996}, MRCLASS = {60G40 (62L15)}, MRNUMBER = {MR1466704 (98k:60066)}, MRREVIEWER = {Alexander V. Gnedin}, } @article {MR1384628, AUTHOR = {KUNO, T.}, TITLE = {A practical algorithm for minimizing a rank-two saddle function on a polytope}, JOURNAL = {J. Oper. Res. Soc. Japan}, FJOURNAL = {Journal of the Operations Research Society of Japan}, VOLUME = {39}, YEAR = {1996}, NUMBER = {1}, PAGES = {63--76}, ISSN = {0453-4514}, CODEN = {JORJAS}, MRCLASS = {90C26 (65K05 90C30)}, MRNUMBER = {MR1384628 (97a:90051)}, } @article {MR1232739, AUTHOR = {BRUSS, F.T. and FERGUSON, T.S.}, TITLE = {Minimizing the expected rank with full information}, JOURNAL = {J. Appl. Probab.}, FJOURNAL = {Journal of Applied Probability}, VOLUME = {30}, YEAR = {1993}, NUMBER = {3}, PAGES = {616--626}, ISSN = {0021-9002}, CODEN = {JPRBAM}, MRCLASS = {60G40 (62L15)}, MRNUMBER = {MR1232739 (94m:60090)}, MRREVIEWER = {Robert Kertz}, } @incollection {MR945004, AUTHOR = {DAVIS, C.}, TITLE = {Completing a matrix so as to minimize the rank}, BOOKTITLE = {Topics in operator theory and interpolation}, SERIES = {Oper. Theory Adv. Appl.}, VOLUME = {29}, PAGES = {87--95}, PUBLISHER = {Birkh\"auser}, ADDRESS = {Basel}, YEAR = {1988}, MRCLASS = {47A20 (15A03)}, MRNUMBER = {MR945004 (89d:47010)}, MRREVIEWER = {T. Ando}, } @article {MR3718806, AUTHOR = {Yeralan, S.N. and Davis, T.A. and Sid-Lakhdar, .M. and Ranka, .}, TITLE = {Algorithm 980: sparse {QR} factorization on the {GPU}}, JOURNAL = {ACM Trans. Math. Software}, FJOURNAL = {Association for Computing Machinery. Transactions on Mathematical Software}, VOLUME = {44}, YEAR = {2017}, NUMBER = {2}, PAGES = {Art. 17, 29}, ISSN = {0098-3500}, MRCLASS = {65F25 (65Y10 65Y15)}, MRNUMBER = {3718806}, DOI = {10.1145/3065870}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1145/3065870}, } @Article{Davis:2006:ACS, author = "T.A. DAVIS", title = "Algorithm 849: A Concise Sparse {Cholesky} Factorization Package", journal = "{ACM} Transactions on Mathematical Software", volume = "31", number = "4", month = dec, year = "2005", pages = "587--591", URL = "http://doi.acm.org/10.1145/1114268.1114277", abstract = "The LDL software package is a set of short, concise routines for factorizing symmetric positive-definite sparse matrices, with some applicability to symmetric indefinite matrices. Its primary purpose is to illustrate much of the basic theory of sparse matrix algorithms in as concise a code as possible, including an elegant method of sparse symmetric factorization that computes the factorization row-by-row but stores it column-by-column. The entire symbolic and numeric factorization consists of less than 50 lines of code. The package is written in C, and includes a MATLAB interface.", } @article {MR2771611, AUTHOR = {Didi Biha, M. and Meurs, M.-J.}, TITLE = {An exact algorithm for solving the vertex separator problem}, JOURNAL = {J. Global Optim.}, FJOURNAL = {Journal of Global Optimization. An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering}, VOLUME = {49}, YEAR = {2011}, NUMBER = {3}, PAGES = {425--434}, ISSN = {0925-5001}, MRCLASS = {05C85 (90C27 90C57)}, MRNUMBER = {2771611}, DOI = {10.1007/s10898-010-9568-y}, URL = {https://doi.org/10.1007/s10898-010-9568-y}, } @article {MR3926357, AUTHOR = {Cornaz, D. and Magnouche, Y. and Mahjoub, A.R. and Martin, S.}, TITLE = {The multi-terminal vertex separator problem: polyhedral analysis and branch-and-cut}, JOURNAL = {Discrete Appl. Math.}, FJOURNAL = {Discrete Applied Mathematics. The Journal of Combinatorial Algorithms, Informatics and Computational Sciences}, VOLUME = {256}, YEAR = {2019}, PAGES = {11--37}, ISSN = {0166-218X}, MRCLASS = {90C57 (05C40 90C10)}, MRNUMBER = {3926357}, DOI = {10.1016/j.dam.2018.10.005}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1016/j.dam.2018.10.005}, } @article {MR3742304, AUTHOR = {Hager, W.W. and Hungerford, J.T. and Safro, I.}, TITLE = {A multilevel bilinear programming algorithm for the vertex separator problem}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {69}, YEAR = {2018}, NUMBER = {1}, PAGES = {189--223}, ISSN = {0926-6003}, MRCLASS = {90C35 (90C06 90C20 90C27)}, MRNUMBER = {3742304}, MRREVIEWER = {Karuthedath Arippurathu Vidya}, DOI = {10.1007/s10589-017-9945-2}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10589-017-9945-2}, } @techreport{HagerHung:13, author = "W.W. Hager and J.T. Hungerford", year = "2013", title = "A continuous quadratic programming formulation of the vertex separator problem", institution = "University of Florida, Gainesville", type = "Report", number = "", } @article {Hager:04, AUTHOR = {Hager, W.W. and Park, S.}, TITLE = {Global convergence of {SSM} for minimizing a quadratic over a sphere}, JOURNAL = {Math. Comp.}, FJOURNAL = {Mathematics of Computation}, VOLUME = {74}, YEAR = {2005}, NUMBER = {251}, PAGES = {1413--1423}, ISSN = {0025-5718}, CODEN = {MCMPAF}, MRCLASS = {90C20 (65K05)}, MRNUMBER = {2137009 (2006e:90083)}, MRREVIEWER = {Michael Hinterm{\"u}ller}, DOI = {10.1090/S0025-5718-04-01731-4}, URL = {http://dx.doi.org/10.1090/S0025-5718-04-01731-4}, } @TECHREPORT {Davis:97, author = "T.A. DAVIS and W.W. Hager", title = "Modifying a sparse {C}holesky factorization", institution = "Computer and Information Science and Engineering Department", address= "University of Florida, Gainsville", year = "1997", number = "TR97-003"} @article{dax:503, author = {A. DAX}, collaboration = {}, title = {Classroom Note:An Elementary Proof of Farkas' Lemma}, publisher = {SIAM}, year = {1997}, journal = {SIAM Review}, volume = {39}, number = {3}, pages = {503-507}, keywords = {Farkas' lemma; elementary proof; active set method}, url = {http://link.aip.org/link/?SIR/39/503/1}, doi = {10.1137/S0036144594295502} } @article {Deerwester, AUTHOR = {Deerwester, S. and Dumais, S.T. and Furnas, G.W. and Landauer, T.K. and Harshman, R.}, TITLE = {Indexing by Latent Semantic Analysis}, JOURNAL = {Journal of the American Society for Information Science}, publisher = {American Documentation Institute}, VOLUME = {41}, YEAR = {1990}, NUMBER = {6}, PAGES = {391-407} } @techreport{Yurtseveretal, author = "Yurtsever, A. and Udell, M. and Tropp, J.A. and Cevher, V.", title = "Sketchy Decisions: convex low-rank matrix optimization with optimal storage", year = 2017, note = "arXiv:1702.06838"} @ARTICLE{2016arXiv160900048T, author = {{Tropp}, J.A. and {Yurtsever}, A. and {Udell}, M. and {Cevher}, V. }, title = "{Practical sketching algorithms for low-rank matrix approximation}", journal = {ArXiv e-prints}, archivePrefix = "arXiv", eprint = {1609.00048}, primaryClass = "cs.NA", keywords = {Computer Science - Numerical Analysis, Computer Science - Data Structures and Algorithms, Mathematics - Numerical Analysis, Statistics - Computation, Statistics - Machine Learning, Primary 65F30, Secondary 68W20}, year = 2016, month = aug, adsurl = {http://adsabs.harvard.edu/abs/2016arXiv160900048T}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } @BOOK {Deb:59, author = "G. DEBREU", title = "Theory of Value: An Axiomatic Analysis of Economic Equilibrium", city = "New York", year = "1959", publisher = "John Wiley and Sons"} @article {Delage10, AUTHOR = {Delage, E. and Ye, Y.}, TITLE = {Distributionally robust optimization under moment uncertainty with application to data-driven problems}, JOURNAL = {Oper. Res.}, FJOURNAL = {Operations Research}, VOLUME = {58}, YEAR = {2010}, NUMBER = {3}, PAGES = {595--612}, ISSN = {0030-364X}, CODEN = {OPREAI}, MRCLASS = {90C15 (62P05 91B06)}, MRNUMBER = {2680566 (2011f:90087)}, MRREVIEWER = {Ilse M. Schoeman}, DOI = {10.1287/opre.1090.0741}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1287/opre.1090.0741}, } @TECHREPORT {DelDen:78, author = "J.P. DELAHAYE and J. DENEL", title = "Equivalences des continuit\'{e}s des applications multivoques dans les espaces topologiques", institution = "Laboratoire de Calcul, University of Lille I", year = "1978", number = "111"} @article {MR82m:14011, AUTHOR = {DELFS, H. and KNEBUSCH, M.}, TITLE = {Semialgebraic topology over a real closed field. {II}. {B}asic theory of semialgebraic spaces}, JOURNAL = {Math. Z.}, FJOURNAL = {Mathematische Zeitschrift}, VOLUME = {178}, YEAR = {1981}, NUMBER = {2}, PAGES = {175--213}, ISSN = {0025-5874}, CODEN = {MAZEAX}, MRCLASS = {14G30 (14A20)}, MRNUMBER = {82m:14011}, MRREVIEWER = {Thomas C. Craven}, } @ARTICLE {dp1:90, author = "C. DELORME and S. POLJAK", title = "Laplacian eigenvalues and the maximum cut problem", journal = "Math. Programming", volume = "62", number = "3", pages = "557-574", year = "1993"} @ARTICLE {dp2:91, author = "C. DELORME and S. POLJAK", title = "The performance of an eigenvalue bound on the max-cut problem in some classes of graphs", journal = dm, volume = "111", pages = "145-156", year = "1993"} @ARTICLE {dp3:91, author = "C. DELORME and S. POLJAK", title = "Combinatorial properties and the complexity of a max--cut approximation", journal = ejc, volume = "14", pages ="313-333", year = "1993"} @ARTICLE {DeEiStei:82, author = "R.S Dembo and S.C. Eisenstat and T. Steihaug", title = "Inexact {N}ewton methods", journal = "SIAM J. Numer. Anal.", year = "1982", volume = "19", pages = "400-408"} @book {DR, AUTHOR = {Demyanov, V.F. and Rubinov, A.M.}, TITLE = {Approximate methods in optimization problems}, PUBLISHER = {American Elsevier Publishing Co., Inc., New York}, YEAR = {1970}, PAGES = {ix+256}, MRCLASS = {49.20 (65.00)}, MRNUMBER = {0266018 (42 \#927)}, } @ARTICLE{dembo82, AUTHOR = "R.S. Dembo and S.C. Eisenstat and T. Steihaug", TITLE = "Inexact {{N}ewton} methods", JOURNAL = sinum, YEAR = 1982, VOLUME = 19, NUMBER = 2, MONTH = apr, PAGES = "190--212" } @ARTICLE{dembo83, AUTHOR = "R.S. Dembo and T. Steihaug", TITLE = "Truncated {{N}ewton} algorithms for large scale unconstrained optimization", JOURNAL = mp, YEAR = 1983, VOLUME = 26, NUMBER = 72, PAGES = "190--212" } @TECHREPORT{dembo83a, AUTHOR = "R. S. Dembo", TITLE = "A primal truncated newton algorithm with application to large-scale nonlinear network optimization", INSTITUTION = "Yale University", YEAR = 1983, TYPE = "Working Paper: Series B", NUMBER = 72, ADDRESS = "Yale School of Organization and Management" } @article {MR2047430, AUTHOR = {DENG, Y-B. and HU, X-Y. and ZHANG, L.}, TITLE = {Least squares solution of {$BXA\sp T=T$} over symmetric, skew-symmetric, and positive semidefinite {$X$}}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {25}, YEAR = {2003}, NUMBER = {2}, PAGES = {486--494 (electronic)}, ISSN = {0895-4798}, MRCLASS = {15A24 (65F20)}, MRNUMBER = {MR2047430 (2004m:15021)}, } @ARTICLE {DemMor:73, author = "S.N. DEMING and S.L. MORGAN", title = "Simplex optimization of variables in {A}nalytical {C}hemistry", journal = "Anal. Chem.", year = "1973", volume = "45", number = "3", pages = "278-283"} @ARTICLE {DemMor:74, author = "S.N. DEMING and S.L. MORGAN", title = "Simplex optimization of analytical chemical methods", journal = "Anal. Chem.", year = "1974", volume = "46", number = "9", pages = "1170-1181"} @ARTICLE {DemMa:71, author = "V.F. DEM'JANOV and V.N. MALOZEMOV", title = "On the theory of nonlinear minimax problems", journal = "Russian Math. Soc.", year = "1971", volume = "26", pages = "57-115"} @BOOK {DemMa:74qq, author = "V.F. DEM'JANOV and V.N. MALOZEMOV", title = "On the theory of nonlinear minimax problems", city = "New York - Toronto", year = "1974", publisher = "John Wiley and Sons"} @BOOK {DemMa:74, author = "V.F. DEM'JANOV and V.N. MALOZEMOV", title = "Introduction to Minimax", city = "New York", year = "1974", note = "translated from Russian", publisher = "Dover Publications"} @ARTICLE {DemRu:80, author = "V.F. DEM'JANOV and A.M. RUBINOV", title = "On quasidifferentiable functionals", journal = "Soviet Math. Dokl.", year = "1980", volume = "21", pages = "14-17"} @article {MR2001h:65036, AUTHOR = {DEMMEL, J.W.}, TITLE = {Accurate singular value decompositions of structured matrices}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {21}, YEAR = {1999}, NUMBER = {2}, PAGES = {562--580 (electronic)}, ISSN = {1095-7162}, MRCLASS = {65F10 (65F20)}, MRNUMBER = {2001h:65036}, MRREVIEWER = {Stefano Serra Capizzano}, } @article {MR2000j:65044, AUTHOR = {DEMMEL, J.W. and GU, M. and Eisenstat, S. and SLAPNI{\v{C}}AR, I. and VESELI{\'C}, K. and DRMA{\v{C}}, Z.}, TITLE = {Computing the singular value decomposition with high relative accuracy}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {299}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {21--80}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {65F15 (15A18 65G99)}, MRNUMBER = {2000j:65044}, MRREVIEWER = {Jan Z{\'{\i}}tko}, } @inproceedings {MR94m:65212, AUTHOR = {DEMMEL, J.W.}, TITLE = {Steve {S}male and the geometry of ill-conditioning}, BOOKTITLE = {From Topology to Computation: Proceedings of the Smalefest (Berkeley, CA, 1990)}, PAGES = {305--316}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {1993}, MRCLASS = {65Y20 (65R30)}, MRNUMBER = {94m:65212}, } @article {MR94h:65044, AUTHOR = {DEMMEL, J.W. and GRAGG, W.}, TITLE = {On computing accurate singular values and eigenvalues of matrices with acyclic graphs}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {185}, YEAR = {1993}, PAGES = {203--217}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {65F30 (15A18)}, MRNUMBER = {94h:65044}, } @article {MR92k:65079, AUTHOR = {DEMMEL, J.W.}, TITLE = {The componentwise distance to the nearest singular matrix}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {13}, YEAR = {1992}, NUMBER = {1}, PAGES = {10--19}, ISSN = {0895-4798}, CODEN = {SJMAEL}, MRCLASS = {65F35}, MRNUMBER = {92k:65079}, } @incollection {MR91m:65124, AUTHOR = {DEMMEL, J.W.}, TITLE = {Nearest defective matrices and the geometry of ill-conditioning}, BOOKTITLE = {Reliable numerical computation}, SERIES = {Oxford Sci. Publ.}, PAGES = {35--55}, PUBLISHER = {Oxford Univ. Press}, ADDRESS = {New York}, YEAR = {1990}, MRCLASS = {65F35}, MRNUMBER = {91m:65124}, } @article {MR88m:65066, AUTHOR = {DEMMEL, J.W.}, TITLE = {The smallest perturbation of a submatrix which lowers the rank and constrained total least squares problems}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {24}, YEAR = {1987}, NUMBER = {1}, PAGES = {199--206}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {65F20 (15A09 15A12)}, MRNUMBER = {88m:65066}, MRREVIEWER = {Mario Arioli}, } @article {MR88i:15014, AUTHOR = {DEMMEL, J.W.}, TITLE = {On condition numbers and the distance to the nearest ill-posed problem}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {51}, YEAR = {1987}, NUMBER = {3}, PAGES = {251--289}, ISSN = {0029-599X}, CODEN = {NUMMA7}, MRCLASS = {15A12 (15A42 15A45 65F35)}, MRNUMBER = {88i:15014}, MRREVIEWER = {Frank Uhlig}, } @article {MR88h:65091, AUTHOR = {DEMMEL, J.W.}, TITLE = {The geometry of ill-conditioning}, JOURNAL = {J. Complexity}, FJOURNAL = {Journal of Complexity}, VOLUME = {3}, YEAR = {1987}, NUMBER = {2}, PAGES = {201--229}, ISSN = {0885-064X}, MRCLASS = {65F35 (12D10)}, MRNUMBER = {88h:65091}, MRREVIEWER = {Henry Wolkowicz}, } @book {MR98m:65001, AUTHOR = {Demmel, J.W.}, TITLE = {Applied numerical linear algebra}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {1997}, PAGES = {xii+419}, ISBN = {0-89871-389-7}, MRCLASS = {65-01 (65Fxx)}, MRNUMBER = {98m:65001}, MRREVIEWER = {William W. Hager}, } @techreport{deka:84, author = "J.W. DEMMEL and B. KAGSTR{\"O}M", year = "1984", title = "Stable Eigendecompositions of Matrix Pencils", institution = "Institute of Information Processing, University of Umea", type = "Report", number = "UMINF-118.84", kwds = "nla, geig, matrix pencil" } @incollection {MR99b:90129, AUTHOR = {DEMPE, S.}, TITLE = {On generalized differentiability of optimal solutions in nonlinear parametric optimization}, BOOKTITLE = {Mathematical programming with data perturbations}, PAGES = {47--63}, PUBLISHER = {Dekker}, ADDRESS = {New York}, YEAR = {1998}, MRCLASS = {90C31 (49J52)}, MRNUMBER = {99b:90129}, MRREVR = {D. Klatte}, } @incollection {MR98e:90180, AUTHOR = {DEMPE, S.}, TITLE = {On generalized differentiability of optimal solutions and its application to an algorithm for solving bilevel optimization problems}, BOOKTITLE = {Recent advances in nonsmooth optimization}, PAGES = {36--56}, PUBLISHER = {World Sci. Publishing}, ADDRESS = {River Edge, NJ}, YEAR = {1995}, MRCLASS = {90C31 (90D65)}, MRNUMBER = {98e:90180}, MRREVR = {Stefan Scholtes}, } @article {MR94d:90062, AUTHOR = {DEMPE, S.}, TITLE = {Directional differentiability of optimal solutions under {S}later's condition}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {59}, YEAR = {1993}, NUMBER = {1, Ser. A}, PAGES = {49--69}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C31 (49J52)}, MRNUMBER = {94d:90062}, MRREVR = {Alexander Shapiro}, } @ARTICLE {Dem:72, author = "A.P. DEMPSTER", title = "Covariance selections", journal = "Biometrics", year = "1972", volume = "28", pages = "157-175"} @INPROCEEDINGS {Dennel:77, author = "J. DENNEL", title = "On the continuity of point-to-set map with applications to optimization", booktitle = "Proceedings of the 2nd Symposium on Operations Research, Aachen", year = "1977"} @INCOLLECTION {Denn:71, author = "J.E. {Dennis Jr.}", title = "Toward a unified convergence theory for {N}ewton-like methods", booktitle = "Nonlinear Functional Analysis and Applications", publisher = "Academic Press", year = "1971", editor = "L.B. Rall", address = "New York, NY"} @INCOLLECTION {Denn:73, author = "J.E. {Dennis Jr.}", title = "Some computational techniques for the nonlinear least squares problem", booktitle = "Numerical Solutions of Systems of Nonlinear Equations", publisher = "Academic Press", year = "1973", editor = "G.D. Byrne and C.A. Hall", pages = "157-183", address = "New York, NY"} @INCOLLECTION {Denn:77, author = "J.E. {Dennis Jr.}", title = "Nonlinear least squares and equations", booktitle = "The State of the Art in Numerical Analysis", publisher = "Academic Press", year = "1977", editor = "D. Jacobs", pages = "269-312", address = "London"} @INCOLLECTION {Denn:78, author = "J.E. {Dennis Jr.}", title = "A brief introduction to quasi-{N}ewton methods", booktitle = "Numerical Analysis", publisher = "AMS", year = "1978", editor = "G.H. Golub and J. Oliger", pages = "19-52", address = "Providence, Rhode Island"} @INPROCEEDINGS {Denn:84, author = "J.E. {Dennis Jr.}", title = "A user's guide to nonlinear optimization algorithms", booktitle = "Proceedings of the IEEE, vol. 72 \#12", year = "1984"} @incollection {MR1203343, AUTHOR = {Gay, D.M. and Kaufman, L.}, TITLE = {Tradeoffs in algorithms for separable nonlinear least squares}, BOOKTITLE = {Computational and applied mathematics, {I} ({D}ublin, 1991)}, PAGES = {179--183}, PUBLISHER = {North-Holland, Amsterdam}, YEAR = {1992}, MRCLASS = {65K05}, MRNUMBER = {1203343}, } @ARTICLE {DennGaWe:81a, author = "J.E. {Dennis Jr.} and D.M. Gay and R.E. WELSCH", title = "An adaptive nonlinear least-squares algorithm", journal = "TOMS", year = "1981", volume = "7", pages = "348-368"} @ARTICLE {DennGaWe:81b, author = "J.E. {Dennis Jr.} and D.M. Gay and R.E. WELSCH", title = "Algorithm 573 {NL2SOL} - {A}n adaptive nonlinear least-squares algorithm [{E}4]", journal = "TOMS", year = "1981", volume = "7", pages = "369-383"} @ARTICLE {DennMar:82, author = "J.E. {Dennis Jr.} and E.S. MARWIL", title = "Direct secant updates of matrix factorizations", journal = "Math. Comp.", year = "1982", volume = "38", pages = "459-474"} @ARTICLE {DennMei:79, author = "J.E. {Dennis Jr.} and H.H. MEI", title = "Two new unconstrained optimization algorithms which use function and gradient values", journal = "J. Optim. Theory Appl.", year = "1979", volume = "28", pages = "453-482"} @ARTICLE {DennMo:74, author = "J.E. {Dennis Jr.} and J.J. Mor\'{e}", title = "A characterization of superlinear convergence and its application to quasi-{N}ewton methods", journal = "Math. Comp.", year = "1974", volume = "28", pages = "549-560"} @ARTICLE {DennMo:77, author = "J.E. {Dennis Jr.} and J.J. Mor\'{e}", title = "Quasi-{N}ewton methods, motivation and theory", journal = "SIAM Review", year = "1977", volume = "19", pages = "46-89"} @techreport{DennStei:98, author = "J.E. Dennis and T. Steihaug", year = "1998", title = "A {F}erris-{M}angasarian technique applied to linear least squares problems", institution = "Rice University", type = "CRPC Report", keywords = "least squares, parallel", number = "MS41" } @ARTICLE {DennSch:79, author = "J.E. {Dennis Jr.} and R.B. Schnabel", title = "Least change secant updates for quasi-{N}ewton methods", journal = "SIAM Review", year = "1979", volume = "21", pages = "443-459"} @INCOLLECTION {DennSch:81, author = "J.E. {Dennis Jr.} and R.B. Schnabel", title = "A new derivation of symmetric and positive definite secant updates", booktitle = "Nonlinear Programming 4", publisher = "Academic Press", year = "1981", editor = "O.L. Mangasarian and R.R. Meyer and S.M. Robinson", pages = "167-199", address = "New York, NY"} @BOOK {DennSch:83, AUTHOR = {{Dennis Jr.}, J.E. and Schnabel, R.B.}, TITLE = {Numerical methods for unconstrained optimization and nonlinear equations}, NOTE = {Corrected reprint of the 1983 original}, SERIES = {Classics in Applied Mathematics}, VOLUME = {16}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {1996}, PAGES = {xvi+378}, ISBN = {0-89871-364-1}, } @TECHREPORT {DennSch:87, author = "J.E. {Dennis Jr.} and R.B. Schnabel", title = "A view of unconstrained optimization", institution = "Department of Computer Science, University of Colorado", year = "1987", number = "CU-CS-376-87", address = "Boulder, CO", note = "To appear in Handbooks in Operations Research and Management Science. Handbook 1: Optimization. G.L. Nemhauser, A.H.G. Rinnooy Kan and M.J. Todd, editors"} @TECHREPORT {DennShVu:85, author = "J.E. {Dennis Jr.} and S. SHENG and P.H. VU", title = "A memoryless augmented {G}auss-{N}ewton method for nonlinear least-squares problems", institution = "Department of Mathematical Sciences, Rice University", year = "1985", number = "TR85-1", address = "Houston, TX"} @ARTICLE {DennTap:76, author = "J.E. {Dennis Jr.} and R.A. Tapia", title = "Supplementary terminology for nonlinear iterative methods", journal = "SIGNUM Newsletter", year = "1976", volume = "11", number = "4", pages = "4-6"} @ARTICLE {DennWal:81, author = "J.E. {Dennis Jr.} and H.F. WALKER", title = "Convergence theorems for least-change secant update methods", journal = "SIAM J. Numer. Anal.", year = "1981", volume = "18", pages = "949-987"} @TECHREPORT {DennWal:83, author = "J.E. {Dennis Jr.} and H.F. WALKER", title = "Inaccuracy in quasi-{N}ewton methods: local improvement theorems", institution = "Department of Mathematical Sciences, Rice University", year = "1983", number = "TR83-11", address = "Houston, TX"} @ARTICLE {DennWal:85, author = "J.E. {Dennis Jr.} and H.F. WALKER", title = "Least-change sparse secant update methods with inaccurate secant conditions", journal = "SIAM J. Numer. Anal.", year = "1985", volume = "22", pages = "760-778"} @INCOLLECTION {DennWoo:87, author = "J.E. {Dennis Jr.} and D.J. WOODS", title = "Optimization and microcomputers: {T}he {N}elder-{M}ead simplex algorithm", booktitle = "New Computing Environments: Microcomputers in Large-Scale Computing", publisher = "SIAM", year = "1987", editor = "A. Wouk", pages = "116-122", address = "Philadelphia"} @TECHREPORT {DennHeinkVic:95, author = "J.E. {Dennis Jr.} and M. HEINKENSCHLOSS and L.N. VICENTE", title = "Trust-region interior-point SQP algorithms for a class of nonlinear programming problems", institution = "Department of Mathematical Sciences, Rice University", year = "1995", number = "CRPC-TR95512", address = "Houston, TX"} @ARTICLE {DenRoSwa:77, author = "M.B. DENTON and M.W. ROUTH and P.A. SWARTZ", title = "Performance of the super modified {S}implex", journal = "Anal. Chem.", year = "1977", volume = "49", number = "9", pages = "1422-1428"} @BOOK {Deuf:96, author = "P. DEUFLHARD", title = "{N}ewton Techniques for Highly Nonlinear Problems - Theory and Algorithms", publisher = "Academic Press,Inc.", note = "(To be published)", year = "1996"} @incollection {MR1742997, AUTHOR = {Deutsch, F.}, TITLE = {The role of the strong conical hull intersection property in convex optimization and approximation}, BOOKTITLE = {Approximation theory IX, Vol. I. (Nashville, TN, 1998)}, SERIES = {Innov. Appl. Math.}, PAGES = {105--112}, PUBLISHER = {Vanderbilt Univ. Press}, ADDRESS = {Nashville, TN}, YEAR = {1998}, MRCLASS = {90C46 (41A65)}, MRNUMBER = {MR1742997 (2001c:90098)}, MRREVIEWER = {Wu Li}, } @incollection {MR96e:46027, AUTHOR = {DEUTSCH, F.}, TITLE = {The angle between subspaces of a {H}ilbert space}, BOOKTITLE = {Approximation theory, wavelets and applications (Maratea, 1994)}, SERIES = {NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.}, VOLUME = {454}, PAGES = {107--130}, PUBLISHER = {Kluwer Acad. Publ.}, ADDRESS = {Dordrecht}, YEAR = {1995}, MRCLASS = {46C05 (47A05 65J05)}, MRNUMBER = {96e:46027}, } @ARTICLE {DeDe:88, author = "P. DEWILDE and E.F.A. DEPRETTERE", title = "The generalized {S}chur algorithm: approximation and hierarchy", journal = "Operator Theory: Advances and Applications", year = "1988", volume = "29", publisher = "Birkhauser Verlag Basel", pages = "97-116"} @article {MR95h:90102, AUTHOR = {DIETRICH, H.}, TITLE = {Global optimization conditions for certain nonconvex minimization problems}, JOURNAL = {J. Global Optim.}, FJOURNAL = {Journal of Global Optimization. An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering}, VOLUME = {5}, YEAR = {1994}, NUMBER = {4}, PAGES = {359--370}, ISSN = {0925-5001}, CODEN = {JGOPEO}, } @article{int:Dikin1, author = "I. I. DIKIN", title = "Iterative solution of problems of linear and quadratic programming", journal = "Doklady Akademii Nauk SSSR", volume = "174", year = "1967", pages = "747--748", note = "Translated in~: {\em Soviet Mathematics Doklady}, 8:674--675, 1967" } @article {Di, AUTHOR = {DINKELBACH, W.}, TITLE = {On nonlinear fractional programming}, JOURNAL = {Management Sci.}, VOLUME = {13}, YEAR = {1967}, PAGES = {492--498}, MRCLASS = {90.58}, MRNUMBER = {39 #3819}, } @ARTICLE {DipGri:79, author = "G. DIPILLO and L. GRIPPO", title = "A new class of augmented {L}agrangians in nonlinear programming", journal = "SIAM J. Control Optim.", year = "1979", volume = "17", pages = "618-628"} @ARTICLE{deuermeyer, AUTHOR = "D. DEUERMEYER", TITLE = "Large-scale solutions in structural analysis", JOURNAL = "CRAY Channels", VOLUME = "12", NUMBER = "1", PAGES = "15 - 17", YEAR = "1990"} @ARTICLE{devenow:96, AUTHOR = "A. DEVENOW and I. WELCH", TITLE = "Rational herding in financial economics", JOURNAL = "European Economic Review", VOLUME = "40", NUMBER = "3-5", PAGES = "603 - 615", YEAR = "1996"} @ARTICLE {Dix1:72a, author = "L.C.W. Dixon", title = "Quasi-{N}ewton family generate identical points, part {I}", journal = "Math. Prog.", year = "1972", volume = "2", pages = "383-387"} @ARTICLE {Dix2:72b, author = "L.C.W. Dixon", title = "Quasi-{N}ewton family generate identical points, part {II}", journal = "Math. Prog.", year = "1972", volume = "3", pages = "345-358"} @INCOLLECTION {Dix:72, author = "L.C.W. Dixon", title = "The choice of step length, a crucial factor in the performance of variable metric algorithms", booktitle = "Numerical Methods for Nonlinear Optimization", publisher = "Academic Press", year = "1972", editor = "F. Lootsma", pages = "149-170", address = "New York, NY"} @ARTICLE {Dix:91, author = "L.C.W. Dixon", title = "On the impact of automatic differentiation on the relative performance of parallel truncated {N}ewton and variable metric algorithms", journal = siopt, year = "1991", volume = "1", pages = "475-486"} @TECHREPORT {DHM:84, author = "L.C.W. Dixon and S.E. HERSOM and Z.A. MAANY", title = "Initial experience obtained solving the low thrust satellite trajectory optimisation problem", institution = "The Hatfield Polytechnic Numerical Optimization Centre", year = "1984", number = "T.R. 152"} @BOOK {DixSz:75, author = "L.C.W. Dixon and G.P. SZEGO", title = "Towards Global Optimization, 1", publisher = "North-Holland", year = "1975", address = "Amsterdam"} @BOOK {DixSz:78, author = "L.C.W. Dixon and G.P. SZEGO", title = "Towards Global Optimization, 2", publisher = "North-Holland", year = "1978", address = "Amsterdam"} @article {MR2567299, AUTHOR = {Djordjevi{\'c}, D.S. and Din{\v{c}}i{\'c}, N.{\v{C}}.}, TITLE = {Reverse order law for the {M}oore-{P}enrose inverse}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {361}, YEAR = {2010}, NUMBER = {1}, PAGES = {252--261}, ISSN = {0022-247X}, CODEN = {JMANAK}, MRCLASS = {15A09}, MRNUMBER = {2567299 (2010i:15007)}, MRREVIEWER = {Gustavo Corach}, DOI = {10.1016/j.jmaa.2009.08.056}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/j.jmaa.2009.08.056}, } @article {MR1875515, AUTHOR = {Dolan, E.D. and Mor\'{e}, J.J.}, TITLE = {Benchmarking optimization software with performance profiles}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {91}, YEAR = {2002}, NUMBER = {2, Ser. A}, PAGES = {201--213}, ISSN = {0025-5610}, MRCLASS = {90-04 (90C30)}, MRNUMBER = {MR1875515 (2002j:90001)}, } @INPROCEEDINGS {DonSchn:86, author = "J.R. DONALDSON and R.B. Schnabel", title = "Computational experience with confidence regions and confidence intervals for nonlinear least squares", booktitle = "Computer Science and Statistics: Proceedings of the 17th Conference on the Interface", year = "1986", editor = "D.M. Allen", pages = "83-93", publisher = "North-Holland", address = "Amsterdam"} @ARTICLE {DonSchn:87, author = "J.R. DONALDSON and R.B. Schnabel", title = "Computational experience with confidence regions and confidence intervals for nonlinear least squares", journal = "Technometrics", year = "1987", volume = "29", pages = "67-82"} @article{dh72, AUTHOR = "W.E.\ Donath and A.J.\ Hoffman", TITLE = "Algorithms for Partitioning Graphs and Computer Logic Based on Eigenvectors of Connection Matrices", JOURNAL = " IBM Technical Disclosure Bulletin", VOLUME = " 15", NUMBER ="3", YEAR = "1972", PAGES = "938--944", } @ARTICLE {DoHo:73, author = "W.E. Donath and A.J. Hoffman", TITLE = {Lower bounds for the partitioning of graphs}, JOURNAL = {IBM J. Res. Develop.}, FJOURNAL = {International Business Machines Corporation. Journal of Research and Development}, VOLUME = {17}, YEAR = {1973}, PAGES = {420--425}, ISSN = {0018-8646}, MRCLASS = {05C99}, MRNUMBER = {MR0329965 (48 \#8304)}, MRREVIEWER = {Moshe Rosenfeld} } @ARTICLE{Donoho:94, AUTHOR = {D.~L.~Donoho and I.~M.~Johnstone}, TITLE = {Ideal spatial adaptation by wavelet shrinkage}, JOURNAL = {Biometrika}, YEAR = {1994}, VOLUME = {81}, NUMBER = {3}, PAGES = {425--455} } @ARTICLE{Donoho:95, AUTHOR = {D.~L.~Donoho and I.~M.~Johnstone}, TITLE = {Adapting to Unknown Smoothness via Wavelet Shrinkage}, JOURNAL = {Journal of the American Statistical Association}, YEAR = {1995}, VOLUME = {90}, NUMBER = {432}, PAGES = {1200--1224} } @ARTICLE{Donoho:SHRINK, AUTHOR = {D.~L.~Donoho and I.~M.~Johnstone and G.~Kerkyacharian and D.~Picard}, TITLE = {Wavelet Shrinkage: asymptopia?}, JOURNAL = {Journal of the Royal Statistical Society, Ser.~B}, YEAR = {1995}, VOLUME = {57}, PAGES = {301--337} } @article{DrMaMu:08, Author = {P. Drineas and M.W. Mahoney and S. Muthukrishnan}, Doi = {10.1137/07070471X}, Journal = {SIAM Journal on Matrix Analysis and Applications}, Keywords = {CUR matrix decomposition; random sampling algorithms; data analysis; approximate least squares}, Number = {2}, Pages = {844-881}, Publisher = {SIAM}, Title = {Relative-Error $CUR$ Matrix Decompositions}, Url = {http://link.aip.org/link/?SML/30/844/1}, Volume = {30}, Year = {2008} } @article {MR2001f:65050, AUTHOR = {Drma{\v{c}}, Z.}, TITLE = {On principal angles between subspaces of {E}uclidean space}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {22}, YEAR = {2000}, NUMBER = {1}, PAGES = {173--194 (electronic)}, ISSN = {1095-7162}, MRCLASS = {65F30 (65D99 65G50)}, MRNUMBER = {2001f:65050}, MRREVIEWER = {A. Barraud}, } @article {MR3303206, AUTHOR = {Daniilidis, A. and Drusvyatskiy, D. and Lewis, A.S.}, TITLE = {Orbits of geometric descent}, JOURNAL = {Canad. Math. Bull.}, FJOURNAL = {Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques}, VOLUME = {58}, YEAR = {2015}, NUMBER = {1}, PAGES = {44--50}, ISSN = {0008-4395}, MRCLASS = {49J53 (34A60 37C10)}, MRNUMBER = {3303206}, DOI = {10.4153/CMB-2014-013-8}, URL = {http://dx.doi.org/10.4153/CMB-2014-013-8}, } @article {MR3299130, AUTHOR = {Drusvyatskiy, D. and Ioffe, A.D. and Lewis, A.S.}, TITLE = {Curves of descent}, JOURNAL = {SIAM J. Control Optim.}, FJOURNAL = {SIAM Journal on Control and Optimization}, VOLUME = {53}, YEAR = {2015}, NUMBER = {1}, PAGES = {114--138}, ISSN = {0363-0129}, MRCLASS = {49J52 (14P15 26D10 37B35)}, MRNUMBER = {3299130}, DOI = {10.1137/130920216}, URL = {http://dx.doi.org/10.1137/130920216}, } @article {MR3271275, AUTHOR = {Drusvyatskiy, D. and Larsson, M.}, TITLE = {Approximating functions on stratified sets}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {367}, YEAR = {2015}, NUMBER = {1}, PAGES = {725--749}, ISSN = {0002-9947}, MRCLASS = {57N80 (26B05 58A35)}, MRNUMBER = {3271275}, DOI = {10.1090/S0002-9947-2014-06412-X}, URL = {http://dx.doi.org/10.1090/S0002-9947-2014-06412-X}, } @article {MR3258532, AUTHOR = {Drusvyatskiy, D. and Lewis, A.S.}, TITLE = {Optimality, identifiability, and sensitivity}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Optimization Society}, VOLUME = {147}, YEAR = {2014}, NUMBER = {1-2, Ser. A}, PAGES = {467--498}, ISSN = {0025-5610}, MRCLASS = {49J53 (49J52 49Q12 90C30 90C31)}, MRNUMBER = {3258532}, MRREVIEWER = {Adam B. Levy}, DOI = {10.1007/s10107-013-0730-4}, URL = {http://dx.doi.org/10.1007/s10107-013-0730-4}, } @article {DrusvLewis:2017, AUTHOR = {Drusvyatskiy, D. and Lewis, A.S.}, TITLE = {Error bounds, quadratic growth, and linear convergence of proximal methods}, JOURNAL = {mor}, VOLUME = {to appear}, YEAR = {2017}, NUMBER = {}, PAGES = {}, } @article {MR3205737, AUTHOR = {Daniilidis, A. and Drusvyatskiy, D. and Lewis, A.S.}, TITLE = {Orthogonal invariance and identifiability}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {35}, YEAR = {2014}, NUMBER = {2}, PAGES = {580--598}, ISSN = {0895-4798}, MRCLASS = {53B25 (15B57 58C25)}, MRNUMBER = {3205737}, MRREVIEWER = {Chee-Khian Sim}, DOI = {10.1137/130916710}, URL = {http://dx.doi.org/10.1137/130916710}, } @article {MR3071860, AUTHOR = {Drusvyatskiy, D. and Lewis, A.S.}, TITLE = {Semi-algebraic functions have small subdifferentials}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {140}, YEAR = {2013}, NUMBER = {1, Ser. B}, PAGES = {5--29}, ISSN = {0025-5610}, MRCLASS = {49J52 (14P10 54C60 57N80 58C07)}, MRNUMBER = {3071860}, MRREVIEWER = {Aris Daniilidis}, DOI = {10.1007/s10107-012-0624-x}, URL = {http://dx.doi.org/10.1007/s10107-012-0624-x}, } @article {MR3033107, AUTHOR = {Drusvyatskiy, D. and Lewis, A.S.}, TITLE = {Tilt stability, uniform quadratic growth, and strong metric regularity of the subdifferential}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {23}, YEAR = {2013}, NUMBER = {1}, PAGES = {256--267}, ISSN = {1052-6234}, CODEN = {SJOPE8}, MRCLASS = {49J53 (49J52 49K40 90C31)}, MRNUMBER = {3033107}, MRREVIEWER = {Shawn Xianfu Wang}, DOI = {10.1137/120876551}, URL = {http://dx.doi.org/10.1137/120876551}, } @article {MR2861332, AUTHOR = {Drusvyatskiy, D. and Ioffe, A.D. and Lewis, A.S.}, TITLE = {The dimension of semialgebraic subdifferential graphs}, JOURNAL = {Nonlinear Anal.}, FJOURNAL = {Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods}, VOLUME = {75}, YEAR = {2012}, NUMBER = {3}, PAGES = {1231--1245}, ISSN = {0362-546X}, CODEN = {NOANDD}, MRCLASS = {49J52 (14P10 54C60 58A35)}, MRNUMBER = {2861332 (2012k:49026)}, MRREVIEWER = {Nicolas Hadjisavvas}, DOI = {10.1016/j.na.2011.07.040}, URL = {http://dx.doi.org/10.1016/j.na.2011.07.040}, } @article {MR2784817, AUTHOR = {Drusvyatskiy, D. and Lewis, A.S.}, TITLE = {Generic nondegeneracy in convex optimization}, JOURNAL = {Proc. Amer. Math. Soc.}, FJOURNAL = {Proceedings of the American Mathematical Society}, VOLUME = {139}, YEAR = {2011}, NUMBER = {7}, PAGES = {2519--2527}, ISSN = {0002-9939}, CODEN = {PAMYAR}, MRCLASS = {49J53 (26B25 47N10 90C25 90C46)}, MRNUMBER = {2784817 (2012b:49024)}, MRREVIEWER = {Rafa{\l}K. Goebel}, DOI = {10.1090/S0002-9939-2010-10692-5}, URL = {http://dx.doi.org/10.1090/S0002-9939-2010-10692-5}, } @incollection {MR1341386, AUTHOR = {Dru\.zkowski, Ludwik M.}, TITLE = {The {J}acobian conjecture: survey of some results}, BOOKTITLE = {Topics in complex analysis ({W}arsaw, 1992)}, SERIES = {Banach Center Publ.}, VOLUME = {31}, PAGES = {163--171}, PUBLISHER = {Polish Acad. Sci. Inst. Math., Warsaw}, YEAR = {1995}, MRCLASS = {14E07 (13B10 26B10)}, MRNUMBER = {1341386}, MRREVIEWER = {L. Andrew Campbell}, } @article {MR1639689, AUTHOR = {Chamberland, Marc}, TITLE = {Global asymptotic stability, additive neural networks, and the {J}acobian conjecture}, NOTE = {Geoffrey J. Butler Memorial Conference in Differential Equations and Mathematical Biology (Edmonton, AB, 1996)}, JOURNAL = {Canad. Appl. Math. Quart.}, FJOURNAL = {The Canadian Applied Mathematics Quarterly}, VOLUME = {5}, YEAR = {1997}, NUMBER = {4}, PAGES = {331--339}, ISSN = {1073-1849}, MRCLASS = {34D05 (34C99 58F10)}, MRNUMBER = {1639689}, MRREVIEWER = {Jaume Llibre}, } @article {MR0286492, AUTHOR = {DRYGAS, H.}, TITLE = {On a generalization of the {F}arkas theorem}, JOURNAL = {Unternehmensforschung}, VOLUME = {13}, YEAR = {1969}, PAGES = {283--290}, MRCLASS = {90.58}, MRNUMBER = {MR0286492 (44 \#3701)}, MRREVIEWER = {J. Abrham}, } @TECHREPORT {DuNoRe:84, author = "I.S. DUFF and J. Nocedal and J.K. REID", title = "The use of linear programming for the solution of sparse sets of nonlinear equations", institution = "Department of Electrical Engineering and Computer Science, Northwestern University", year = "1984", number = "CSS 145", address = "Evanston,IL"} @INCOLLECTION {DuRe:79, author = "I.S. DUFF and J. K. REID", title = "Performance evaluation of codes for sparse matrices", booktitle = "Performance Evaluation of Numerical Software", publisher = "North-Holland", year = "1979", editor = "L.D.Fosdick", pages = "121-135", address = "Amsterdam"} @article {MR0503731, AUTHOR = {Duffin, R.J.}, TITLE = {Clark's theorem on linear programs holds for convex programs}, JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.}, FJOURNAL = {Proceedings of the National Academy of Sciences of the United States of America}, VOLUME = {75}, YEAR = {1978}, NUMBER = {4}, PAGES = {1624--1626}, ISSN = {0027-8424}, MRCLASS = {90C05}, MRNUMBER = {0503731}, MRREVIEWER = {A. Gewirtz}, } @INCOLLECTION {Duff:56, author = "R.J. Duffin", title = "Infinite programs", booktitle = "Linear Equalities and Related Systems", publisher = "Princeton University Press", year = "1956", editor = "A.W. Tucker", pages = "157-170", address = "Princeton, NJ"} @incollection {MR85e:90057, AUTHOR = {Duffin, R.J. and JEROSLOW, R. G. and KARLOVITZ, L. A.}, TITLE = {Duality in semi-infinite linear programming}, BOOKTITLE = {Semi-infinite programming and applications (Austin, Tex., 1981)}, PAGES = {50--62}, SERIES = {Lecture Notes in Econom. and Math. Systems}, VOLUME = {215}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1983}, } @ARTICLE {DuElVi:79, author = "S.R.K. DUTTA and R.A. {EL-ATTAR} and M. VIDYASAGAR", title = "An algorithm for $l_{n}$-norm minimization with applications to nonlinear $l_{m}$-approximation", journal = "SIAM J. Num. Anal.", year = "1979", volume = "6", pages = "70-86"} @ARTICLE{D83 , AUTHOR="R.L. DYKSTRA", TITLE="An algorithm for restricted least squares regression", JOURNAL="J. Amer. Stat.", YEAR="1983", VOLUME="78", PAGES="839--842 "} @article {MR973051, AUTHOR = {Gohberg, I. and Koltracht, I.}, TITLE = {Efficient algorithm for {T}oeplitz plus {H}ankel matrices}, JOURNAL = {Integral Equations Operator Theory}, FJOURNAL = {Integral Equations and Operator Theory}, VOLUME = {12}, YEAR = {1989}, NUMBER = {1}, PAGES = {136--142}, ISSN = {0378-620X}, MRCLASS = {65F05 (15A06 47A15 47B35)}, MRNUMBER = {973051}, MRREVIEWER = {H. R. Shen}, DOI = {10.1007/BF01199761}, URL = {https://doi.org/10.1007/BF01199761}, } @incollection {MR892133, AUTHOR = {Ellis, R.L. and Gohberg, I. and Lay, D.}, TITLE = {Band extensions, maximum entropy and the permanence principle}, BOOKTITLE = {Maximum entropy and {B}ayesian methods in applied statistics ({C}algary, {A}lta., 1984)}, PAGES = {131--155}, PUBLISHER = {Cambridge Univ. Press, Cambridge}, YEAR = {1986}, MRCLASS = {15A57 (42A82 47B35)}, MRNUMBER = {892133}, MRREVIEWER = {L. Rodman}, URL = {https://doi.org/10.1017/CBO9780511569678.010}, } @article {MR0353038, AUTHOR = {Gohberg, I.C. and Semencul, A.A.}, TITLE = {The inversion of finite {T}oeplitz matrices and their continual analogues}, JOURNAL = {Mat. Issled.}, FJOURNAL = {Akademiya Nauk Moldavsko\u\i \ SSR. Institut Matematiki s Vychislitel\cprime nym Tsentrom. Matematicheskie Issledovaniya}, VOLUME = {7}, YEAR = {1972}, NUMBER = {2(24)}, PAGES = {201--223, 290}, ISSN = {0542-9994}, MRCLASS = {47B35}, MRNUMBER = {0353038}, MRREVIEWER = {A. Devinatz}, } @ARTICLE {DymGoh:81, author = "H. Dym and I. Gohberg", TITLE = {Extensions of band matrices with band inverses}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {36}, YEAR = {1981}, PAGES = {1--24}, ISSN = {0024-3795}, MRCLASS = {15A23 (15A09)}, MRNUMBER = {604325}, MRREVIEWER = {Shoon K. Kim}, URL = {https://doi.org/10.1016/0024-3795(81)90215-9}, } %EEEEEEEEEEEEE @article {MR1290398, AUTHOR = {Edelman, A. and Kostlan, E.}, TITLE = {How many zeros of a random polynomial are real?}, JOURNAL = {Bull. Amer. Math. Soc. (N.S.)}, FJOURNAL = {American Mathematical Society. Bulletin. New Series}, VOLUME = {32}, YEAR = {1995}, NUMBER = {1}, PAGES = {1--37}, ISSN = {0273-0979}, CODEN = {BAMOAD}, MRCLASS = {60G99 (30B20 42A05)}, MRNUMBER = {1290398 (95m:60082)}, MRREVIEWER = {Kambiz Farahmand}, DOI = {10.1090/S0273-0979-1995-00571-9}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1090/S0273-0979-1995-00571-9}, } @article {MR1376652, AUTHOR = {Edelman, A. and Kostlan, E.}, TITLE = {Erratum: ``{H}ow many zeros of a random polynomial are real?'' [{B}ull.\ {A}mer.\ {M}ath.\ {S}oc.\ ({N}.{S}.)\ {\bf 32} (1995), no.\ 1, 1--37; {MR}1290398 (95m:60082)]}, JOURNAL = {Bull. Amer. Math. Soc. (N.S.)}, FJOURNAL = {American Mathematical Society. Bulletin. New Series}, VOLUME = {33}, YEAR = {1996}, NUMBER = {3}, PAGES = {325}, ISSN = {0273-0979}, CODEN = {BAMOAD}, MRCLASS = {60G99 (30B20 42A05)}, MRNUMBER = {1376652}, DOI = {10.1090/S0273-0979-96-00678-7}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1090/S0273-0979-96-00678-7}, } @BOOK {Ef:80, author = "H.B. EFIMOV", title = "Higher Geometry", publisher = "Mir", year = "1980", note = "Translated from the Russian by P.C. Sinha", address = "Moscow"} @ARTICLE {Eis:81, author = "S.C. Eisenstat", title = "Efficient implementation of a class of preconditioned conjugate gradient methods", journal = "SIAM J. Sci. Stat. Comp.", year = "1981", volume = "2", pages = "1-4"} @ARTICLE {EisElSch:83, author = "S.C. Eisenstat and H.C. ELMAN and M.H. SCHULTZ", title = "Variational iterative methods for non-symmetric systems of linear equations", journal = "SIAM J. Numer. Anal.", year = "1983", volume = "20", pages = "345-357"} @ARTICLE {EisGuSchShe:82, author = "S.C. Eisenstat and M.C. GURSKY and M.H. SCHULTZ and A.H. SHERMAN", title = "Yale sparse matrix package {I}: The symmetric codes", journal = "Internat. J. Numer. Methods Engrg.", year = "1982", volume = "18", pages = "1141-1151"} @BOOK {EkeTem:76, author = "I. EKELAND and R. TEMAM", title = "Convex Analysis and Variational Problems", publisher = "North-Holland", year = "1976", address = "Amsterdam"} @article {MR2000d:65067, AUTHOR = {Eld{\'e}n, L. and Park, H.}, TITLE = {A {P}rocrustes problem on the {S}tiefel manifold}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {82}, YEAR = {1999}, NUMBER = {4}, PAGES = {599--619}, ISSN = {0029-599X}, CODEN = {NUMMA7}, MRCLASS = {65F20 (15A24)}, MRNUMBER = {2000d:65067}, MRREVIEWER = {Jian-Ping Zhu}, } @TECHREPORT {Elm:82, author = "H.C. ELMAN", title = "Iterative methods for large, sparse, nonsymmetric systems of linear equations", institution = "Yale University", year = "1982", type = "Research Report", number = "229", address = "New Haven, CT"} @ARTICLE {Elfv:80, author = "T. ELFVING", title = "Block iterative methods for consistent and inconsistent linear systems", journal = "Numer. Math.", year = "1980", volume = "35", pages = "1-12"} @ARTICLE {Erh:95, author = "J. ERHEL", title = "A parallel {GMRES} version for general sparse matrices", journal = "ETNA", year = "1995", volume = "3", note = "URL http://etna.mcs.kent.edu/vol.3.1995/index.html", pages = "160-176"} @techreport{EGI, AUTHOR = "E.~ERDO\u{G}AN and D.~Goldfarb and G.~Iyengar", TITLE = "Robust portfolio management", TYPE = "CORC Technical Report", NUMBER = "TR-2004-11", INSTITUTION = "IEOR Dept., Columbia University", ADDRESS = "New York, NY", YEAR = "2004", } @article {MR2059740, AUTHOR = {ERIKSSON, J. and GULLIKSSON, M.E.}, TITLE = {Local results for the {G}auss-{N}ewton method on constrained rank-deficient nonlinear least squares}, JOURNAL = {Math. Comp.}, FJOURNAL = {Mathematics of Computation}, VOLUME = {73}, YEAR = {2004}, NUMBER = {248}, PAGES = {1865--1883 (electronic)}, ISSN = {0025-5718}, CODEN = {MCMPAF}, MRCLASS = {65K10 (65F22)}, MRNUMBER = {MR2059740 (2005d:65095)}, MRREVIEWER = {Serge G. Kruk}, } @INCOLLECTION {EskSchna:88a, author = "E. ESKOW and R.B. Schnabel", title = "Using mathematical modeling to aid in parallel algorithm development", booktitle = "Parallel Processing for Scientific Computation", publisher = "SIAM", year = "1988", editor = "G. Rodrique", pages = "368-376", address = "Philadelphia"} @TECHREPORT {EskSchna:88b, author = "E. ESKOW and R.B.Schnabel", title = "A new modified {C}holesky factorization", institution = "Department of Computer Science, University of Colorado", year = "1988", number = "CU-CS-415-88", address = "Boulder, CO", note = "Submitted to SIAM J. Sci. Stat. Comp."} @ARTICLE {El:70, author = "L. ELSNER", title = "Monotonie und randspektrum bei vollstetigen operatoren", journal = "Archive for Rational Mechanics and Analysis", year = "1970", volume = "36", pages = "356-365"} @article {MR1884909, AUTHOR = {Epelman, M. and Freund, R.M.}, TITLE = {A new condition measure, preconditioners, and relations between different measures of conditioning for conic linear systems}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {12}, YEAR = {2002}, NUMBER = {3}, PAGES = {627--655 (electronic)}, ISSN = {1052-6234}, MRCLASS = {90C08 (90C25 90C31 90C60)}, MRNUMBER = {1884909 (2003b:90051)}, MRREVIEWER = {Joaqu{\'{\i}}m J. J{\'u}dice}, DOI = {10.1137/S1052623400373829}, URL = {http://dx.doi.org/10.1137/S1052623400373829}, } @article {MR1782151, AUTHOR = {Epelman, M. and Freund, R.M.}, TITLE = {Condition number complexity of an elementary algorithm for computing a reliable solution of a conic linear system}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {88}, YEAR = {2000}, NUMBER = {3, Ser. A}, PAGES = {451--485}, ISSN = {0025-5610}, MRCLASS = {90C08 (90C60)}, MRNUMBER = {1782151 (2002g:90054)}, } @ARTICLE{2018arXiv180704428E, author = {{Erdogdu}, M.A. and {Ozdaglar}, A. and {Parrilo}, P.A. and {Denizcan Vanli}, N.}, title = "{Convergence Rate of Block-Coordinate Maximization Burer-Monteiro Method for Solving Large SDPs}", journal = {ArXiv e-prints}, archivePrefix = "arXiv", eprint = {1807.04428}, primaryClass = "math.OC", keywords = {Mathematics - Optimization and Control, Computer Science - Machine Learning, Statistics - Machine Learning}, year = 2018, month = jul, adsurl = {http://adsabs.harvard.edu/abs/2018arXiv180704428E}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } %FFFFFFFFF @book {Fabozzi:07, AUTHOR = {F.J. Fabozzi and P.N. Kolm and D.A. Pachamanova and S.M. Focardi}, TITLE = {Robust Portfolio Optimization and Management}, SERIES = {Frank j. Fabozzi Series}, PUBLISHER = {John Wiley, NJ}, YEAR = {2007}, PAGES = {xi+495}, } @book{facchinei2003finite, title = {Finite-dimensional variational inequalities and complementarity problems}, author = {Facchinei, F. and Pang, J.-S.}, volume = {1}, year = {2003}, publisher = {Springer} } @article {MR1777080, AUTHOR = {Facchinei, Francisco and Fischer, Andreas and Kanzow, Christian}, TITLE = {On the identification of zero variables in an interior-point framework}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {10}, YEAR = {2000}, NUMBER = {4}, PAGES = {1058--1078 (electronic)}, ISSN = {1052-6234}, MRCLASS = {90C51 (90C33)}, MRNUMBER = {1777080 (2001f:90069)}, MRREVIEWER = {Gong Yun Zhao}, DOI = {10.1137/S1052623498339739}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/S1052623498339739}, } @article {MR1660110, AUTHOR = {Facchinei, Francisco and Fischer, Andreas and Kanzow, Christian}, TITLE = {On the accurate identification of active constraints}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {9}, YEAR = {1999}, NUMBER = {1}, PAGES = {14--32 (electronic)}, ISSN = {1052-6234}, MRCLASS = {90C30 (65K05)}, MRNUMBER = {1660110 (99k:90152)}, MRREVIEWER = {Stefan Scholtes}, DOI = {10.1137/S1052623496305882}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/S1052623496305882}, } @TECHREPORT {FaFiKa:98, author = "F. Facchinei and A. Fischer and C. Kanzow", title = "On the Identification of Zero Variables in an Interior-Point Framework", address = "Computer Sciences Department, University of Wisconsin", year = "1998"} @article {MR0075510, AUTHOR = {Kuhn, H.W.}, TITLE = {The {H}ungarian method for the assignment problem}, JOURNAL = {Naval Res. Logist. Quart.}, FJOURNAL = {Naval Research Logistics Quarterly}, VOLUME = {2}, YEAR = {1955}, PAGES = {83--97}, ISSN = {0028-1441}, MRCLASS = {90.0X}, MRNUMBER = {MR0075510 (17,759d)}, MRREVIEWER = {D. Gale}, } @techreport{FanFanLv:07, AUTHOR = "J. Fan, Y. Fan, J. Lv", TITLE = "High Dimensional Covariance Matrix Estimation Using a Factor Model", TYPE = "Technical Report", NUMBER = "math.ST/0701124 at arxiv.org", INSTITUTION = "Princeton University", ADDRESS = "Princeton, NJ", URL = "http://arxiv.org/abs/math.ST/0701124", YEAR = "2007", } @INCOLLECTION{fan56, AUTHOR ="K. Fan", EDITOR ="H.W. Kuhn AND A.W. Tucker", TITLE ="On systems of linear inequalities", BOOKTITLE ="Linear inequalities and related systems", PUBLISHER = "Princeton University Press", PAGES ={99--156}, YEAR =1956 } @ARTICLE {Fan:51, author = "K.~FAN", title = "Maximum properties and inequalities for the eigenvalues of completely continuous operators", journal = "Proc.\ Nat.\ Acad.\ Sci.\ U.S.A.", year = "1951", volume = "37", pages = "760-766"} @ARTICLE {Fan:49, author = "K. Fan", title = " On a theorem of {W}eyl concerning eigenvalues of linear transformations I", journal = "Proc.\ Nat.\ Acad.\ Sci.\ U.S.A.", year = "1949", volume = "35", pages = "652--655"} @ARTICLE {Fan:50, author = "K.~Fan", title = " On a theorem of {W}eyl concerning eigenvalues of linear transformations II", journal = "Proc.\ Nat.\ Acad.\ Sci.\ U.S.A.", year = "1950", volume = "36", pages = "31--35"} @ARTICLE {Faren:92, author = "D.R. FARENICK", title = "Kerin-{M}ilman-type problems for compact matricially convex sets", journal = laa, keywords = "matricial coefficients", year = "1992", volume = "162-164", pages = "325-334"} @ARTICLE {Farkas:02, author = "J. FARKAS", title = {\"{U}ber die theorie der einfachen ungleichungen}, keywords = "Farkas Lemma", year = "1902", journal = "J. reine angew. Math.", volume = "124", pages = "1--24"} @article{Fawzi_2018, title={Semidefinite Approximations of the Matrix Logarithm}, volume={19}, ISSN={1615-3383}, url={http://dx.doi.org/10.1007/s10208-018-9385-0}, DOI={10.1007/s10208-018-9385-0}, number={2}, journal={Foundations of Computational Mathematics}, publisher={Springer Science and Business Media LLC}, author={Fawzi, H. and Saunderson, J. and Parrilo, P.A.}, year={2018}, month={Mar}, pages={259?96} } @misc{cifuentes2017local, title={On the local stability of semidefinite relaxations}, author={Diego Cifuentes and Sameer Agarwal and Pablo A. Parrilo and Rekha R. Thomas}, year={2017}, eprint={1710.04287}, archivePrefix={arXiv}, primaryClass={math.OC} } @book {MR41:1976, AUTHOR = {Federer, H.}, TITLE = {Geometric measure theory}, SERIES = {Die Grundlehren der mathematischen Wissenschaften, Band 153}, PUBLISHER = {Springer-Verlag New York Inc., New York}, YEAR = {1969}, PAGES = {xiv+676}, MRCLASS = {28.80 (26.00)}, MRNUMBER = {41 \#1976}, MRREVIEWER = {J. E. Brothers}, } @article {Fei:95, AUTHOR = {FEIGE, U.}, TITLE = {Randomized graph products, chromatic numbers, and the {L}ov\'asz $\vartheta$-function}, JOURNAL = {Combinatorica}, FJOURNAL = {Combinatorica. An International Journal on Combinatorics and the Theory of Computing}, VOLUME = {17}, YEAR = {1997}, NUMBER = {1}, PAGES = {79--90}, ISSN = {0209-9683}, MRCLASS = {05C35 (90C27)}, MRNUMBER = {99f:05059}, } @article {FeiKrau:00, AUTHOR = {Feige, U. and Krauthgamer, R}, TITLE = {Finding and certifying a large hidden clique in a semi-random graph}, JOURNAL = {Random Structures and Algorithms}, VOLUME = {16}, YEAR = {2000}, NUMBER = {2}, PAGES = {195--202}, } @ARTICLE {FeOttSth:84, author = "G.S. FELL and J.M. OTTOWAY and P.R. STHAPIT", title = "Determination of lead in natural and tap waters by flame atomic-fluorescence spectrometry", journal = "Analyst", year = "1984", volume = "109", pages = "1061"} @TECHREPORT {Fen:51, author = "W. FENCHEL", title = "Convex Cones, Sets and Functions", address = "Princeton University", note = "mimeographed lecture notes", year = "1951"} @article{FerMesMore:98, author = "M.C. Ferris and M.P. MESNIER and J.J. Mor\'{e}", title = "{NEOS} and {Condor}: {Solving} Optimization Problems Over the {Internet}", journal = toms, volume = 26, number = 1, pages = "1-18", year = 2000, bibdate = "Fri Dec 8 07:48:19 GMT 2000" } @book {MR2383072, AUTHOR = {Ferris, M.C. and Mangasarian, O.L. and Wright, S.J.}, TITLE = {Linear programming with {MATLAB}}, SERIES = {MPS/SIAM Series on Optimization}, VOLUME = {7}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {2007}, PAGES = {xii+266}, ISBN = {978-0-898716-43-6}, MRCLASS = {90-01 (90-04 90C05)}, MRNUMBER = {MR2383072 (2008k:90002)}, } @techreport{Ferreiragoncalvesoliveira:10, AUTHOR = "O.P. FERREIRA, M.L.N. GONCALVES, P.R. OLIVEIRA", TITLE = "Local convergence analysis of {G}auss-{N}ewton's method under majorant condition", TYPE = "Technical Report", NUMBER = "", INSTITUTION = "Universidade Federal de Rio de Janeiro", ADDRESS = "Rio de Janeiro, Brazil", YEAR = "2010" } @BOOK {Fia:83, author = "A.V. Fiacco", title = "Introduction to Sensitivity and Stability Analysis in Nonlinear Programming", publisher = "Academic Press", series = "Mathematics in Science and Engineering", volume = "165", year = "1983"} @BOOK {FS, author = "A.V. Fiacco", title = "Introduction to Sensitivity and Stability Analysis in Nonlinear Programming", publisher = "Academic Press", series = "Mathematics in Science and Engineering", volume = "165", year = "1983"} @BOOK {FiaKor:83, author = "A.V. Fiacco and G.P. K.O. KORTANEK (eds.)", title = "Semi-infinite Programming and Applications", publisher = "Springer-Verlag", year = "1983", address = "Berlin"} @BOOK {FiaMc:68, author = "A.V. Fiacco and G.P. McCORMICK", title = "Nonlinear Programming: Sequential Unconstrained Minimization Techniques", publisher = "John Wiley \& Sons", year = "1968", address = "New York, NY"} @book {MR91d:90089, author = "A.V. Fiacco and G.P. McCormick", TITLE = {Nonlinear programming}, EDITION = {Second (First 1968)}, NOTE = {Sequential unconstrained minimization techniques}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {1990}, PAGES = {xvi+210}, ISBN = {0-89871-254-8}, MRCLASS = {90C30 (01A75 90-02)}, MRNUMBER = {91d:90089}, } @article {MR2055352, AUTHOR = {Fiedler, Miroslav}, TITLE = {Complementary basic matrices}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {384}, YEAR = {2004}, PAGES = {199--206}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A57}, MRNUMBER = {MR2055352}, } @article {MR2022283, AUTHOR = {Fiedler, Miroslav}, TITLE = {Basic matrices}, NOTE = {Special issue on the Combinatorial Matrix Theory Conference (Pohang, 2002)}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {373}, YEAR = {2003}, PAGES = {143--151}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A23}, MRNUMBER = {MR2022283 (2004k:15020)}, } @ARTICLE {FiBuRe:87, author = "G. Finke and R.E. Burkard and F. Rendl", title = "Quadratic assignment problems", journal = adm, year = "1987", volume = "31", pages = "61-82"} @incollection {MR878775, AUTHOR = {Finke, G. and Burkard, R.E. and Rendl, F.}, TITLE = {Quadratic assignment problems}, BOOKTITLE = {Surveys in combinatorial optimization (Rio de Janeiro, 1985)}, SERIES = {North-Holland Math. Stud.}, VOLUME = {132}, PAGES = {61--82}, PUBLISHER = {North-Holland}, ADDRESS = {Amsterdam}, YEAR = {1987}, MRCLASS = {90C09 (90B05)}, MRNUMBER = {MR878775 (88e:90057)}, MRREVIEWER = {Peter Brucker}, } @ARTICLE{Finsler:37, AUTHOR = {P. Finsler}, TITLE = {\"{U}ber das {V}orkommen definiter und semidefiniter {F}ormen in {S}charen quadratischer {F}ormen}, JOURNAL = {Comment. Math. Helv.}, YEAR = {1937}, volume = {9}, number = {}, pages = {188--192}, month = {}, note = {}, abstract = {}, keywords = {}, source = {}, } @book {MR56:1159, AUTHOR = {FISHER, S.D. and JEROME, J.W.}, TITLE = {Minimum norm extremals in function spaces}, NOTE = {With applications to classical and modern analysis, Lecture Notes in Mathematics, Vol. 479}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1975}, PAGES = {viii+209}, MRCLASS = {49-02}, MRNUMBER = {56 #1159}, MRREVR = {Werner Krabs}, } @techreport{FisherSW:07, AUTHOR = "FISCHER, A. and SHUKLA, P.K. and WANG, M.", TITLE = "On the inexactness level of robust {L}evenberg-{M}arquardt methods", TYPE = "Technical Report", NUMBER = "", INSTITUTION = "Chinese Academy of Sciences", ADDRESS = "Beijing, China", YEAR = "2007" } @article {MR2002j:90109, AUTHOR = {Fischer, Andreas}, TITLE = {Modified {W}ilson's method for nonlinear programs with nonunique multipliers}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {24}, YEAR = {1999}, NUMBER = {3}, PAGES = {699--727}, ISSN = {0364-765X}, MRCLASS = {90C53 (90C30)}, MRNUMBER = {2002j:90109}, MRREVIEWER = {E. Marchi}, } @ARTICLE {Fla:86, author = "J. FLACHS", title = "On the generation of updates for quasi-{N}ewton methods", journal = "J. Optim. Theory Appl.", year = "1986", volume = "48", pages = "379-417"} @INCOLLECTION {Flet:70a, author = "R. Fletcher", title = "A class of methods for nonlinear programming with termination and convergence properties", booktitle = "Integer and Nonlinear Programming", publisher = "North-Holland", year = "1970", editor = "J. Abadie", address = "Amsterdam"} @ARTICLE {Flet:70b, author = "R. Fletcher", title = "A new approach to variable metric algorithms", journal = "Comput. J.", year = "1970", volume = "13", pages = "317-322"} @TECHREPORT {Flet:71, author = "R. Fletcher", title = "A modified {M}arquardt subroutine for nonlinear least squares", institution = "A.E.R.E. Harwell", year = "1971", number = "TP 476"} @BOOK {Flet:80, author = "R. Fletcher", title = "Practical Methods of Optimization, vol. 1, Unconstrained Optimization", publisher = "John Wiley \& Sons", year = "1980", address = "New York, NY"} @BOOK {Flet:81a, author = "R. Fletcher", title = "Practical Methods of Optimization, vol. 2, Constrained Optimization", publisher = "John Wiley \& Sons", year = "1981", address = "Chichester"} @INCOLLECTION {Flet:81b, author = "R. Fletcher", title = "Methods for nonlinear constraints", booktitle = "Nonlinear Optimization 1981", publisher = "Academic Press", year = "1981", editor = "M.J.D. Powell", pages = "185-212", address = "New York, NY"} @ARTICLE {Flet:81c, author = "R. Fletcher", title = "A nonlinear programming problem in statistics (educational testing)", journal = "SIAM J. Sci. Stat. Comput.", year = "1981", volume = "2", pages = "257-267"} @ARTICLE {Flet:85, author = "R. Fletcher", title = "Semi-definite matrix constraints in optimization", journal = SJCO, year = "1985", volume = "23", pages = "493-513"} @BOOK {Flet:87, author = "R. Fletcher", title = "Practical Methods of Optimization", publisher = "John Wiley \& Sons", year = "1987", address = "New York, NY"} @BOOK{fletcher87, AUTHOR = "R. Fletcher", TITLE = "Practical Methods of Optimization", PUBLISHER = "John Wiley \& Sons", YEAR = 1987, EDITION = "second", NOTE = "Intermediate. Nice overall survey." } @ARTICLE {Flet:91, author = "R. Fletcher", title = "A new variational result for quasi-{N}ewton formulae", journal = siopt, year = "1991", volume = "1", pages = "18-21"} @ARTICLE {FlePow:63, author = "R. Fletcher and M.J.D. Powell", title = "A rapidly convergent descent method for minimization", journal = "Comput. J.", year = "1963", volume = "6", pages = "163-168"} @TECHREPORT {FleXu:85, author = "R. Fletcher and C. XU", title = "Hybrid methods for nonlinear least squares", institution = "Department of Mathematical Sciences, University of Dundee", year = "1985", number = "NA/92"} @article {FlJa:93, author = "O.E. Flippo and B. Jansen", title = "Duality and sensitivity in nonconvex quadratic optimization over an ellipsoid", volume = "94", number = "1", journal = "European J. Oper. Res.", year = "1996", pages = "167-178"} @book {MR97a:90004, TITLE = {State of the art in global optimization}, EDITOR = {FLOUDAS, C.A. and Pardalos, P.M.}, NOTE = {Computational methods and applications, Papers from the conference held at Princeton University, Princeton, New Jersey, April 28--30, 1995}, PUBLISHER = {Kluwer Academic Publishers}, ADDRESS = {Dordrecht}, YEAR = {1996}, PAGES = {x+651}, ISBN = {0-7923-3838-3}, MRCLASS = {90-06 (65K05 90C30)}, MRNUMBER = {97a:90004}, } @book {MR96f:90013, TITLE = {State of the art in global optimization: computational methods and applications}, EDITOR = {Floudas, C. A. and Pardalos, P. M.}, NOTE = {Papers from the conference held at Princeton University, Princeton, New Jersey, April 28--30, 1995, J. Global Optim. {\bf 7} (1995), no. 2}, PUBLISHER = {Kluwer Academic Publishers Group}, ADDRESS = {Dordrecht}, YEAR = {1995}, PAGES = {i--ii and 113--227}, ISSN = {0925-5001}, CODEN = {JGOPEO}, MRCLASS = {90-06 (65K05 90C30)}, MRNUMBER = {96f:90013}, } @book {MR96f:90005, TITLE = {State of the art in global optimization: computational methods and applications}, EDITOR = {Floudas, C. A. and Pardalos, P. M.}, NOTE = {Selected papers from the conference held at Princeton University, Princeton, New Jersey, April 28--30, 1995, J. Global Optim. {\bf 7} (1995), no. 4}, PUBLISHER = {Kluwer Academic Publishers Group}, ADDRESS = {Dordrecht}, YEAR = {1995}, PAGES = {i--iv and 337--454}, ISSN = {0925-5001}, CODEN = {JGOPEO}, MRCLASS = {90-02 (65K05 90-06 90C30)}, MRNUMBER = {96f:90005}, } @book {MR95d:90006, TITLE = {Conference on {C}omputational {M}ethods in {G}lobal {O}ptimization. {I}{I}}, EDITOR = {Floudas, C. A. and Pardalos, P. M.}, NOTE = {Papers from the conference held at Princeton University, Princeton, New Jersey, May 10--11, 1991, J. Global Optim. {\bf 2} (1992), no. 3}, PUBLISHER = {Kluwer Academic Publishers Group}, ADDRESS = {Dordrecht}, YEAR = {1992}, PAGES = {i--iv and 229--311}, ISSN = {0925-5001}, CODEN = {JGOPEO}, MRCLASS = {90-06 (65K05 90C30)}, MRNUMBER = {95d:90006}, } @book {MR95d:90005, TITLE = {Conference on {C}omputational {M}ethods in {G}lobal {O}ptimization. {I}}, EDITOR = {Floudas, C. A. and Pardalos, P. M.}, NOTE = {Papers from the conference held at Princeton University, Princeton, New Jersey, May 10--11, 1991, J. Global Optim. {\bf 2} (1992), no. 1}, PUBLISHER = {Kluwer Academic Publishers Group}, ADDRESS = {Dordrecht}, YEAR = {1992}, PAGES = {iii--vi and 1--112}, ISSN = {0925-5001}, CODEN = {JGOPEO}, MRCLASS = {90-06 (90C30)}, MRNUMBER = {95d:90005}, } @book {MR92i:90010, TITLE = {Recent advances in global optimization}, EDITOR = {Floudas, Christodoulos A. and Pardalos, Panos M.}, NOTE = {Papers from the conference held at Princeton University, Princeton, New Jersey, May 10--11, 1991}, PUBLISHER = {Princeton University Press}, ADDRESS = {Princeton, NJ}, YEAR = {1992}, PAGES = {x+633}, ISBN = {0-691-08740-7; 0-691-02527-4}, MRCLASS = {90-06 (65K10 90C10 90C30 90C90)}, MRNUMBER = {92i:90010}, } @book {MR2001a:90001, AUTHOR = {Floudas, Christodoulos A.}, TITLE = {Deterministic global optimization}, NOTE = {Theory, methods and applications}, PUBLISHER = {Kluwer Academic Publishers}, ADDRESS = {Dordrecht}, YEAR = {2000}, PAGES = {xviii+739}, ISBN = {0-7923-6014-1}, MRCLASS = {90-02 (90C26 90C57 90C59)}, MRNUMBER = {2001a:90001}, MRREVIEWER = {Harold P. Benson}, } @BOOK {FoVan:82, author = "J.D. FOLEY and A. {VAN DAM}", title = "Fundamentals of Interactive Computer Graphics", publisher = "Addison-Wesley", year = "1982", series = "Reading", address = "Massachusetts"} @TECHREPORT {Fon:83, author = "R. FONTECILLA", title = "The lack of positive definiteness in the {H}essian in constrained optimization", institution = "Department of Computer Science, University of Maryland", year = "1983", number = "TR 1334", address = "College Park, Maryland"} @TECHREPORT {FonSteiTa:83, author = "R. FONTECILLA and T. Steihaug and R.A. Tapia", title = "A convergence theory for a class of quasi-{N}ewton methods for constrained optimization", institution = "Department of Mathematical Sciences, Rice University", year = "1983", number = "TR83-15", address = "Houston, TX"} @ARTICLE {ConTa:91, author = "M. CONTRERAS and R.A. Tapia", title = "Sizing the {BFGS} and {DFP} updates: A numerical study", year = "1993", volume = "78", journal = jota, number = "1" } @article{DBLP:journals/corr/FountoulakisGM16, author = {K. Fountoulakis and D.F. Gleich and M.W. Mahoney}, title = {An optimization approach to locally-biased graph algorithms}, journal = {CoRR}, volume = {abs/1607.04940}, year = {2016}, url = {http://arxiv.org/abs/1607.04940}, archivePrefix = {arXiv}, eprint = {1607.04940}, timestamp = {Wed, 07 Jun 2017 14:43:04 +0200}, biburl = {https://dblp.org/rec/bib/journals/corr/FountoulakisGM16}, bibsource = {dblp computer science bibliography, https://dblp.org} } @ARTICLE{2016arXiv160201886F, author = {{Fountoulakis}, K. and {Roosta-Khorasan}, F. and {Shun}, J. and {Cheng}, X. and {Mahoney}, M.W.}, title = "{Variational Perspective on Local Graph Clustering}", journal = {ArXiv e-prints}, archivePrefix = "arXiv", eprint = {1602.01886}, primaryClass = "math.OC", keywords = {Mathematics - Optimization and Control}, year = 2016, month = feb, adsurl = {http://adsabs.harvard.edu/abs/2016arXiv160201886F}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } @ARTICLE {Fourier:1826, author = "J.B.J. Fourier", title = "Solution d'une question particuliere du calcul des ineqalites", year = "1826", volume = "", journal = "Bull. sci. Soc. Philom.", pages ="99-100", number = "" } @article {MR0334869, AUTHOR = {Grattan-Guinness, I.}, TITLE = {Joseph {F}ourier's anticipation of linear programming}, JOURNAL = {Operational Res. Quart.}, FJOURNAL = {Operational Research Quarterly}, VOLUME = {21}, YEAR = {1970}, PAGES = {361--364}, ISSN = {0030-3623}, MRCLASS = {90-03}, MRNUMBER = {0334869 (48 \#13187)}, MRREVIEWER = {Kenneth May}, } @ARTICLE {For:78, author = "B. FORD", title = "Parameters for the environment for transportable numerical software", journal = "TOMS", year = "1978", volume = "4", pages = "100-103"} @ARTICLE {ForPen:96, author = "W.F. FORD and J.A. PENNLINE", title = "Accelerated convergence in {N}ewton's method", journal = "SIAM Review", year = "1996", volume = "38", pages = "658-659"} @BOOK {For:88, author = "F. FORG{\'{O}}", title = "Nonconvex Programming", publisher = "Akad{\'{e}}miai Kiad{\'{o}}", year = "1988", address = "Budapest"} @article {MR1980444, AUTHOR = "A. FORSGREN and P.E. GILL and M.H. Wright", TITLE = {Interior methods for nonlinear optimization}, JOURNAL = {SIAM Rev.}, FJOURNAL = {SIAM Review}, VOLUME = {44}, YEAR = {2002}, NUMBER = {4}, PAGES = {525--597 (electronic) (2003)}, ISSN = {0036-1445}, MRCLASS = {90C51 (65K05 90-02 90C30)}, MRNUMBER = {MR1980444 (2004c:90098)}, MRREVIEWER = {E. Alper Y{\i} ld{\i} r{\i} m}, } @article{ipm:Forsgren4, AUTHOR = "A.\ FORSGREN and P.E.\ GILL", TITLE = "Primal-dual interior methods for nonconvex nonlinear programming", TYPE = "Technical Report", NUMBER = "NA 96-3", INSTITUTION = "Dept. of Mathematics, University of California", ADDRESS = "San Diego", YEAR = "1998", JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, volume = "8", pages = "1132-1152"} @article{ipm:Forsgren3, AUTHOR = "A.\ FORSGREN and P.E.\ GILL and J.R. SHINNERL", TITLE = "Stability of symmetric ill--conditioned systems arising in interior methods for constrained optimization", TYPE = "Technical Report", NUMBER = "NA 96-3", INSTITUTION = "Dept. of Mathematics, University of California", ADDRESS = "San Diego", YEAR = "1996", JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, volume = "17", pages = "187-211"} @article {MR94g:90038, AUTHOR = {FORREST, J. J. and Goldfarb, D.}, TITLE = {Steepest-edge simplex algorithms for linear programming}, JOURNAL = mprog, FJOURNAL = {Mathematical Programming}, VOLUME = {57}, YEAR = {1992}, NUMBER = {3, Ser. A}, PAGES = {341--374}, ISSN = {0025-5610}, CODEN = {MHPGA4}, } @article {MR2177779, AUTHOR = {FORTIN, C.}, TITLE = {Computing the local-nonglobal minimizer of a large scale trust-region subproblem}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {16}, YEAR = {2005}, NUMBER = {1}, PAGES = {263--296 (electronic)}, ISSN = {1052-6234}, MRCLASS = {90C20 (90C30)}, MRNUMBER = {MR2177779 (2006g:90076)}, MRREVIEWER = {Qin Ni}, } @article {Foster:03, AUTHOR = {L.V. FOSTER}, TITLE = {Solving Rank-Deficient and Ill-posed Problems Using UTV and QR Factorizations}, journal = simax, VOLUME = {25}, YEAR = {2003}, NUMBER = {2}, PAGES = {582--600}, } @inproceedings {MR820987, AUTHOR = {Freund, R.M.}, TITLE = {Postoptimal analysis of a linear program under simultaneous changes in matrix coefficients}, NOTE = {Mathematical programming, I}, JOURNAL = {Math. Programming Stud.}, FJOURNAL = {Mathematical Programming Study}, NUMBER = {24}, volume = {}, YEAR = {1985}, PAGES = {1--13}, ISSN = {0303-3929}, MRCLASS = {90C05 (90C31)}, MRNUMBER = {820987}, MRREVIEWER = {T. Gal}, } @article {FrJaSch:96, AUTHOR = {FREUND, R.W. and JARRE, F. and SCHAIBLE, S.}, TITLE = {On self-concordant barrier functions for conic hulls and fractional programming}, JOURNAL = mprog, FJOURNAL = {Mathematical Programming}, VOLUME = {74}, YEAR = {1996}, NUMBER = {3, Ser. A}, PAGES = {237--246}, ISSN = {0025-5610}, CODEN = {MHPGA4}, } @phdthesis{ordonez:02, AUTHOR= "ORD{\'O}{\~N}EZ, F.", year = "2002", title = "On the Explanatory Value of Condition Numbers for Convex Optimization: Theoretical Issues and Computational Experience", school = "MIT", address = "Cambridge, MA", } @article {OrdFreund, AUTHOR = { ORD{\'O}{\~N}EZ, F. and FREUND, R.M.}, TITLE = {Computational experience and the explanatory value of condition measures for linear optimization}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {14}, YEAR = {2003}, NUMBER = {2}, PAGES = {307--333 (electronic)}, ISSN = {1052-6234}, MRCLASS = {90C60 (90C05)}, MRNUMBER = {MR2048168 (2005f:90175)}, MRREVIEWER = {Joaqu{\'{\i}}m J. J{\'u}dice}, } @article {MR2125143, AUTHOR = {Freund, R.M. and Ord{\'o}{\~n}ez, F.}, TITLE = {On an extension of condition number theory to nonconic convex optimization}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {30}, YEAR = {2005}, NUMBER = {1}, PAGES = {173--194}, ISSN = {0364-765X}, MRCLASS = {90C60 (90C22 90C25)}, MRNUMBER = {MR2125143 (2005k:90227)}, MRREVIEWER = {Javier F. Pe{\~n}a}, } @article{Freund96f, author = {R.W. FREUND and F. JARRE}, title = {A {QMR}-based interior-point algorithm for solving linear programs}, journal = {Mathematical Programming, Series~B}, volume = {76}, pages = {183--210}, year = {1996} } @article{Freund93, author = {R.W. FREUND and M.H. GUTKNECHT and N.M. NACHTIGAL}, title = {An Implementation of the Look-Ahead {L}anczos Algorithm for Non-{H}ermitian Matrices}, journal = {SIAM Journal on Scientific Computing}, volume = {14}, pages = {137--158}, year = {1993} } @ARTICLE {FoGo:65, author = "G.E. FORSYTHE and G.H. Golub", TITLE = {On the stationary values of a second-degree polynomial on the unit sphere}, JOURNAL = {J. Soc. Indust. Appl. Math.}, VOLUME = {13}, YEAR = {1965}, PAGES = {1050--1068}, MRCLASS = {65.30}, MRNUMBER = {33 \#3453}, MRREVIEWER = {A. V. Balakrishnan}, } @BOOK {Fos:79, author = "L. FOSDICK", title = "Performance Evaluation of Numerical Software", publisher = "North-Holland", year = "1979", address = "Amsterdam"} @article {MR90b:65019, AUTHOR = {FRALEY, C.}, TITLE = {Computational behavior of {G}auss-{N}ewton methods}, JOURNAL = {SIAM J. Sci. Statist. Comput.}, FJOURNAL = {Society for Industrial and Applied Mathematics. Journal on Scientific and Statistical Computing}, VOLUME = {10}, YEAR = {1989}, NUMBER = {3}, PAGES = {515--532}, ISSN = {0196-5204}, CODEN = {SIJCD4}, MRCLASS = {65D10 (65H10 65K05 90C30)}, MRNUMBER = {90b:65019}, } address = "New York, NY"} @techreport{Fraley:89, AUTHOR = "FRALEY, C", TITLE = "Software performance on nonlinear least-squares problems", TYPE = "Technical Report", NUMBER = "STAN-CS-89", INSTITUTION = "Stanford University", ADDRESS = "Stanford, Calif.", YEAR = "1989", } @article {MR2085947, AUTHOR = {FRANGIONI, A. and GENTILE, C.}, TITLE = {New preconditioners for {KKT} systems of network flow problems}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {14}, YEAR = {2003}, NUMBER = {3}, PAGES = {894--913 (electronic)}, ISSN = {1052-6234}, MRCLASS = {90C51 (65F10 90C05 90C35)}, MRNUMBER = {MR2085947 (2005h:90165)}, MRREVIEWER = {Michal Ko{\v{c}}vara}, } @ARTICLE {FrSchna:84, author = "P.D. FRANK and R.B. Schnabel", title = "Tensor methods for nonlinear equations", journal = "SIAM J. Numer. Anal.", year = "1984", volume = "21", number = "5", pages = "815-843"} @article {FW-alg, AUTHOR = {Frank, M. and Wolfe, P.}, TITLE = {An algorithm for quadratic programming}, JOURNAL = {Naval Res. Logist. Quart.}, FJOURNAL = {Naval Research Logistics Quarterly}, VOLUME = {3}, YEAR = {1956}, PAGES = {95--110}, ISSN = {0028-1441}, MRCLASS = {90.0X}, MRNUMBER = {0089102 (19,619e)}, } @incollection {MR1672237, AUTHOR = {Francfort, G.A. and Marigo, J.-J.}, TITLE = {Cracks in fracture mechanics: a time indexed family of energy minimizers}, BOOKTITLE = {Variations of domain and free-boundary problems in solid mechanics ({P}aris, 1997)}, SERIES = {Solid Mech. Appl.}, VOLUME = {66}, PAGES = {197--202}, PUBLISHER = {Kluwer Acad. Publ., Dordrecht}, YEAR = {1999}, MRCLASS = {73M25 (73V25)}, MRNUMBER = {1672237}, DOI = {10.1007/978-94-011-4738-5_23}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/978-94-011-4738-5_23}, } @INCOLLECTION {FrSchna:87, author = "P.D. FRANK and R.B. Schnabel", title = "Solving systems of nonlinear equations by tensor methods", booktitle = "The State of the Art in Numerical Analysis", publisher = "Clarendon Press", year = "1987", editor = "A. Iserles and M.J.D. Powell", pages = "245-271", address = "Oxford"} @TECHREPORT {FrMeVa:85, author = "B.A. FREEDMAN and M.S. MEKETON and R.J. Vanderbei", title = "A modification of {K}armarkar's linear programming algorithm", institution = "AT\&T Bell Laboratories", year = "1985", address = "Holmdel, NJ"} @BOOK{Friedman90, author = {J. W. Friedman}, title = {Game theory with applications to economics}, series = {}, volume = {}, publisher = {Oxford University Press}, address = {New York, {NY}}, year = {1990} } @TECHREPORT {FrJa:93, author = "R.W. FREUND and F. JARRE", title = "An interior-point method for convex fractional programming", institution = "AT\&T Bell Laboratories", number = "Manuscript No. 93-03", year = "1993", address = "Murray Hill, NJ"} @TECHREPORT {FrJaSch:94, author = "R.W. FREUND and F. JARRE and S. SCHAIBLE", title = "On interior-point methods for fractional programs and their convex reformulation", institution = "AT\&T Bell Laboratories", number = "Manuscript No. 94-17", year = "1994", keywords = "fractional programming; interior points", address = "Murray Hill, NJ"} @ARTICLE {int:Freund100, author = "R.M. FREUND and S. MIZUNO", title = "Interior point methods: current status and future directions", journal = "OPTIMA", year = "1996", volume = "51"} @ARTICLE {FrisAd:00, author = "M.I. FRISWELL and S. ADHIKARI", title = "Derivatives of complex eigenvectors using {N}elson's method", journal = "AIAA Journal", year = "2000", volume = "38", number = "12", pages = "2355-2357"} @ARTICLE {FrFuKi:92, author = "B. FRITZSCHE and S. FUCHS and B. KIRSTEIN", title = "On an inverse problem of entropy optimization and related questions", journal = "Optimization", year = "1992", volume = "26", pages = "359-384"} @ARTICLE {fur:10, author = "S. Furuichi and M. Lin", title = "A matrix trace inequality and its application", journal = laa, year = "2010", volume = "433", pages = "1324-1328"} @ARTICLE {M.Lin:10, author = "M. Lin", title = "Comparison of the trace of two inverse matrices", journal = "IMAGE", year = "2010", volume = "Problem 45.5", pages = "Fall"} %GGGGGGGGGG @ARTICLE {Gal:86, author = "T. GAL", title = "Shadow prices and sensitivity analysis in linear programming under degeneracy, state-of-the-art-survey", journal = "OR Spektrum", year = "1986", volume = "8", pages = "59-71", kwds = "sensitivity analysis" } @article {MR2160671, AUTHOR = {Gal{\'a}ntai, A.}, TITLE = {On the rate of convergence of the alternating projection method in finite dimensional spaces}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {310}, YEAR = {2005}, NUMBER = {1}, PAGES = {30--44}, ISSN = {0022-247X}, CODEN = {JMANAK}, MRCLASS = {65J15 (47A50)}, MRNUMBER = {2160671 (2006m:65101)}, DOI = {10.1016/j.jmaa.2004.12.050}, URL = {http://dx.doi.org/10.1016/j.jmaa.2004.12.050}, } @article {MR0286458, AUTHOR = {GALE, D.}, TITLE = {The jeep once more or jeeper by the dozen}, JOURNAL = {Amer. Math. Monthly}, FJOURNAL = {The American Mathematical Monthly}, VOLUME = {77}, YEAR = {1970}, PAGES = {493--501}, ISSN = {0002-9890}, MRCLASS = {90.30}, MRNUMBER = {MR0286458 (44 \#3667)}, MRREVIEWER = {D. Hochst{\"a}dter}, } @INCOLLECTION {GaKuTu:51, author = "D. Gale and H.W. Kuhn and A.W. Tucker", title = "Linear programming and the theory of games", booktitle = "Activity Analysis of Production and allocation", publisher = "Wiley", year = "1951", editor = "T.C. Koopmans", address = "New York"} @techreport{Gan:78, author = "W. GANDER", title = "On the linear least squares problem with a quadratic constraint", institution = "Department of Computer Science, Stanford University", note = "Habilitationsschrift ETH Zurich", year = "1978", number = "STAN-CS-78-697", address = "Stanford, CA"} @ARTICLE {Gan:81, author = "W. GANDER", title = "Least squares with a quadratic constraint", journal = "Numer. Math.", year = "1981", volume = "36", pages = "291-307", note = "This is the abbreviated version of the technical report published in 1978"} @TECHREPORT{GaGoMa:88, AUTHOR = "W. GANDER and G. Golub and U. von MATT ", TITLE = "A Constrained Eigenvalue Problem", INSTITUTION = "Institut fur Informatik ETH-Zentrum, CH-8092 Zurich Switzerland", YEAR = 1988 } \@ARTICLE {GaGoMa:89, author = "W. GANDER and G.H. Golub and U. von MATT", TITLE = {A constrained eigenvalue problem}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {114/115}, YEAR = {1989}, PAGES = {815--839}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A18 (15A23)}, MRNUMBER = {90e:15008}, MRREVIEWER = {Lajos L{\'a}szl{\'o}}, } @incollection {MR92k:65067, AUTHOR = {Gander, Walter and Golub, Gene H. and von Matt, Urs}, TITLE = {A constrained eigenvalue problem}, BOOKTITLE = {Numerical linear algebra, digital signal processing and parallel algorithms (Leuven, 1988)}, SERIES = {NATO Adv. Sci. Inst. Ser. F Comput. Systems Sci.}, VOLUME = {70}, PAGES = {677--686}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1991}, MRCLASS = {65F15}, MRNUMBER = {92k:65067}, } @article {MR638124, AUTHOR = {Kre\u\i\! n, M.G. and Na\u\i\! mark, M.A.}, TITLE = {The method of symmetric and {H}ermitian forms in the theory of the separation of the roots of algebraic equations}, NOTE = {Translated from the Russian by O. Boshko and J. L. Howland}, JOURNAL = {Linear and Multilinear Algebra}, FJOURNAL = {Linear and Multilinear Algebra}, VOLUME = {10}, YEAR = {1981}, NUMBER = {4}, PAGES = {265--308}, ISSN = {0308-1087}, MRCLASS = {12D10 (12-02 12E12 15A63)}, MRNUMBER = {638124}, URL = {https://doi.org/10.1080/03081088108817420}, } @book {MR1908601, AUTHOR = {Gantmacher, F. P. and Krein, M. G.}, TITLE = {Oscillation matrices and kernels and small vibrations of mechanical systems}, EDITION = {Revised}, NOTE = {Translation based on the 1941 Russian original, Edited and with a preface by Alex Eremenko}, PUBLISHER = {AMS Chelsea Publishing, Providence, RI}, YEAR = {2002}, PAGES = {viii+310}, ISBN = {0-8218-3171-2}, MRCLASS = {34L05 (15A18 34A30 34B05 45B05 47G10 74H45)}, MRNUMBER = {1908601}, DOI = {10.1090/chel/345}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1090/chel/345}, } @BOOK {Ga:59, author = "F.R. Gantmacher", title = "The Theory of Matrices", publisher = "Chelsea", year = "1959", Note = "Vol. I and II (transl.)", address = "New York"} @TECHREPORT {GaHiMo:80, author = "B.S. GARBOW and K.E. HILLSTROM and J.J. Mor\'{e}", title = "User guide for {MINPACK}-1", institution = "Argonne National Labs", year = "1980", number = "ANL-80-74", address = "Argonne, IL", note = "Available from National Technical Information Service, Springfield, Virginia"} @ARTICLE {GaHiMo:81a, author = "B.S. GARBOW and K.E. HILLSTROM and J.J. Mor\'{e}", title = "Testing unconstrained optimization software", journal = "TOMS", year = "1981", volume = "7", number = "1", pages = "17-41"} @ARTICLE {GaHiMo:81b, author = "B.S. GARBOW and K.E. HILLSTROM and J.J. Mor\'{e}", title = "Fortran subroutines for testing unconstrained optimization software", journal = "TOMS", year = "1981", volume = "7", pages = "136-140"} @book {MR2027633, AUTHOR = {GASS, S.I.}, TITLE = {Linear programming}, EDITION = {fifth}, NOTE = {Methods and applications}, PUBLISHER = {Dover Publications Inc.}, ADDRESS = {Mineola, NY}, YEAR = {2003}, PAGES = {xii+532}, ISBN = {0-486-43284-X}, MRCLASS = {90-02 (90C05)}, MRNUMBER = {MR2027633 (2004i:90002)}, URL = {http://links.jstor.org.proxy.lib.uwaterloo.ca/sici?sici=0002-9890(196002)67:2<197:LPMAA>2.0.CO;2-M&origin=MSN}, } @techreport{garclima:04, AUTHOR = "S. PEREZ-GARCIA and M. GONZALEZ-LIMA", TITLE = "On a non-inverse approach for solving the linear systems arising in primal-dual interior point methods for linear programming", TYPE = "Technical Report", NUMBER = "2004-01", INSTITUTION = "Simon Bolivar University", ADDRESS = "Center for Statistical and Mathematical Software, Caracas, Venezuela", YEAR = "2004", } @ARTICLE {DomMan:06, author = "J. DOMINGUEZ and M.D. GONZALEZ-LIMA", title = "A primal-dual interior-point algorithm for quadratic programming", journal = "Numerical Algorithms", year = "2006", volume = "105", URL = "http://dx.doi.org/10.1007/s11075-006-9019-5", pages = "1-30"} @ARTICLE {GarMan:76, author = "U.M. {GARCIA-PALOMARES} and O.L. Mangasarian", title = "Superlinearly convergent quasi-{N}ewton algorithms for nonlinearly constrained optimization problems", journal = "Math. Prog.", year = "1976", volume = "11", pages = "1-13"} @ARTICLE {GaGeMoNeSchn:86, author = "T.J. GARDNER and I.M. GERARD and C.R. MOWERS and E. NEMETH and R.B. Schnabel", title = "{DPUP: A} distributed processing utilities package", journal = "SIGNUM Newsletter ", year = "1986", volume = "21", pages = "5-19"} @BOOK {GJ:79, author = "M.R. GAREY and D.S. Johnson", title = "Computers and Intractability: A guide to the theory of NP--completeness", publisher = "Freeman", year = "1979", address = "San Francisco"} @BOOK {GarNem:72, author = "R.S. GARFINKEL and G.L. NEMHAUSER", title = "Integer Programming", publisher = "John Wiley \& Sons", year = "1972", address = "New York, NY"} @book {MR82e:01122d, AUTHOR = {GAU{\SS}, C.F.}, TITLE = {Werke. {B}and {IV}}, NOTE = {Reprint of the 1873 original}, PUBLISHER = {Georg Olms Verlag}, ADDRESS = {Hildesheim}, YEAR = {1973}, PAGES = {viii+492}, MRCLASS = {01A75}, MRNUMBER = {82e:01122d}, MRREVIEWER = {C. J. Scriba}, } @article {MR929571, AUTHOR = {Gautschi, W. and Inglese, G.}, TITLE = {Lower bounds for the condition number of {V}andermonde matrices}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {52}, YEAR = {1988}, NUMBER = {3}, PAGES = {241--250}, ISSN = {0029-599X}, CODEN = {NUMMA7}, MRCLASS = {65F35 (15A12)}, MRNUMBER = {MR929571 (89b:65108)}, MRREVIEWER = {Ludwig Elsner}, } @book {MR96b:01038, AUTHOR = {GAU{\SS}, C.F.}, TITLE = {Theoria combinationis observationum erroribus minimis obnoxiae/{T}heory of the combination of observations least subject to errors}, SERIES = {Classics in Applied Mathematics}, VOLUME = {11}, NOTE = {Pars prior. Pars posterior. Supplementum/Part One. Part Two. Supplement, Dual Latin-English text, Translated and with an introduction and afterword by G. W. Stewart}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {1995}, PAGES = {xii+241}, ISBN = {0-89871-347-1}, MRCLASS = {01A75 (01A55)}, MRNUMBER = {96b:01038}, MRREVIEWER = {Zeno G. Swijtink}, } @article {MR0489903, AUTHOR = {Gauvin, J.}, TITLE = {A necessary and sufficient regularity condition to have bounded multipliers in nonconvex programming}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {12}, YEAR = {1977}, NUMBER = {1}, PAGES = {136--138}, ISSN = {0025-5610}, MRCLASS = {90C30}, MRNUMBER = {0489903}, MRREVIEWER = {Albert Buckley}, } @incollection {MR1358394, AUTHOR = {Gauvin, Jacques}, TITLE = {Degeneracy, normality, stability in mathematical programming}, BOOKTITLE = {Recent developments in optimization (Dijon, 1994)}, SERIES = {Lecture Notes in Econom. and Math. Systems}, VOLUME = {429}, PAGES = {136--141}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1995}, MRCLASS = {90C31 (65K05 90C05)}, MRNUMBER = {MR1358394}, } @article {MR589261, AUTHOR = {Gauvin, Jacques}, TITLE = {Shadow prices in nonconvex mathematical programming}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {19}, YEAR = {1980}, NUMBER = {3}, PAGES = {300--312}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C30}, MRNUMBER = {MR589261 (82b:90096)}, MRREVIEWER = {M. Yamasaki}, } @article {MR0441352, AUTHOR = {Gauvin, J. and Tolle, J.W.}, TITLE = {Differential stability in nonlinear programming}, JOURNAL = {SIAM J. Control Optimization}, FJOURNAL = {SIAM Journal on Control and Optimization}, VOLUME = {15}, YEAR = {1977}, NUMBER = {2}, PAGES = {294--311}, ISSN = {1095-7138}, MRCLASS = {90C30}, MRNUMBER = {MR0441352 (55 \#14215)}, MRREVIEWER = {Werner Krabs}, } @ARTICLE {Gay:79, author = "D.M. Gay", title = "Some convergence properties of {B}royden's method", journal = "SIAM J. Numer. Anal.", year = "1979", volume = "16", pages = "623-630"} @ARTICLE {Gay:81, author = "D.M. Gay", title = "Computing optimal locally constrained steps", journal = "SIAM J. Sci. Statist. Comput.", year = "1981", volume = "2", pages = "186-197"} @INPROCEEDINGS {Gay:83, author = "D.M. Gay", title = "A trust region approach to linearly constrained optimization", booktitle = "Proceedings of the Dundee Biennial Conference on Numerical Analysis", year = "1983"} @INCOLLECTION {GaySch:78, author = "D.M. Gay and R.B. Schnabel", title = "Solving systems of nonlinear equations by {B}royden's method with projected updates", booktitle = "Nonlinear Programming 3", publisher = "Academic Press", year = "1978", editor = "O.L. Mangasarian and R.R. Meyer and S.M. Robinson", pages = "245-281", address = "New York, NY"} @techreport{gow, AUTHOR = " Gay, D.M. and Overton, M.L. and Wright, M.H. ", TITLE = "A primal-dual interior method for nonconvex nonlinear programming", TYPE = "Technical Report", NUMBER = "97-4-08", INSTITUTION = "Bell Laboratories", ADDRESS = "Murray Hill, NJ", YEAR = "1997", } @ARTICLE {Geoff:68, author = "M. GEOFFRION", title = "Proper efficient and the theory of vector maximization", journal = jmaa, year = "1968", volume = "22", pages = "618-630"} @ARTICLE {Gerlach:94, author = "J. GERLACH", title = "Accelerated convergence in {N}ewton's method", journal = "SIAM Review", year = "1994", volume = "36", pages = "272-276"} @TECHREPORT {Gibbons, author = "L.E. GIBBONS and D.W. HEARN and P.M. Pardalos", title = "A continuous based heuristic for the maximum clique problem", institution = "DIMACS Series in Discrete Mathematics and Theoretical Computer Science", year = "1996", volume = "26", pages = "103-124"} @ARTICLE {GiGoMuSa:74, author = "P.E. GILL and G.H. Golub and W. MURRAY and M.A. Saunders", title = "On projected {N}ewton barrier methods for linear programming and an equivalence to Karmarkar's projective method", journal = "Math. Programming", year = "1986", volume = "36", number = "2", pages = "183--209"} @ARTICLE {GiMu:72, author = "P.E. GILL and W. MURRAY", title = "Quasi-{N}ewton methods for unconstrained optimization", journal = "IMA J. Appl. Math.", year = "1972", volume = "9", pages = "91-108"} @ARTICLE {GiMuSaToWr:86, author = "P.E. GILL and W. MURRAY and M.A. Saunders and J. A. TOMLIN and M.H. Wright", title = "Quasi-{N}ewton methods for unconstrained optimization", journal = "IMA J. Appl. Math.", year = "1972", volume = "9", pages = "91-108"} @MANUAL {GiGoMuWr:83, author = "P.E. GILL and G.H. Golub and W. MURRAY and M.H. Wright", title = "User's guide for {SOL/NPSOL}: a {F}ortran package for nonlinear programming", organization = "Department of Operations Research, Stanford University", year = "1983", address = "Stanford, CA"} @BOOK {GiMuWr:81, author = "P.E. GILL and W. MURRAY and M.H. Wright", title = "Practical Optimization", publisher = "Academic Press", year = "1981", address = "New York, London, Toronto, Sydney and San Francisco"} @BOOK{gmw81, AUTHOR = "P. E. GILL and W. MURRAY and M. H. Wright", TITLE = "Practical Optimization", PUBLISHER = "Academic Press", YEAR = 1981, NOTE = "Intermediate. Excellent treatment of numerical issues." } @ARTICLE {Gla:79, author = "S.T. GLAD", title = "Properties of updating methods for the multipliers in augmented {L}agrangians", journal = "Journal Optim. Theory Appl.", year = "1979", volume = "28", pages = "135-156"} @ARTICLE {GlaGol:77, author = "S.T. GLAD and A. GOLDSTEIN", title = "Optimization of functions whose values are subject to small errors", journal = "BIT", year = "1977", volume = "17", pages = "160"} @BOOK {GlGu:78, author = "K. GLASHOFF and S. GUSTAFSON", title = "Linear Optimzation and Approximation", publisher = "Springer-Verlag", series = "Applied Mathematical Sciences", volume = "45", year = "1978", address = "Verlag Basel"} @article {MR88j:65088, AUTHOR = {Gilbert, John R. and Heath, Michael T.}, TITLE = {Computing a sparse basis for the null space}, JOURNAL = {SIAM J. Algebraic Discrete Methods}, FJOURNAL = {Society for Industrial and Applied Mathematics. Journal on Algebraic and Discrete Methods}, VOLUME = {8}, YEAR = {1987}, NUMBER = {3}, PAGES = {446--459}, ISSN = {0196-5212}, CODEN = {STAMDU}, } @article {MR1953822, AUTHOR = {Goffin, Jean-Louis and Vial, Jean-Philippe}, TITLE = {Convex nondifferentiable optimization: a survey focused on the analytic center cutting plane method}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods \& Software}, VOLUME = {17}, YEAR = {2002}, NUMBER = {5}, PAGES = {805--867}, ISSN = {1055-6788}, MRCLASS = {90C25 (49J52 90-02)}, MRNUMBER = {MR1953822 (2004c:90039)}, MRREVIEWER = {Claudia A. Sagastiz{\'a}bal}, } @article {MR1687276, AUTHOR = {Goffin, Jean-Louis and Vial, Jean-Philippe}, TITLE = {Shallow, deep and very deep cuts in the analytic center cutting plane method}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {84}, YEAR = {1999}, NUMBER = {1, Ser. A}, PAGES = {89--103}, ISSN = {0025-5610}, MRCLASS = {90C30 (65K05 90C48)}, MRNUMBER = {MR1687276 (2000c:90080)}, MRREVIEWER = {L{\'u}cio Tunes dos Santos}, } @BOOK {GoLaRo:83, author = "I. Gohberg and P. Lancaster and L. Rodman", title = "Matrices and Indefinite Scalar Products", publisher = "Birkhauser", year = "1983", address = "Verlag Basel"} @book {MR2186302, AUTHOR = {Gohberg, I. and Lancaster, P. and Rodman, L.}, TITLE = {Indefinite linear algebra and applications}, PUBLISHER = {Birkh\"auser Verlag}, ADDRESS = {Basel}, YEAR = {2005}, PAGES = {xii+357}, ISBN = {978-3-7643-7349-8; 3-7643-7349-0}, MRCLASS = {15-02 (46C20 47B50)}, MRNUMBER = {2186302 (2006j:15001)}, MRREVIEWER = {Hans Havlicek}, } @article {MR0102437, AUTHOR = {Gomory, R.E.}, TITLE = {Outline of an algorithm for integer solutions to linear programs}, JOURNAL = {Bull. Amer. Math. Soc.}, FJOURNAL = {Bulletin of the American Mathematical Society}, VOLUME = {64}, YEAR = {1958}, PAGES = {275--278}, ISSN = {0002-9904}, MRCLASS = {90.00 (06.60)}, MRNUMBER = {0102437}, MRREVIEWER = {A. Charnes}, DOI = {10.1090/S0002-9904-1958-10224-4}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1090/S0002-9904-1958-10224-4}, } @BOOK{glr82, author = "I. Gohberg and P. Lancaster and L. Rodman", TITLE = "Matrix polynomials", PUBLISHER = "Academic Press", YEAR =1982 } @article {MR1478041, AUTHOR = {Gondzio, J.}, TITLE = {Presolve analysis of linear programs prior to applying an interior point method}, JOURNAL = {INFORMS J. Comput.}, FJOURNAL = {INFORMS Journal on Computing}, VOLUME = {9}, YEAR = {1997}, NUMBER = {1}, PAGES = {73--91}, ISSN = {1091-9856}, MRCLASS = {90C05}, MRNUMBER = {MR1478041 (99a:90120)}, MRREVIEWER = {Michael L. Dowling}, } @article {MR2460738, AUTHOR = {Gondzio, J. and Grothey, A.}, TITLE = {A new unblocking technique to warmstart interior point methods based on sensitivity analysis}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {19}, YEAR = {2008}, NUMBER = {3}, PAGES = {1184--1210}, ISSN = {1052-6234}, MRCLASS = {90C51 (65K05 90C20)}, MRNUMBER = {2460738 (2009k:90129)}, MRREVIEWER = {Hiroshi Yabe}, DOI = {10.1137/060678129}, URL = {http://dx.doi.org/10.1137/060678129}, } @article {MR1904181, AUTHOR = {M{\'e}sz{\'a}ros, C. and Gondzio, J.}, TITLE = {Addendum to: ``{P}resolve analysis of linear programs prior to applying an interior point method'' [{I}{N}{F}{O}{R}{M}{S} {J}. {C}omput. {\bf 9} (1997), no. 1, 73--91; {M}{R} 99a:90120] by {G}ondzio}, JOURNAL = {INFORMS J. Comput.}, FJOURNAL = {INFORMS Journal on Computing}, VOLUME = {13}, YEAR = {2001}, NUMBER = {2}, PAGES = {169--170}, ISSN = {0899-1499}, MRCLASS = {90C05}, MRNUMBER = {1 904 181}, } @INCOLLECTION {GoGrothey:06, AUTHOR = {Gondzio, J. and GROTHEY, A.}, title = "Solving Nonlinear Financial Planning Problems with 109 Decision Variables on Massively Parallel Architectures", booktitle = "Computational Finance and its Applications II, WIT Transactions on Modelling and Simulation", publisher = "WIT Press", year = "2006", editor = "M. Costantino, C.A. Brebbia" } @article {MR1972218, AUTHOR = {Gondzio, J. and GROTHEY, A.}, TITLE = {Reoptimization with the primal-dual interior point method}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {13}, YEAR = {2002}, NUMBER = {3}, PAGES = {842--864 (electronic) (2003)}, ISSN = {1095-7189}, MRCLASS = {90C51 (90C08)}, MRNUMBER = {1 972 218}, } @article {MR3457450, AUTHOR = {Gonzaga, C.C. and Schneider, R.M.}, TITLE = {On the steepest descent algorithm for quadratic functions}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {63}, YEAR = {2016}, NUMBER = {2}, PAGES = {523--542}, ISSN = {0926-6003}, MRCLASS = {90C20 (90C52)}, MRNUMBER = {3457450}, MRREVIEWER = {Gerardo Toraldo}, DOI = {10.1007/s10589-015-9775-z}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s10589-015-9775-z}, } @article {MR3128750, AUTHOR = {Gonzalez-Lima, M. and Oliveira, A.R.L. and Oliveira, D.E.}, TITLE = {A robust and efficient proposal for solving linear systems arising in interior-point methods for linear programming}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {56}, YEAR = {2013}, NUMBER = {3}, PAGES = {573--597}, ISSN = {0926-6003}, MRCLASS = {90C51 (90C05)}, MRNUMBER = {3128750}, DOI = {10.1007/s10589-013-9572-5}, URL = {http://dx.doi.org/10.1007/s10589-013-9572-5}, } @article {MR2563953, AUTHOR = {Gonz{\'a}lez-Lima, M. and Montes de Oca, F.}, TITLE = {A {N}ewton-like method for nonlinear system of equations}, JOURNAL = {Numer. Algorithms}, FJOURNAL = {Numerical Algorithms}, VOLUME = {52}, YEAR = {2009}, NUMBER = {3}, PAGES = {479--506}, ISSN = {1017-1398}, MRCLASS = {65H10 (90C30)}, MRNUMBER = {2563953 (2011a:65129)}, MRREVIEWER = {Miodrag Petkovi{\'c}}, DOI = {10.1007/s11075-009-9294-z}, URL = {http://dx.doi.org/10.1007/s11075-009-9294-z}, } @article {MR2783220, AUTHOR = {Gonzalez-Lima, M. and Hager, W.W. and Zhang, H.}, TITLE = {An affine-scaling interior-point method for continuous knapsack constraints with application to support vector machines}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {21}, YEAR = {2011}, NUMBER = {1}, PAGES = {361--390}, ISSN = {1052-6234}, CODEN = {SJOPE8}, MRCLASS = {90C06 (90C51)}, MRNUMBER = {2783220 (2012a:90106)}, MRREVIEWER = {Ning Ruan}, DOI = {10.1137/090766255}, URL = {http://dx.doi.org/10.1137/090766255}, } @book {barv_book, AUTHOR = {Barvinok, A.}, TITLE = {A course in convexity}, SERIES = {Graduate Studies in Mathematics}, VOLUME = {54}, PUBLISHER = {American Mathematical Society, Providence, RI}, YEAR = {2002}, PAGES = {x+366}, ISBN = {0-8218-2968-8}, MRCLASS = {52-02 (49N15 52-01 90-02 90C05 90C22 90C25)}, MRNUMBER = {1940576}, MRREVIEWER = {P. McMullen}, DOI = {10.1090/gsm/054}, URL = {http://dx.doi.org/10.1090/gsm/054}, } @article {MR2500832, AUTHOR = {Al-Jeiroudi, G. and Gondzio, J.}, TITLE = {Convergence analysis of the inexact infeasible interior-point method for linear optimization}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {141}, YEAR = {2009}, NUMBER = {2}, PAGES = {231--247}, ISSN = {0022-3239}, CODEN = {JOTABN}, MRCLASS = {90C05 (90C06 90C51)}, MRNUMBER = {MR2500832 (2009m:90076)}, MRREVIEWER = {Hemanta K. Baruah}, DOI = {10.1007/s10957-008-9500-5}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s10957-008-9500-5}, } @article {MR2424164, AUTHOR = {Al-Jeiroudi, G. and Gondzio, J. and Hall, J.}, TITLE = {Preconditioning indefinite systems in interior point methods for large scale linear optimisation}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods \& Software}, VOLUME = {23}, YEAR = {2008}, NUMBER = {3}, PAGES = {345--363}, ISSN = {1055-6788}, MRCLASS = {90C05 (65F10 90C51)}, MRNUMBER = {MR2424164 (2009e:90032)}, MRREVIEWER = {Jiu Ding}, DOI = {10.1080/10556780701535910}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1080/10556780701535910}, } @article {MR99a:90120, AUTHOR = {Gondzio, J.}, TITLE = {Presolve analysis of linear programs prior to applying an interior point method}, JOURNAL = {INFORMS J. Comput.}, FJOURNAL = {INFORMS Journal on Computing}, VOLUME = {9}, YEAR = {1997}, NUMBER = {1}, PAGES = {73--91}, ISSN = {0899-1499}, MRCLASS = {90C05}, MRNUMBER = {99a:90120}, MRREVIEWER = {Michael L. Dowling}, } @ARTICLE{Goreinov08howto, author = {S.A. Goreinov and I.V. Oseledets and D.V. Savostyanov and E.E. Tyrtyshnikov and N. L. Zamarashkin}, title = {How to find a good submatrix}, journal = {Research Report 08-10, ICM HKBU, Kowloon Tong, Hong Kong}, year = {2008}, pages = {08--10}, url={http://citeseerx.ist.psu.edu/viewdoc/summary;jsessionid=09D8CC8B7977922A73590DDD45F59667?doi=10.1.1.505.6808} } @incollection {MR2648622, AUTHOR = {Goreinov, S.A. and Oseledets, I.V. and Savostyanov, D.V. and Tyrtyshnikov, E.E. and Zamarashkin, N.L.}, TITLE = {How to find a good submatrix}, BOOKTITLE = {Matrix methods: theory, algorithms and applications}, PAGES = {247--256}, PUBLISHER = {World Sci. Publ., Hackensack, NJ}, YEAR = {2010}, MRCLASS = {65F99}, MRNUMBER = {2648622}, DOI = {10.1142/9789812836021_0015}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1142/9789812836021_0015}, } @incollection {MR1850400, AUTHOR = {Goreinov, S.A. and Tyrtyshnikov, E.E.}, TITLE = {The maximal-volume concept in approximation by low-rank matrices}, BOOKTITLE = {Structured matrices in mathematics, computer science, and engineering, {I} ({B}oulder, {CO}, 1999)}, SERIES = {Contemp. Math.}, VOLUME = {280}, PAGES = {47--51}, PUBLISHER = {Amer. Math. Soc., Providence, RI}, YEAR = {2001}, MRCLASS = {15A60}, MRNUMBER = {1850400}, DOI = {10.1090/conm/280/4620}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1090/conm/280/4620}, } @article {MR85k:90102, AUTHOR = {Tomlin, J. A. and Welch, J. S.}, TITLE = {Formal optimization of some reduced linear programming problems}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {27}, YEAR = {1983}, NUMBER = {2}, PAGES = {232--240}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C05}, MRNUMBER = {85k:90102}, } @incollection {MR1307169, AUTHOR = {Fourer, R. and Gay, D.M.}, TITLE = {Experience with a primal presolve algorithm}, BOOKTITLE = {Large scale optimization (Gainesville, FL, 1993)}, PAGES = {135--154}, PUBLISHER = {Kluwer Acad. Publ.}, ADDRESS = {Dordrecht}, YEAR = {1994}, MRCLASS = {90C30 (90C08)}, MRNUMBER = {1 307 169}, } @phdthesis{hendrickson:91, AUTHOR= "B. Hendrickson", year = "1991", title = "The molecule problem: Determining conformation from pairwise distances", school = "Cornell University", address = "Ithaca, New York", } @ARTICLE{hen92, AUTHOR= "B. Hendrickson", TITLE = "Conditions for unique graph realizations", JOURNAL="SIAM J. Comput.", VOLUME=21 , PAGES ={65--84} , YEAR =1992 } @article {MR92m:05182, AUTHOR= "B. Hendrickson", TITLE = {Conditions for unique graph realizations}, JOURNAL = {SIAM J. Comput.}, FJOURNAL = {SIAM Journal on Computing}, VOLUME = {21}, YEAR = {1992}, NUMBER = {1}, PAGES = {65--84}, ISSN = {0097-5397}, CODEN = {SMJCAT}, MRCLASS = {05C85}, MRNUMBER = {92m:05182}, } @article {MR1257633, AUTHOR = {GRIMES, R.G. and Lewis, J.G. and SIMON, H.D.}, TITLE = {A shifted block {L}anczos algorithm for solving sparse symmetric generalized eigenproblems}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {15}, YEAR = {1994}, NUMBER = {1}, PAGES = {228--272}, ISSN = {0895-4798}, CODEN = {SJMAEL}, MRCLASS = {65F15 (65F50 73K12 73V20)}, MRNUMBER = {MR1257633 (94k:65054)}, MRREVIEWER = {Colette Lebaud}, } @ARTICLE {GrzeSta:85, author = "S.M. GRZEGORSKI", title = "Orthogonal projections on convex sets for {N}ewton-like methods", journal = "SIAM J. Numer. Anal.", year = "1985", volume = "22", pages = "1208-1219"} @article {MR0258249, AUTHOR = {Goldfarb, D.}, TITLE = {A family of variable-metric methods derived by variational means}, JOURNAL = {Math. Comp.}, FJOURNAL = {Mathematics of Computation}, VOLUME = {24}, YEAR = {1970}, PAGES = {23--26}, ISSN = {0025-5718}, MRCLASS = {65.30}, MRNUMBER = {MR0258249 (41 \#2896)}, } @article {GI, AUTHOR = {Goldfarb, D. and Iyengar, G.}, TITLE = {Robust portfolio selection problems}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {28}, YEAR = {2003}, NUMBER = {1}, PAGES = {1--38}, ISSN = {0364-765X}, MRCLASS = {90C20 (90C22 91B28)}, MRNUMBER = {MR1961265 (2004f:90098)}, MRREVIEWER = {Reha H. T{\"u}t{\"u}nc{\"u}}, } @ARTICLE {Goldf:76, author = "D. Goldfarb", title = "Factorized variable metric methods for unconstrained optimization", journal = "Math. Comp.", year = "1976", volume = "30", pages = "796-811"} @ARTICLE {Goldf:70, author = "D. Goldfarb", title = "A family of variable metric methods derived by variational means", journal = "Math. Comp.", year = "1970", volume = "24", pages = "23-26"} @article {MR0452649, AUTHOR = {Goldfarb, D. and REID, J.K.}, TITLE = {A practicable steepest-edge simplex algorithm}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {12}, YEAR = {1977}, NUMBER = {3}, PAGES = {361--371}, ISSN = {0025-5610}, MRCLASS = {90C05}, MRNUMBER = {MR0452649 (56 \#10928)}, MRREVIEWER = {J. A. Tomlin}, } @article {MR2031774, AUTHOR = {Goldfarb, D. and Scheinberg, K.}, TITLE = {A product-form {C}holesky factorization method for handling dense columns in interior point methods for linear programming}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {99}, YEAR = {2004}, NUMBER = {1, Ser. A}, PAGES = {1--34}, ISSN = {0025-5610}, MRCLASS = {90C51 (65K05 90C05)}, MRNUMBER = {2 031 774}, } @ARTICLE {GoQuTr:66, author = "S.M. GOLDFELDT and R.E. QUANDT and H.F. TROTTER", title = "Maximization by quadratic hill-climbing", journal = "Econometrica", year = "1966", volume = "34", pages = "541-551"} @BOOK {Golds:67, author = "A.A. GOLDSTEIN", title = "Constructive Real Analysis", publisher = "Harper \& Row", year = "1967", address = "New York, NY"} @BOOK {Golds:72, author = "E.G. GOL{'}STEIN", title = "Theory of Convex Programming", publisher = "American Mathematical Society", year = "1972", address = "Providence , RI"} \@ARTICLE {Gol:87, author = "B. GOLLAN", title = "Eigenvalue perturbations and nonlinear parametric optimization", journal = "Mathematical Programming Studies", year = "1987", volume = "30", pages = "67-81" } @article {GoYe02, AUTHOR = {Golub, G.H. and Ye, Q.}, TITLE = {An inverse free preconditioned {K}rylov subspace method for symmetric generalized eigenvalue problems}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {24}, YEAR = {2002}, NUMBER = {1}, PAGES = {312--334 (electronic)}, ISSN = {1064-8275}, MRCLASS = {65F15}, MRNUMBER = {1924427 (2003h:65048)}, MRREVIEWER = {E. Kreyszig}, DOI = {10.1137/S1064827500382579}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/S1064827500382579}, } @ARTICLE {GoNaVa:79, author = "G.H. Golub and S. NASH and C. Van Loan", title = "A {H}essenberg-{S}chur method for the problem AX+XB=C", journal = "IEEE Transactions on Automatic Control", year = "1979", volume = "AC-24", pages = "909-913"} @ARTICLE {GoPe:73, author = "G.H. Golub and V. PEREYRA", title = "The differentiation of pseudo-inverses and non-linear least squares problems whose variables separate", journal = "SIAM J. Numer. Anal.", year = "1973", volume = "10", pages = "413-432"} @BOOK {GoVan:79, author = "G.H. Golub and C.F. {Van Loan}", title = "Matrix Computations", publisher = "Johns Hopkins University Press", address = "Baltimore, Maryland", EDITION = {$3^{nd}$}, year= {1996} } @ARTICLE{GoMa:90, AUTHOR = "G. Golub and U. von MATT ", TITLE = "Quadratically Constrained Least Squares and Quadratic Problems", journal = "Numer. Math.", YEAR = "1991", volume = "59", pages = "561-580" } @techreport{Golub.Matt:1997:TRF, author = "G. H. Golub and U. von MATT", title = "Tikhonov Regularization for Large Scale Problems", institution = "Stanford University", year = "1997", number = "SCCM-97-03" } @incollection {MR2000k:65080, author = "G. H. Golub and U. von MATT", TITLE = {Tikhonov regularization for large scale problems}, BOOKTITLE = {Scientific computing (Hong Kong, 1997)}, PAGES = {3--26}, PUBLISHER = {Springer}, ADDRESS = {Singapore}, YEAR = {1997}, MRCLASS = {65F22 (65J20)}, MRNUMBER = {2000k:65080}, MRREVIEWER = {Otmar Scherzer}, } @article {Golub:1997:GCV, author = "G. H. Golub and U. {von MATT}", title = "Generalized Cross-Validation for Large-Scale Problems", journal = "Journal of Computational and Graphical Statistics", volume = "6", number = "1", pages = "1--34", month = mar, year = "1997", ISSN = "1061-8600", mrclass = "62J05", mrnumber = "98j:62052", mrreviewer = "Girdhar G. Agarwal" } @ARTICLE {Greenb:81, author = "A. GREENBAUM", title = "Behavior of the conjugate gradient algorithm in finite precision arithmetic", journal = "SIAM J. Sci. Statist. Comput.", year = "1981"} @book {MR98g:90003, TITLE = {Advances in sensitivity analysis and parametric programming}, EDITOR = {Gal, Tomas and Greenberg, Harvey J.}, PUBLISHER = {Kluwer Academic Publishers}, ADDRESS = {Boston, MA}, YEAR = {1997}, PAGES = {xxiv+581}, ISBN = {0-7923-9917-X}, MRCLASS = {90-06 (90B10 90C05 90C30 90C31)}, MRNUMBER = {98g:90003}, } @TechReport{Gr97_MIPbib, author = "H.J. GREENBERG", title = "An Annotated Bibliography for Post-solution Analysis in Mixed Integer Programming and Combinatorial Optimization", type = "{CCM No. 108}", institution = "Center for Computational Mathematics, Mathematics Department, University of Colorado at Denver", address = "Denver, CO, http://www-math.cudenver.edu/~hgreenbe/reports.html", year = "1997" } @Book{Math_Programming_Glossary, author = "H.J. GREENBERG", title = "{\it Mathematical Programming Glossary}", publisher ="{World Wide Web}", address = "{http://www-math.cudenver.edu/~hgreenbe/glossary/glossary.html}", year = "1996", } @TECHREPORT {intprogrsens, author = "H.J. GREENBERG", title = "An annotated bibliography for post-solution analysis in mixed integer programming and combinatorial optimization", address = "{http://www-math.cudenver.edu/~hgreenbe}", year = "1997", } @TECHREPORT {greenberg:70, author = "H.J. GREENBERG", title = "Lagrangian duality gaps: their source and resolution", address = "Southern Methodist University", year = "1970", } @ARTICLE {Go:86, author = "N.I.M. Gould", title = "On the accurate determination of search directions for simple differentiable penalty functions", journal = "IMA J. Num. Anal.", volume = "6", pages = "357-372", year = "1986"} @article {MR2601719, AUTHOR = {Gould, N.I.M. and Robinson, D.P. and Thorne, H.S.}, TITLE = {On solving trust-region and other regularised subproblems in optimization}, JOURNAL = {Math. Program. Comput.}, FJOURNAL = {Mathematical Programming Computation}, VOLUME = {2}, YEAR = {2010}, NUMBER = {1}, PAGES = {21--57}, ISSN = {1867-2949}, MRCLASS = {90C30 (65K10 90C26)}, MRNUMBER = {2601719 (2011c:90097)}, MRREVIEWER = {Warren L. Hare}, DOI = {10.1007/s12532-010-0011-7}, URL = {http://dx.doi.org/10.1007/s12532-010-0011-7}, } @article {MR45:6415, AUTHOR = {Gould, F.J. and Tolle, J.W.}, TITLE = {Geometry of optimality conditions and constraint qualifications}, JOURNAL = {Math. Programming}, VOLUME = {2}, YEAR = {1972}, NUMBER = {1}, PAGES = {1--18}, MRCLASS = {90C05}, MRNUMBER = {45 \#6415}, MRREVIEWER = {R. W. Cottle}, } @techreport{GoHrNo:98, AUTHOR = "Gould, N.I.M. and HRIBAR, M.E J. Nocedal", TITLE = "On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization", TYPE = "Report", ADDRESS = "OTC 98/06 Optimization Technology Center", YEAR = "1998", } @techreport{GoOrSaTo:01, AUTHOR = "Gould, N.I.M. and ORBAN, D. and SARTENAER, A. and Toint, Ph.L.", TITLE = "Componentwise fast convergence in the solution of full-rank systems of nonlinear equations", TYPE = "TR/PA/00/56", address = "Toulouse Cedex 1, France", institution = "CERFACS", YEAR = "2001", } @ARTICLE {Graeub:47, author = "W. GRAEUB", title = "Die Grundelhren der Mathematischen Wissenschaften", journal = "Linear Algebra - uncertain", year = "1947 - uncertain", volume = "47 - uncertain", pages = "158-163"} @ARTICLE {Greens:70, author = "J.L. GREENSTADT", title = "Variations on variable-metric methods", journal = "Math. Comp.", year = "1970", volume = "24", pages = "1-22"} @book {MR98j:65023, AUTHOR = {GREENBAUM, A.}, TITLE = {Iterative methods for solving linear systems}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {1997}, PAGES = {xiv+220}, ISBN = {0-89871-396-X}, MRCLASS = {65F10 (65-02 65F50)}, MRNUMBER = {98j:65023}, MRREVIEWER = {R. P. Tewarson}, } @INCOLLECTION{ Griewank2003AMV, AUTHOR = "A. Griewank", TITLE = "A Mathematical View of Automatic Differentiation", booktitle = "Acta Numerica", VOLUME = "12", YEAR = "2003", PAGES = "321--398", publisher = "Cambridge University Press", doi = "10.1017/S0962492902000132", abstract = "Automatic, or algorithmic, differentiation addresses the need for the accurate and efficient calculation of derivative values in scientific computing. To this end procedural programs for the evaluation of problem-specific functions are transformed into programs that also compute the required derivative values at the same numerical arguments in floating point arithmetic. Disregarding many important implementation issues, we examine in this article complexity bounds and other more mathematical aspects of the program transformation task sketched above.", ad_theotech = "General" } @incollection {MR760465, AUTHOR = {Griewank, A. and Toint, Ph.L.}, TITLE = {Numerical experiments with partially separable optimization problems}, BOOKTITLE = {Numerical analysis (Dundee, 1983)}, SERIES = {Lecture Notes in Math.}, VOLUME = {1066}, PAGES = {203--220}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1984}, MRCLASS = {90C30 (49D37 65K10)}, MRNUMBER = {MR760465 (85h:90102)}, } @ARTICLE {Griew:82, author = "A.O. Griewank", title = "A short proof of the {D}ennis-{S}chnabel theorem", journal = "BIT", year = "1982", volume = "22", pages = "252-256"} @TECHREPORT {Griew:83, author = "A.O. Griewank", title = "Note on the weighting of {S}chubert's update for discretizations of ordinary differential equations", institution = "Department of Mathematics, Southern Methodist University", year = "1983"} @INCOLLECTION {Griew:88, author = "A.O. Griewank", title = "On automatic differentiation", booktitle = "Mathematical Programming 1988", publisher = "Kluwer Academic Publishers", year = "1988", address = "Japan"} @ARTICLE {GrTo:82a, author = "A.O. Griewank and Ph.L. Toint", title = "Partitioned variable metric updates for large sparse optimization problems", journal = "Numer. Math.", year = "1982", volume = "39", pages = "37-119"} @ARTICLE {GrTo:82b, author = "A.O. Griewank and Ph.L. Toint", title = "Local convergence analysis for partitioned quasi-{N}ewton updates in the {B}royden class", journal = "Numer. Math.", year = "1982", volume = "39", pages = "429-448"} @INCOLLECTION {GrTo:82c, author = "A.O. Griewank and Ph.L. Toint", title = "On the unconstrained optimization of partially separable functions", booktitle = "Nonlinear Optimization", publisher = "Academic Press", year = "1982", editor = "M.J.D. Powell", address = "London"} @book {MR37:2085, AUTHOR = {GR{\"U}NBAUM, B.}, TITLE = {Convex polytopes}, NOTE = {With the cooperation of Victor Klee, M. A. Perles and G. C. Shephard. Pure and Applied Mathematics, Vol. 16}, PUBLISHER = {Interscience Publishers John Wiley \& Sons, Inc., New York}, YEAR = {1967}, PAGES = {xiv+456}, MRCLASS = {52.10}, MRNUMBER = {37 #2085}, MRREVR = {G. T. Sallee}, } @article {MR32:448, AUTHOR = {GR{\"U}NBAUM, B.}, TITLE = {On the facial structure of convex polytopes}, JOURNAL = {Bull. Amer. Math. Soc.}, VOLUME = {71}, YEAR = {1965}, PAGES = {559--560}, MRCLASS = {52.10}, MRNUMBER = {32 #448}, MRREVR = {H. T. Croft}, } @TECHREPORT {GuEi:94, author = "M. GU and S.C. Eisenstat", title = "A divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem", institution = "Department of Computer Science, Yale University", year = "1994", number = "RR-932"} @ARTICLE {Guig:69, author = "M. Guignard", title = "Generalized {K}uhn-{T}ucker conditions for mathematical programming problems in a {B}anach Space", journal = "SIAM J. of Control", year = "1969", volume = "7", number = "2", pages = "232-241"} @article {MR41:1383, AUTHOR = {KORTANEK, K. O. and EVANS, J. P.}, TITLE = {Asymptotic {L}agrange regularity for pseudoconcave programming with weak constraint qualification}, JOURNAL = {Operations Res.}, VOLUME = {16}, YEAR = {1968}, PAGES = {849--857}, MRCLASS = {90.58}, MRNUMBER = {41 #1383}, MRREVR = {A. Ben-Israel}, } @article {MR45:9698, AUTHOR = {ZLOBEC, S.}, TITLE = {Optimality conditions for mathematical programming problems}, JOURNAL = {Glasnik Mat. Ser. III}, VOLUME = {6(26)}, YEAR = {1971}, PAGES = {187--192}, MRCLASS = {90C30}, MRNUMBER = {45 #9698}, MRREVR = {J. Stoer}, } @article {MR81g:90094, AUTHOR = {NIEUWENHUIS, J. W.}, TITLE = {Another application of {G}uignard's generalized {K}uhn-{T}ucker conditions}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {30}, YEAR = {1980}, NUMBER = {1}, PAGES = {117--125}, ISSN = {0022-3239}, CODEN = {JOTABN}, MRCLASS = {90C48 (46G05 90C30)}, MRNUMBER = {81g:90094}, MRREVR = {{\cedla{S}}tefan {\cedla{T}}igan}, } @incollection {MR1310581, AUTHOR = {GRAVER, J.E. and SERVATIUS, B. and SERVATIUS, H.}, TITLE = {Abstract rigidity in {$m$}-space}, BOOKTITLE = {Jerusalem combinatorics '93}, SERIES = {Contemp. Math.}, VOLUME = {178}, PAGES = {145--151}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {1994}, MRCLASS = {05B35 (05C10)}, MRNUMBER = {MR1310581 (95j:05064)}, MRREVIEWER = {Raul Cordovil}, } @book {MR1251062, AUTHOR = {GRAVER, J.E. and SERVATIUS, B. and SERVATIUS, H.}, TITLE = {Combinatorial rigidity}, SERIES = {Graduate Studies in Mathematics}, VOLUME = {2}, PUBLISHER = {American Mathematical Society}, ADDRESS = {Providence, RI}, YEAR = {1993}, PAGES = {x+172}, ISBN = {0-8218-3801-6}, MRCLASS = {52C25 (05B35 05C50 70C20)}, MRNUMBER = {MR1251062 (95b:52034)}, MRREVIEWER = {Robert Connelly}, } @techreport {Grcar:10, AUTHOR = "J.F. Grcar", TITLE = {Spectral Condition Numbers of Orthogonal Projections and Full Rank Linear Least Squares Residuals}, institution = "California", address = "California", note = {arXiv:1003.2737v3}, year = "2010"} @techreport {Grcar:12, AUTHOR = "J.F. Grcar", TITLE = {Optimal sensitivity analysis of linear least squares}, institution = "Lawrence Berkeley National Laboratory", address = "California", note = {LBNL-52434}, year = "2012"} @article {MR0071874, AUTHOR = {Peaceman, D.W. and Rachford, Jr., H.H.}, TITLE = {The numerical solution of parabolic and elliptic differential equations}, JOURNAL = {J. Soc. Indust. Appl. Math.}, VOLUME = {3}, YEAR = {1955}, PAGES = {28--41}, MRCLASS = {65.0X}, MRNUMBER = {0071874}, MRREVIEWER = {M. A. Hyman}, } @article{doi:10.1137/13090849X, author = {He, B. and Liu, H. and Wang, Z. and Yuan, X.}, title = {A Strictly Contractive {P}eaceman--{R}achford Splitting Method for Convex Programming}, journal = {SIAM Journal on Optimization}, volume = {24}, number = {3}, pages = {1011-1040}, year = {2014}, doi = {10.1137/13090849X}, URL = {https://doi.org/10.1137/13090849X}, eprint = {https://doi.org/10.1137/13090849X}} @ARTICLE{2015arXiv150602221G, author = {{Gu}, Y. and {Jiang}, B. and {Han}, D.}, title = "{A semi-proximal-based strictly contractive {P}eaceman-{R}achford splitting method}", journal = {arXiv e-prints}, keywords = {Mathematics - Optimization and Control}, year = "2015", month = "Jun", eid = {arXiv:1506.02221}, pages = {arXiv:1506.02221}, archivePrefix = {arXiv}, eprint = {1506.02221}, primaryClass = {math.OC}, adsurl = {https://ui.adsabs.harvard.edu/abs/2015arXiv150602221G}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } @book {MR1976856, AUTHOR = {Gr{\"u}nbaum, Branko}, TITLE = {Convex polytopes}, SERIES = {Graduate Texts in Mathematics}, VOLUME = {221}, EDITION = {Second}, NOTE = {Prepared and with a preface by Volker Kaibel, Victor Klee and G{\"u}nter M. Ziegler}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {2003}, PAGES = {xvi+468}, ISBN = {0-387-00424-6; 0-387-40409-0}, MRCLASS = {52-01 (52Bxx)}, MRNUMBER = {1976856 (2004b:52001)}, MRREVIEWER = {Alexander Zvonkin}, DOI = {10.1007/978-1-4613-0019-9}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/978-1-4613-0019-9}, } @book{guenin2014gentle, title={A Gentle Introduction to Optimization}, author={Guenin, B. and K{\"o}nemann, J. and Tun{\c{c}}el, L.}, isbn={9781107053441}, lccn={2014008067}, url={https://books.google.ca/books?id=9m1ingEACAAJ}, year={2014}, publisher={Cambridge University Press} } @TECHREPORT {Guler:94, author = "O. G{\" U}LER", title = "Barrier functions in interior point methods", institution = "Department of Mathematics and Statistics, University of Maryland Baltimore County", keywords = "semidefinite programming; cone programming; sdp; coneprog", year = "1994"} @TECHREPORT {Guler:95, author = "O. G{\" U}LER", title = "Generalized linear complementarity Problems", institution = "Department of Mathematics and Statistics, University of Maryland Baltimore County", keywords = "complementarity", year = "1995"} @article {MR94j:90021, AUTHOR = {G{\"u}ler, O. and Den Hertog, D. and Roos, C. and Terlaky, T. and Tsuchiya, T.}, TITLE = {Degeneracy in interior point methods for linear programming: a survey}, NOTE = {Degeneracy in optimization problems}, JOURNAL = {Ann. Oper. Res.}, FJOURNAL = {Annals of Operations Research}, VOLUME = {46/47}, YEAR = {1993}, NUMBER = {1-4}, PAGES = {107--138}, ISSN = {0254-5330}, MRCLASS = {90C05 (90-02)}, MRNUMBER = {94j:90021}, } @article {MR2489429, AUTHOR = {G\"{u}ler, O. and G\"{u}rtuna, F. and Shevchenko, O.}, TITLE = {Duality in quasi-{N}ewton methods and new variational characterizations of the {DFP} and {BFGS} updates}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods \& Software}, VOLUME = {24}, YEAR = {2009}, NUMBER = {1}, PAGES = {45--62}, ISSN = {1055-6788}, MRCLASS = {90C26 (65K10 90C53)}, MRNUMBER = {2489429}, MRREVIEWER = {Dexuan Xie}, DOI = {10.1080/10556780802367205}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1080/10556780802367205}, } @article {MR96k:90033, AUTHOR = {GUO, T. D. and WU, S. Q.}, TITLE = {A modified homogeneous and self-dual linear programming algorithm}, JOURNAL = {Systems Sci. Math. Sci.}, FJOURNAL = {Systems Science and Mathematical Sciences}, VOLUME = {8}, YEAR = {1995}, NUMBER = {3}, PAGES = {270--277}, ISSN = {1000-9590}, CODEN = {SMASE2}, } @article {MR2354237, AUTHOR = {Gutman, P-O. and Ioslovich, I.}, TITLE = {On the generalized {W}olfe problem: preliminary analysis of nonnegative large-scale linear programming problems with group constraints}, JOURNAL = {Avtomat. i Telemekh.}, FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Avtomatika i Telemekhanika}, YEAR = {2007}, NUMBER = {8}, PAGES = {116--125}, volume ={}, ISSN = {0005-2310}, MRCLASS = {90C05 (90C06)}, MRNUMBER = {2354237 (2008g:90062)}, MRREVIEWER = {C. Ilioi}, DOI = {10.1134/S0005117907080115}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1134/S0005117907080115}, } @ARTICLE {Gut:46, author = "L. GUTTMAN", title = "Enlargement methods for computing the inverse matrix", journal = ams, year = "1946", volume = "17", pages = "336-343"} %HHHHHHHH @article {MR110773, AUTHOR = {Hartman, P.}, TITLE = {On functions representable as a difference of convex functions}, JOURNAL = {Pacific J. Math.}, FJOURNAL = {Pacific Journal of Mathematics}, VOLUME = {9}, YEAR = {1959}, PAGES = {707--713}, ISSN = {0030-8730}, MRCLASS = {26.00}, MRNUMBER = {110773}, MRREVIEWER = {E. G. Straus}, URL = {http://projecteuclid.org.proxy.lib.uwaterloo.ca/euclid.pjm/1103039111}, } @ARTICLE {Hadamard:02, author = "J. HADAMARD", title = " Sur les problemes aux derivees partielles et leur signification physique", journal = "Princeton University Bulletin", pages = "49--52", year = "1902", volume = "", } @book {MR14:474f, AUTHOR = {HADAMARD, J.}, TITLE = {Lectures on {C}auchy's problem in linear partial differential equations}, PUBLISHER = {Dover Publications, New York}, YEAR = {1953}, PAGES = {iv+316}, MRCLASS = {36.0X}, MRNUMBER = {14,474f}, } @PHDTHESIS {Ha:89, author = "S.W. Hadley", title = "Continuous optimization approaches for the quadratic assignment problem ", school = "University of Waterloo", year = "1989", address = "Waterloo, Canada"} @ARTICLE{HaMaVa:92, AUTHOR = "S.W. Hadley and B.L. Mark and A. Vannelli ", TITLE = "An efficient eigenvector approach for finding netlist partitions", YEAR = "1992", volume= "11", JOURNAL = "IEEE Transactions on Computer-Aided Design", pages = "885-892", } @ARTICLE{Hae:79, AUTHOR = "W. HAEMERS", TITLE = "On some problems of {L}ov\'{a}sz concerning the {S}hannon capacity of graphs", YEAR = "1979", volume= "25", JOURNAL = "IEEE Transactions on Information Theory", pages = "231-232", } @article {MR2001g:65031, author = {W.W. Hager}, TITLE = {Iterative methods for nearly singular linear systems}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {22}, YEAR = {2000}, NUMBER = {2}, PAGES = {747--766 (electronic)}, ISSN = {1095-7197}, MRCLASS = {65F10 (65F50 65Y20 90C22)}, MRNUMBER = {2001g:65031}, MRREVIEWER = {Henry Wolkowicz}, } @article {HagerZhang:06, author = {W.W. Hager and H. ZHANG}, TITLE = {A new active set algorithm for box constrained optimization}, journal = siopt, VOLUME = {to appear}, YEAR = {2006}, NUMBER = {}, PAGES = { (electronic)} } @article {MR2177774, author = {W.W. Hager and H. ZHANG}, TITLE = {A new conjugate gradient method with guaranteed descent and an efficient line search}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {16}, YEAR = {2005}, NUMBER = {1}, PAGES = {170--192 (electronic)}, ISSN = {1052-6234}, MRCLASS = {90C52 (90C06 90C26)}, MRNUMBER = {MR2177774 (2006m:90214)}, MRREVIEWER = {Stephen C. Billups}, } @incollection {MR1987236, AUTHOR = {Hager, W.W.}, TITLE = {The dual active set algorithm and the iterative solution of linear programs}, BOOKTITLE = {Novel approaches to hard discrete optimization (Waterloo, ON, 2001)}, SERIES = {Fields Inst. Commun.}, VOLUME = {37}, PAGES = {97--109}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {2003}, MRCLASS = {90C05}, MRNUMBER = {1 987 236}, } @article {MR2003a:90027, AUTHOR = {Hager, W.W.}, TITLE = {The dual active set algorithm and its application to linear programming}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {21}, YEAR = {2002}, NUMBER = {3}, PAGES = {263--275}, ISSN = {0926-6003}, CODEN = {CPPPEF}, MRCLASS = {90C05}, MRNUMBER = {2003a:90027}, MRREVIEWER = {Jos F. Sturm}, } @article {MR94b:90088, AUTHOR = {Hager, W.W. and HEARN, D.W.}, TITLE = {Application of the dual active set algorithm to quadratic network optimization}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {1}, YEAR = {1993}, NUMBER = {4}, PAGES = {349--373}, ISSN = {0926-6003}, CODEN = {CPPPEF}, MRCLASS = {90C35 (90C20)}, MRNUMBER = {94b:90088}, MRREVIEWER = {Michael A. Trick}, } @article {MR86f:65083, AUTHOR = {Hager, W. W.}, TITLE = {Condition estimates}, JOURNAL = {SIAM J. Sci. Statist. Comput.}, FJOURNAL = {Society for Industrial and Applied Mathematics. Journal on Scientific and Statistical Computing}, VOLUME = {5}, YEAR = {1984}, NUMBER = {2}, PAGES = {311--316}, ISSN = {0196-5204}, CODEN = {SIJCD4}, } @article {MR2137009, AUTHOR = {Hager, W.W. and Park, S.}, TITLE = {Global convergence of {SSM} for minimizing a quadratic over a sphere}, JOURNAL = {Math. Comp.}, FJOURNAL = {Mathematics of Computation}, VOLUME = {74}, YEAR = {2005}, NUMBER = {251}, PAGES = {1413--1423}, ISSN = {0025-5718}, CODEN = {MCMPAF}, MRCLASS = {90C20 (65K05)}, MRNUMBER = {2137009 (2006e:90083)}, MRREVIEWER = {Michael Hinterm{\"u}ller}, DOI = {10.1090/S0025-5718-04-01731-4}, URL = {http://dx.doi.org/10.1090/S0025-5718-04-01731-4}, } @article {Hager:00, AUTHOR = {Hager, W.W.}, TITLE = {Minimizing a quadratic over a sphere}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {12}, YEAR = {2001}, NUMBER = {1}, PAGES = {188--208}, ISSN = {1052-6234}, MRCLASS = {90C20 (65F10)}, MRNUMBER = {1870591 (2002m:90054)}, MRREVIEWER = {Henry Wolkowicz}, DOI = {10.1137/S1052623499356071}, URL = {http://dx.doi.org/10.1137/S1052623499356071}, } @article {MR2000d:90118, AUTHOR = {Hager, W.W.}, TITLE = {Stabilized sequential quadratic programming}, NOTE = {Computational optimization---a tribute to Olvi Mangasarian, Part I}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {12}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {253--273}, ISSN = {0926-6003}, CODEN = {CPPPEF}, MRCLASS = {90C55 (90C30)}, MRNUMBER = {2000d:90118}, MRREVIEWER = {Doug Ward}, } @ARTICLE {HalMad:85, author = "J. HALD and K. MADSEN", title = "Combined {LP} and quasi-{N}ewton methods for nonlinear $l_{1}$ optimization", journal = "SIAM J. Numer. Anal.", year = "1985", volume = "22", pages = "68-80"} @article {MR1871321, AUTHOR = {Hansen, P.C. and Yalamov, P.Y.}, TITLE = {Computing symmetric rank-revealing decompositions via triangular factorization}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {23}, YEAR = {2001}, NUMBER = {2}, PAGES = {443--458 (electronic)}, ISSN = {0895-4798}, MRCLASS = {65F30 (15A23)}, MRNUMBER = {MR1871321 (2002j:65047)}, } @article {MR1047208, AUTHOR = {Hansen, P.C.}, TITLE = {Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank}, JOURNAL = {SIAM J. Sci. Statist. Comput.}, FJOURNAL = {Society for Industrial and Applied Mathematics. Journal on Scientific and Statistical Computing}, VOLUME = {11}, YEAR = {1990}, NUMBER = {3}, PAGES = {503--518}, ISSN = {0196-5204}, CODEN = {SIJCD4}, MRCLASS = {65F30}, MRNUMBER = {MR1047208 (91e:65058)}, MRREVIEWER = {Lars Eld{\'e}n}, } @ARTICLE{H88, AUTHOR="S.P. HAN ", TITLE="A successive projection method", JOURNAL="Math. Programming ", YEAR="1988", VOLUME="40", PAGES="1--14 "} @article {hastie, AUTHOR = {HASTIE, T. and ROSSET, S. and TIBSHIRANI, R. and ZHU, J.}, TITLE = {The entire regularization path for the support vector machine}, JOURNAL = {J. Mach. Learn. Res.}, FJOURNAL = {Journal of Machine Learning Research (JMLR)}, VOLUME = {5}, YEAR = {2003/04}, PAGES = {1391--1415 (electronic)}, ISSN = {1532-4435}, MRCLASS = {68T05}, MRNUMBER = {MR2248021}, } @ARTICLE {HoVa:97, author = "M. HOLST and S. VANDEWALLE", title = " Schwarz methods: to symmetrize or not to symmetrize", journal = "SIAM J. Numer. Anal.", year = "1997", volume = "34", pages = "699-722"} @TECHREPORT {Hall:94, author = "M. ELHALLABI", title = "An inexact hybrid algorithm for nonlinear systems of equations", institution = "Department of Mathematical Sciences, Rice University", year = "1994", number = "CRPC-TR94372", address = "Houston, TX"} @TECHREPORT {Ha:94, author = "M. ELHALLABI", title = " A global convergence theory for {SLP} and {SQP} trust-region algorithms", institution = "Department of Mathematical Sciences, Rice University", year = "1994", number = "CRPC-TR94371", address = "Houston, TX"} @TECHREPORT {HallTap:95, author = "M. ELHALLABI and R.A. Tapia", title = "An inexact trust-region feasible-point algorithm for nonlinear systems of equalities and inequalities", institution = "Department of Mathematical Sciences, Rice University", year = "1995", number = "CRPC-TR95543", address = "Houston, TX"} @TECHREPORT {HallTap:93, author = "M. ELHALLABI and R.A. Tapia", title = "An inexact trust-region feasible-point algorithm: globalization of {G}auss-{N}ewton method", institution = "Department of Mathematical Sciences, Rice University", year = "1993", number = "TR93-43", address = "Houston, TX"} @ARTICLE {HaHaSi:84, author = "P.L. HAMMER and P. Hansen and B. SIMEONE", title = "Roof duality, complementation and persistency in quadratic 0-1 optimization", journal = mprog, year = "1984", volume = "28", pages = "121-155"} @ARTICLE {HaRu:70, author = "P.L. HAMMER and A.A. RUBIN", title = "Some remarks on quadratic programming with 0-1 variables", journal = "R.I.R.O.", year = "1970", volume = "3", pages = "67-79"} @article{HESSERT2021112451, title = {Moore-{P}enrose inverses of the signless {L}aplacian and edge-{L}aplacian of graphs}, journal = {Discrete Mathematics}, volume = {344}, number = {8}, pages = {112451}, year = {2021}, issn = {0012-365X}, doi = {https://doi.org/10.1016/j.disc.2021.112451}, url = {https://www.sciencedirect.com/science/article/pii/S0012365X21001643}, author = {Ryan Hessert and Sudipta Mallik}, keywords = {Moore-Penrose inverse, Signless Laplacian, Incidence matrix, Tree, Unicyclic graph}, abstract = {The signless Laplacian Q and signless edge-Laplacian S of a given graph may or may not be invertible. The Moore-Penrose inverses of Q and S are studied. In particular, using the incidence matrix, we find combinatorial formulas of the Moore-Penrose inverses of Q and S for trees. Also, we present combinatorial formulas of the inverses of Q and S for odd unicyclic graphs.} } @article {MR2312332, AUTHOR = {Cvetkovi\'{c}, Drago\v{s} and Rowlinson, Peter and Simi\'{c}, Slobodan K.}, TITLE = {Signless {L}aplacians of finite graphs}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {423}, YEAR = {2007}, NUMBER = {1}, PAGES = {155--171}, ISSN = {0024-3795}, MRCLASS = {05C50}, MRNUMBER = {2312332}, MRREVIEWER = {Hong Zhang}, DOI = {10.1016/j.laa.2007.01.009}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1016/j.laa.2007.01.009}, } @article {MR2003i:65039, AUTHOR = {Calvetti, D. and Hansen, P.C. and Reichel, L.}, TITLE = {L-curve curvature bounds via {L}anczos bidiagonalization}, NOTE = {Orthogonal polynomials, approximation theory, and harmonic analysis (Inzel, 2000)}, JOURNAL = {Electron. Trans. Numer. Anal.}, FJOURNAL = {Electronic Transactions on Numerical Analysis}, VOLUME = {14}, YEAR = {2002}, PAGES = {135--150 (electronic)}, ISSN = {1068-9613}, MRCLASS = {65F22 (65F10)}, MRNUMBER = {2003i:65039}, MRREVIEWER = {Lars Eld{\'e}n}, } @book {MR1413298, AUTHOR = {HANKE, M.}, TITLE = {Conjugate gradient type methods for ill-posed problems}, SERIES = {Pitman Research Notes in Mathematics Series}, VOLUME = {327}, PUBLISHER = {Longman Scientific \& Technical}, ADDRESS = {Harlow}, YEAR = {1995}, PAGES = {iv+134}, ISBN = {0-582-27370-6}, MRCLASS = {65J20 (47A50 65J10)}, MRNUMBER = {MR1413298 (97m:65111)}, MRREVIEWER = {M. Z. Nashed}, } @article {MR95b:65043, AUTHOR = {HANKE, M. and Hansen, P.C.}, TITLE = {Regularization methods for large-scale problems}, JOURNAL = {Surveys Math. Indust.}, FJOURNAL = {Surveys on Mathematics for Industry}, VOLUME = {3}, YEAR = {1993}, NUMBER = {4}, PAGES = {253--315}, ISSN = {0938-1953}, CODEN = {SMINER}, MRCLASS = {65F05 (65R20 86A15 86A22)}, MRNUMBER = {95b:65043}, MRREVIEWER = {Lars Eld{\'e}n}, } @techreport {Hansen:2800, author = "P.C. Hansen", title = "The {L}-curve and its use in the numerical treatment of inverse problems", Institution="Technical University of Denmark", year = "1999", url = "http://www.imm.dtu.dk/documents/ftp/tr99/tr15_99.pdf " } @article {MR83a:90129, AUTHOR = {HAMMER, P. L. and Hansen, P.}, TITLE = {Logical relations in quadratic $0-1$\ programming}, JOURNAL = {Rev. Roumaine Math. Pures Appl.}, FJOURNAL = {Acad\'emie de la R\'epublique Populaire Roumaine. Revue Roumaine de Math\'ematiques Pures et Appliqu\'ees}, VOLUME = {26}, YEAR = {1981}, NUMBER = {3}, PAGES = {421--429}, ISSN = {0035-3965}, CODEN = {RRMPB6}, MRCLASS = {90C20}, MRNUMBER = {83a:90129}, MRREVR = {R. {\cedla{S}}erban}, } @ARTICLE {Han:76, author = "S.P. HAN", title = "Superlinearly convergent variable metric algorithms for general nonlinear programming problems", journal = "Math. Prog.", year = "1976", volume = "11", pages = "263-283"} @ARTICLE {Han:77, author = "S.P. HAN", title = "Dual variable metric algorithms for constrained optimization", journal = "SIAM J. Control Optim.", year = "1977", volume = "15", pages = "546-565"} @TECHREPORT {Han:78, author = "S.P. HAN", title = "Superlinear convergence of a minimax method", institution = "Department of Computer Science, Cornell University", year = "1978", number = "TR78-336", address = "Ithaca, NY"} @ARTICLE {Han:81, author = "S.P. HAN", title = "Variable metric methods for minimizing a class of nondifferentiable functions", journal = "Math. Prog.", year = "1981", volume = "20", pages = "1-13"} @INCOLLECTION {HanParYe:90, author = "C.-G. HAN and P.M. Pardalos and Y. YE", title = "Computational aspects of an interior point algorithm for quadratic programming problems with box constraints", booktitle = "Large Scale Numerical Optimization", publisher = "SIAM", editor = "T.F. COLEMAN and Y. LI", year = "1990"} @article {HanParYe:92, author = "C.-G. HAN and P.M. Pardalos and Y. YE", title = "On the solution of indefinite quadratic problems using an interior-point algorithm", journal = "Informatica", volume = "3", number = "4", pages = "474-496", year = "1992"} @inproceedings {HardtMekaRaghWeigz:14, AUTHOR = {M. Hardt and R. Meka and P. Raghavendra and B. Weitz}, TITLE = {Computational Limits for Matrix Completion}, BOOKTITLE = {JMLR Proceedings}, PAGES = {1--23}, PUBLISHER = {JMLR}, YEAR = {2014}, } @ARTICLE {HaLiPo:29, author = "G.H. HARDY and J.E. LITTLEWOOD and G. POLYA", title = "Some simple inequalities satisfied by convex functions", journal = "Messanger Math.", year = "1929", pages = "145-152", volume = "58"} @BOOK {HaLiPo:34, author = "G.H. HARDY and J.E. LITTLEWOOD and G. POLYA", title = "Inequalities", publisher = "Cambridge Univesity Press", year = "1934", Note = "2nd edition 1952", address = "London and New York"} @BOOK {Harary, author = "F. HARARY", title = "Graph Theeory", publisher = "Addison-Wesley", year = "1969"} @TECHREPORT {HaJeYo:81, author = "L.J. HAYES and K.C. JEA and D.M. Young", title = "Generalized conjugate gradient acceleration of iterative methods, part {I}: {T}he symmetrizable case", institution = "Center for Numerical Analysis, University of Texas at Austin", year = "1981", number = "162", address = "Austin, TX"} @TECHREPORT {Heb:73, author = "M.D. Hebden", title = "An algorithm for minimization using exact second derivatives", institution = "Atomic Energy Research Establishment", year = "1973", number = "TP515", address = "Harwell, England"} @PHDTHESIS {Hei91, author = "M. HEINKENSCHLOSS", title = "Gauss-{N}ewton methods for infinite dimensional least squares problems with norm constraints", institution = "Universitat Trier", year = "1991", address = "Mathenatik/Informatik"} @TECHREPORT {Hei:92, author = "M. HEINKENSCHLOSS", title = "On the solution of a two ball trust region subproblem", institution = "Universitat Trier", year = "1992", number = "Nr.92-16", address = "Mathenatik/Informatik"} @ARTICLE {HerSch:90, author = "D. HERSHKOWITZ AND H. Schneider", title = "On the inertia of intervals of matrices", journal = simax, year = "1990", volume = "11", pages = "565-574"} @techreport{Helmke:07, author = "U. HELMKE and K. H{\"U}PER and J. TRUMPF", year = "2207", title = "{N}ewton's method on Gra{\ss}mann manifolds", institution = "", type = "Report", URL = "http://arxiv.org/abs/0709.2205", number = "arXiv:0709.2205" } @incollection {MR2656823, AUTHOR = {Heinig, G. and Rost, K.}, TITLE = {Introduction to {B}ezoutians}, BOOKTITLE = {Numerical methods for structured matrices and applications}, SERIES = {Oper. Theory Adv. Appl.}, VOLUME = {199}, PAGES = {25--118}, PUBLISHER = {Birkh\"auser Verlag, Basel}, YEAR = {2010}, MRCLASS = {15A09 (15A23 65F05)}, MRNUMBER = {2656823}, } @article {MR1781609, AUTHOR = {Helsgaun, K.}, TITLE = {An effective implementation of the {L}in-{K}ernighan traveling salesman heuristic}, JOURNAL = {European J. Oper. Res.}, FJOURNAL = {European Journal of Operational Research}, VOLUME = {126}, YEAR = {2000}, NUMBER = {1}, PAGES = {106--130}, ISSN = {0377-2217}, MRCLASS = {90C27 (90C59)}, MRNUMBER = {1781609}, DOI = {10.1016/S0377-2217(99)00284-2}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/S0377-2217(99)00284-2}, } @ARTICLE {Hes:69, author = "M.R. HESTENES", title = "Multiplier and gradient methods", journal = "J. Optim. Theory Appl.", year = "1969", volume = "4", pages = "303-320"} @article {MR1906754, AUTHOR = {Heinig, G.}, TITLE = {On the reconstruction of {T}oeplitz matrix inverses from columns}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {350}, YEAR = {2002}, PAGES = {199--212}, ISSN = {0024-3795}, MRCLASS = {15A09}, MRNUMBER = {1906754}, MRREVIEWER = {Ronald L. Smith}, URL = {http://www.sciencedirect.com.proxy.lib.uwaterloo.ca/science?_ob=GatewayURL&_origin=MR&_method=citationSearch&_piikey=s0024379502002896&_version=1&md5=29ca86871be992d3d4dd0391b2f9cc8b}, } @book {MR3645404, TITLE = {Handbook of cluster analysis}, SERIES = {Chapman \& Hall/CRC Handbooks of Modern Statistical Methods}, EDITOR = {Hennig, C. and Meila, M. and Murtagh, F. and Rocci, R.}, PUBLISHER = {CRC Press, Boca Raton, FL}, YEAR = {2016}, PAGES = {xx+753}, ISBN = {978-1-4665-5188-6}, MRCLASS = {62-06 (62H30)}, MRNUMBER = {3645404}, } @ARTICLE{HesseLukeNeumann:2014, author={Hesse, R. and Luke, D.R. and Neumann, P.}, journal={Signal Processing, IEEE Transactions on}, title={Alternating Projections and {D}ouglas-{R}achford for Sparse Affine Feasibility}, year={2014}, month={Sept}, volume={62}, number={18}, pages={4868-4881}, keywords={Abstracts;Convergence;Optimization;Projection algorithms;Signal processing algorithms;Sparse matrices;Vectors;Compressed sensing;iterative methods;linear systems;optimization;projection algorithms;sparse matrices}, doi={10.1109/TSP.2014.2339801}, ISSN={1053-587X},} @misc {Phan:2014, author="Phan, Hung M.", title="Linear Convergence of the {D}ouglas-{R}achford Method for Two Closed Sets", year="2014", month="Jan", eprint="arXiv/1401.6509", } @BOOK {Hes:80, author = "M.R. HESTENES", title = "Conjugate Direction Methods In Optimization", publisher = "Springer-Verlag", year = "1980", address = "New York, NY"} @ARTICLE{Hestenes-McShane:40, AUTHOR = {M.R. Hestenes and E.J. McShane}, TITLE = {A theorem on quadratic forms and its application in the calculus of variations}, JOURNAL = {Trans. Amer. Math. Soc.}, YEAR = {1940}, volume = {47}, number = {}, pages = {501--512}, month = {}, note = {}, abstract = {}, keywords = {}, source = {}, } @ARTICLE {Hett:86, author = "R. HETTICH", TITLE = {An implementation of a discretization method for semi-infinite programming}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {34}, YEAR = {1986}, NUMBER = {3}, PAGES = {354--361}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C33}, MRNUMBER = {MR839609 (87f:90125)}, } @ARTICLE {HeGr:90, author = "R. HETTICH and G. GRAMLICH", title = "A note on an implementation of a method for quadratic semi-infinite programming", journal = mprog, year = "1990", volume = "46", number = "2", pages = "249-254"} @ARTICLE {HeHiSp:62, author = "G.R. HEXT and F.R. HIMSWORTH and W. SPENDLEY", title = "Sequential application of simplex design in optimization and evolutionary operation", journal = "Technometrics", year = "1962", volume = "4", number = "4", pages = "441-461"} @article{doi:10.1137/120885991, author = {Al-Mohy, A.H. and Higham, N.J. and Relton, S.D.}, title = {Computing the Fréchet Derivative of the Matrix Logarithm and Estimating the Condition Number}, journal = {SIAM Journal on Scientific Computing}, volume = {35}, number = {4}, pages = {C394-C410}, year = {2013}, doi = {10.1137/120885991}, URL = { https://doi.org/10.1137/120885991 }, eprint = { https://doi.org/10.1137/120885991 } } @article {MR2382048, AUTHOR = {Higham, N.J. and Mackey, D.S. and Tisseur, F. and Garvey, Seamus D.}, TITLE = {Scaling, sensitivity and stability in the numerical solution of quadratic eigenvalue problems}, JOURNAL = {Internat. J. Numer. Methods Engrg.}, FJOURNAL = {International Journal for Numerical Methods in Engineering}, VOLUME = {73}, YEAR = {2008}, NUMBER = {3}, PAGES = {344--360}, ISSN = {0029-5981}, CODEN = {IJNMBH}, MRCLASS = {65N25 (65F15 65H17 74H45 74K05)}, MRNUMBER = {2382048 (2009c:65288)}, MRREVIEWER = {Gh. Adam}, DOI = {10.1002/nme.2076}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1002/nme.2076}, } @article {MR2369292, AUTHOR = {Higham, N.J. and Li, Ren-Cang and Tisseur, Fran{\c{c}}oise}, TITLE = {Backward error of polynomial eigenproblems solved by linearization}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {29}, YEAR = {2007}, NUMBER = {4}, PAGES = {1218--1241}, ISSN = {0895-4798}, MRCLASS = {65F15 (15A18)}, MRNUMBER = {2369292 (2009a:65092)}, MRREVIEWER = {Jens-Peter M. Zemke}, DOI = {10.1137/060663738}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/060663738}, } @article {MR2276551, AUTHOR = {Higham, N.J. and Mackey, D. Steven and Tisseur, Fran{\c{c}}oise}, TITLE = {The conditioning of linearizations of matrix polynomials}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {28}, YEAR = {2006}, NUMBER = {4}, PAGES = {1005--1028}, ISSN = {0895-4798}, MRCLASS = {65F15 (15A18)}, MRNUMBER = {2276551 (2008c:65103)}, MRREVIEWER = {Marc Van Barel}, DOI = {10.1137/050628283}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/050628283}, } @article {MR1780268, AUTHOR = {Higham, N.J. and Tisseur, F.}, TITLE = {A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {21}, YEAR = {2000}, NUMBER = {4}, PAGES = {1185--1201 (electronic)}, ISSN = {0895-4798}, MRCLASS = {65F20 (65F15)}, MRNUMBER = {1780268 (2001d:65051)}, DOI = {10.1137/S0895479899356080}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/S0895479899356080}, } @Book{Higham:2000:MG, author = "D.J. Higham and N.J. HIGHAM", title = "{MATLAB} Guide", publisher = "Society for Industrial and Applied Mathematics", address = "Philadelphia, PA, USA", year = "2000", pages = "xxii+283", ISBN = "0-89871-516-4" } @ARTICLE {Hig:86, author = "N.J. Higham", title = "{N}ewton's method for the matrix square root", journal = "Mathematics of Computation", year = "1986", volume = "46", number = "174", pages = "537-549"} @book {MR2396439, AUTHOR = {Higham, N.J.}, TITLE = {Functions of {M}atrices}, NOTE = {Theory and {C}omputation}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {2008}, PAGES = {xx+425}, ISBN = {978-0-89871-646-7}, MRCLASS = {15-02 (93B40 93C05)}, MRNUMBER = {2396439 (2009b:15001)}, MRREVIEWER = {Daniel Kressner}, DOI = {10.1137/1.9780898717778}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/1.9780898717778}, } @book {MR2135945, AUTHOR = {Higham, Desmond J. and Higham, N.J.}, TITLE = {M{ATLAB} guide}, EDITION = {Second}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {2005}, PAGES = {xxiv+382}, ISBN = {0-89871-578-4}, MRCLASS = {65-00 (00A20)}, MRNUMBER = {2135945}, DOI = {10.1137/1.9780898717891}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/1.9780898717891}, } @book {MR1927606, AUTHOR = {Higham, N.J.}, TITLE = {Accuracy and stability of numerical algorithms}, EDITION = {Second}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {2002}, PAGES = {xxx+680}, ISBN = {0-89871-521-0}, MRCLASS = {65G50 (65-02)}, MRNUMBER = {1927606 (2003g:65064)}, DOI = {10.1137/1.9780898718027}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/1.9780898718027}, } @book {MR1787308, AUTHOR = {Higham, Desmond J. and Higham, N.J.}, TITLE = {M{ATLAB} guide}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {2000}, PAGES = {xxii+283}, ISBN = {0-89871-469-9}, MRCLASS = {65-04 (00A20)}, MRNUMBER = {1787308 (2001e:65003)}, } @book {MR1640787, AUTHOR = {Higham, N.J.}, TITLE = {Handbook of writing for the mathematical sciences}, EDITION = {Second}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {1998}, PAGES = {xvi+302}, ISBN = {0-89871-420-6}, MRCLASS = {00A20}, MRNUMBER = {1640787 (99g:00017)}, DOI = {10.1137/1.9780898719550}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/1.9780898719550}, } @book {MR1368629, AUTHOR = {Higham, N.J.}, TITLE = {Accuracy and stability of numerical algorithms}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {1996}, PAGES = {xxviii+688}, ISBN = {0-89871-355-2}, MRCLASS = {65G05 (65-02 65F05)}, MRNUMBER = {1368629 (97a:65047)}, MRREVIEWER = {S. Hitotumatu}, } @book {MR1223778, AUTHOR = {Higham, N.J.}, TITLE = {Handbook of writing for the mathematical sciences}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {1993}, PAGES = {xii+241}, ISBN = {0-89871-314-5}, MRCLASS = {00A20}, MRNUMBER = {1223778 (94f:00005)}, } @book{Higham:2008:FM, author = "N.J. Higham", title = "Functions of Matrices: {Theory} and Computation", publisher = "Society for Industrial and Applied Mathematics", address = "Philadelphia, PA, USA", year = "2008", pages = "xx+425", isbn = "978-0-898716-46-7" } @ARTICLE {Hig:87, author = "N.J. Higham", title = "A survey of condition number estimation for triangular matrices", journal = "SIAM Rev.", year = "1987", volume = "29", pages = "575-596"} @ARTICLE {Hig:87b, author = "N.J. Higham", title = "Computing real square roots of a real matrix", journal = laa, year = "1987", volume = "88/89", pages = "405-430"} @book {Higbook:93, AUTHOR = {Higham, N.J.}, TITLE = {Handbook of writing for the mathematical sciences}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {1993}, PAGES = {xii+241}, ISBN = {0-89871-314-5}, } @techreport{Higham:1996:RDD, author = "N.J. Higham", title = "Recent Developments in Dense Numerical Linear Algebra", institution = "Manchester Centre for Computational Mathematics", address = "Manchester, England", type = "Numerical Analysis Report", number = "No. 288", pages = "26", month = apr, year = "1996", URL = "ftp://ftp.ma.man.ac.uk/pub/narep/narep288.ps.gz", keywords = "Numerical linear algebra, linear system, least squares problem, eigenvalue problem, LAPACK", note = "To appear in {\em The State of the Art in Numerical Analysis}, I. S. Duff and G. A. Watson, editors, Oxford University Press" } @article {MR2002i:65039, AUTHOR = {DAVIES, P.I. and Higham, N.J. and TISSEUR, F.}, TITLE = {Analysis of the {C}holesky method with iterative refinement for solving the symmetric definite generalized eigenproblem}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {23}, YEAR = {2001}, NUMBER = {2}, PAGES = {472--493 (electronic)}, ISSN = {1095-7162}, MRCLASS = {65F15}, MRNUMBER = {2002i:65039}, MRREVIEWER = {David Scott Watkins}, } @article {MR98e:65036, author = "N.J. Higham", TITLE = {Iterative refinement for linear systems and {LAPACK}}, JOURNAL = {IMA J. Numer. Anal.}, FJOURNAL = {IMA Journal of Numerical Analysis}, VOLUME = {17}, YEAR = {1997}, NUMBER = {4}, PAGES = {495--509}, ISSN = {0272-4979}, CODEN = {IJNADN}, MRCLASS = {65F30}, MRNUMBER = {98e:65036}, } @article {MR92h:65043, author = "N.J. Higham", TITLE = {Iterative refinement enhances the stability of {$QR$} factorization methods for solving linear equations}, JOURNAL = {BIT}, FJOURNAL = {BIT. Numerical Mathematics}, VOLUME = {31}, YEAR = {1991}, NUMBER = {3}, PAGES = {447--468}, ISSN = {0006-3835}, CODEN = {NBITAB}, MRCLASS = {65F05 (65F10 65G05)}, MRNUMBER = {92h:65043}, MRREVIEWER = {James Weldon Demmel}, } @article{Hillier_computationallyefficient, author = {G. Hillier and R. Kan and X. Wang}, title = {Computationally Efficient Recursions for Top-Order Invariant Polynomials with Applications}, journal = {Econometric Theory}, volume = {25}, year = {2009}, pages={211-242}, } @article {MR2472051, AUTHOR = {Hillier, Grant and Kan, Raymond and Wang, Xiaolu}, TITLE = {Computationally efficient recursions for top-order invariant polynomials with applications}, JOURNAL = {Econometric Theory}, FJOURNAL = {Econometric Theory}, VOLUME = {25}, YEAR = {2009}, NUMBER = {1}, PAGES = {211--242}, ISSN = {0266-4666}, MRCLASS = {60E10 (62H05 65C20)}, MRNUMBER = {2472051 (2010c:60060)}, DOI = {10.1017/S0266466608090075}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1017/S0266466608090075}, } @book {MR569591, AUTHOR = {HILLIER, F.S. and LIEBERMAN, G.J.}, TITLE = {Introduction to operations research}, EDITION = {Third}, PUBLISHER = {Holden-Day Inc.}, ADDRESS = {Oakland, Calif.}, YEAR = {1980}, PAGES = {xiv+829}, ISBN = {0-8162-3867-7}, MRCLASS = {90Bxx (90-01)}, MRNUMBER = {MR569591 (82b:90040)}, MRREVIEWER = {A. C. Williams}, } @book {MR1865628, AUTHOR = {Hiriart-Urruty, J.-B. and Lemar{\'e}chal, C.}, TITLE = {Fundamentals of convex analysis}, SERIES = {Grundlehren Text Editions}, NOTE = {Abridged version of {{\i}t Convex analysis and minimization algorithms. I} [Springer, Berlin, 1993; MR1261420 (95m:90001)] and {{\i}t II} [ibid.; MR1295240 (95m:90002)]}, PUBLISHER = {Springer-Verlag, Berlin}, YEAR = {2001}, PAGES = {x+259}, ISBN = {3-540-42205-6}, MRCLASS = {90-01 (26B25 49-01)}, MRNUMBER = {1865628 (2002i:90002)}, DOI = {10.1007/978-3-642-56468-0}, URL = {http://dx.doi.org/10.1007/978-3-642-56468-0}, } @ARTICLE {Hir:79a, author = "J.B. Hiriart-Urruty", title = "Tangent cones, generalized gradients and mathematical programming in {B}anach spaces", journal = "Math. Op. Research", year = "1979", volume = "4", pages = "79-97"} @ARTICLE {Hir:79b, author = "J.B. Hiriart-Urruty", title = "Refinements of necessary optimality conditions in nondifferentiable programming, part {I}", journal = "Appl. Math. Optim.", year = "1979", volume = "5", pages = "63-82"} @ARTICLE {Hir:81, author = "J.B. Hiriart-Urruty", title = "A better insight into the generalized gradient of the absolute value of a function", journal = "Appl. Anal.", year = "1981", volume = "12", pages = "239-249"} @ARTICLE {Hir:82, author = "J.B. Hiriart-Urruty", title = "Refinements of necessary optimality conditions in nondifferentiable programming, part {II}", journal = "Math. Programming Studies", year = "1982", volume = "19", pages = "120-139"} @INCOLLECTION {Hir:89, author = "J.B. Hiriart-Urruty", title = "From convex optimization to nonconvex optimization. Part I: Necessary and sufficient conditions from global optimality", booktitle = "Nonsmooth Optimization and Related Topics", publisher = "Plenum Press", year = "1989", editor = "F.H. Clarke", pages = "219-239"} @article {MR98a:49027, AUTHOR = {Hiriart-Urruty, J.-B. and LEDYAEV, Y.S.}, TITLE = {A note on the characterization of the global maxima of a (tangentially) convex function over a convex set}, JOURNAL = {J. Convex Anal.}, FJOURNAL = {Journal of Convex Analysis}, VOLUME = {3}, YEAR = {1996}, NUMBER = {1}, PAGES = {55--61}, ISSN = {0944-6532}, } @BOOK{HL, author = "J.B. Hiriart-Urruty and C. Lemarechal", TITLE = "Convex Analysis and Minimization Algorithms", PUBLISHER = "Springer-Verlag", YEAR = {1993} } @BOOK{ HiriartUrrutyLemarechal93b, author = "J.B. Hiriart-Urruty and C. Lemarechal", TITLE = {Convex Analysis and Minimization Algorithms II}, PUBLISHER = {Springer}, YEAR = 1993, ADDRESS = {Berlin, Heidelberg}, SERIES = {Grundlehren der mathematischen Wissenschaften}, VOLUME = 306 } @article {Hir03, AUTHOR = {Hiroshima, T.}, TITLE = {Majorization criterion for distillability of a bipartite quantum state}, JOURNAL = {Phys. Rev. Lett.}, VOLUME = {91}, YEAR = {2003}, NUMBER = {5}, PAGES = {4}, } @article {MR97k:49030, AUTHOR = {Clarke, F. H. and Ledyaev, Yu. S. and Hiriart-Urruty, J.-B.}, TITLE = {Global optimality in the calculus of variations}, JOURNAL = {Nonlinear Anal.}, FJOURNAL = {Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal}, VOLUME = {28}, YEAR = {1997}, NUMBER = {7}, PAGES = {1187--1192}, ISSN = {0362-546X}, CODEN = {NOANDD}, } @article {MR1938337, AUTHOR = {DAN, H. and YAMASHITA, N. and FUKUSHIMA, M.}, TITLE = {Convergence properties of the inexact {L}evenberg-{M}arquardt method under local error bound conditions}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods \& Software}, VOLUME = {17}, YEAR = {2002}, NUMBER = {4}, PAGES = {605--626}, ISSN = {1055-6788}, MRCLASS = {65H10}, MRNUMBER = {MR1938337 (2003k:65048)}, } @incollection {MR97d:90088, author = "J.B. Hiriart-Urruty", TITLE = {Conditions for global optimality}, BOOKTITLE = {Handbook of {G}lobal {O}ptimization}, PAGES = {1--26}, SERIES = {Nonconvex Optim. Appl.}, VOLUME = {2}, PUBLISHER = {Kluwer Acad. Publ.}, ADDRESS = {Dordrecht}, YEAR = {1995}, } @article {MR96b:15024, AUTHOR = {Hiriart-Urruty, J.-B. and Ye, D.}, TITLE = {Sensitivity analysis of all eigenvalues of a symmetric matrix}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {70}, YEAR = {1995}, NUMBER = {1}, PAGES = {45--72}, ISSN = {0029-599X}, CODEN = {NUMMA7}, } @article {Hladik:11, AUTHOR = {Hladik, M.}, TITLE = {Tolerance analysis in linear systems and linear programming}, JOURNAL = oms, VOLUME = {26}, YEAR = {2011}, NUMBER = {3}, PAGES = {381--396}, } @INCOLLECTION {HoSch:81, author = "W. HOCK and K. SCHITTKOWSKI", title = "Test examples for nonlinear programming codes", booktitle = "Lecture Notes in Economics and Mathematical Systems \#187", publisher = "Springer-Verlag", year = "1981", address = "Berlin, Heidelberg and New York"} @ARTICLE {HoSch:83, author = "W. HOCK and K. SCHITTKOWSKI", title ="A comparative performance evaluation of 27 nonlinear programming codes", journal = "Computing", year = "1983", volume = "30", pages = "335-358"} @ARTICLE {HoeKenn:70, author = "A.E. HOERL and R.W. KENNARD", title = "Ridge regression: biased estimation for nonorthogonal problems", journal = "Technometrics", year = "1970", volume = "12", pages = "55-67"} @techreport {Hofmann, author = "T. Hofmann", title={Unsupervised learning by probabilistic latent semantic analysis}, journal={Machine learning}, volume={42}, number={1}, pages={177--196}, year={2001}, publisher={Springer} } @inproceedings{pennington2014glove, title={Glove: Global vectors for word representation.}, author={Pennington, J. and Socher, R. and Manning, C.D}, booktitle={EMNLP}, volume={14}, pages={1532--1543}, year={2014} } @inproceedings{socher2012semantic, title={Semantic compositionality through recursive matrix-vector spaces}, author={Socher, R. and Huval, B. and Manning, C.D and Ng, A.Y}, booktitle={Proceedings of the 2012 joint conference on empirical methods in natural language processing and computational natural language learning}, pages={1201--1211}, year={2012}, organization={Association for Computational Linguistics} } @BOOK{HoffKunz:71, AUTHOR = "K. Hoffman and R. KUNZE", TITLE = "Linear algebra, Second edition", PUBLISHER = "Prentice-Hall, Inc", ADDRESS = "Englewood Cliffs, N.J.", YEAR = 1971 } @book {MR43:1998, AUTHOR = {Hoffman, Kenneth and Kunze, Ray}, TITLE = {Linear algebra}, PUBLISHER = {Prentice-Hall Inc.}, ADDRESS = {Englewood Cliffs, N.J.}, YEAR = {1971}, PAGES = {viii+407}, MRCLASS = {15.00}, MRNUMBER = {43 \#1998}, } @ARTICLE {Hog:73a, author = "W.W. Hogan", title = "Point-to-set maps in mathematical programming", journal = "SIAM Review", year = "1973", volume = "3", pages = "591-603"} @ARTICLE {Hog:73b, author = "W.W. Hogan", title = "The continuity of the perturbation function of a convex program", journal = "Operat. Research", year = "1973", volume = "21", pages = "351-352"} @book {MR2279160, TITLE = {Handbook of linear algebra}, SERIES = {Discrete Mathematics and its Applications (Boca Raton)}, EDITOR = {Hogben, L.}, NOTE = {Associate editors: Richard Brualdi, Anne Greenbaum and Roy Mathias}, PUBLISHER = {Chapman \& Hall/CRC, Boca Raton, FL}, YEAR = {2007}, PAGES = {xxx+1370}, ISBN = {978-1-58488-510-8; 1-58488-510-6}, MRCLASS = {15-00 (00A20)}, MRNUMBER = {2279160 (2007j:15001)}, } @article {MR95g:90045, AUTHOR = {HOLMBERG, K.}, TITLE = {Cross decomposition applied to integer programming problems: {D}uality gaps and convexification in parts}, JOURNAL = {Oper. Res.}, FJOURNAL = {Operations Research. The Journal of the Operations Research Society of America}, VOLUME = {42}, YEAR = {1994}, NUMBER = {4}, PAGES = {657--668}, ISSN = {0030-364X}, CODEN = {OPREAI}, } @article {MR94i:90081, AUTHOR = {HOLMBERG, K.}, TITLE = {Generalized cross decomposition applied to nonlinear integer programming problems: duality gaps and convexification in parts}, JOURNAL = {Optimization}, FJOURNAL = {Optimization. A Journal of Mathematical Programming and Operations Research}, VOLUME = {23}, YEAR = {1992}, NUMBER = {4}, PAGES = {341--356}, ISSN = {0233-1934}, } @BOOK{Hol:75, AUTHOR = "R.B. Holmes", TITLE = "Geometric Functional Analysis and its Applications", PUBLISHER = "Springer-Verlag", ADDRESS = "Berlin", YEAR = 1975 } @ARTICLE {HooJee:61, author = "R. HOOKE and T.A. JEEVES", title = "{"Direct search"} solution of numerical and statistical problems", journal = "Journal of the Association for Computing Machinery", year = "1961", volume = "8", number = "2", pages = "212-229"} @BOOK{HoJo:85, AUTHOR = "R.A. Horn and C.R. Johnson", TITLE = {Matrix Analysis}, NOTE = {Corrected reprint of the 1985 original}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {1990}, PAGES = {xiv+561}, ISBN = {0-521-38632-2}, MRCLASS = {15-01}, MRNUMBER = {91i:15001}, } @BOOK{hj85, AUTHOR = "R.A. Horn and C.R. Johnson", TITLE = {Matrix Analysis}, NOTE = {Corrected reprint of the 1985 original}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {1990}, PAGES = {xiv+561}, ISBN = {0-521-38632-2}, MRCLASS = {15-01}, MRNUMBER = {91i:15001}, } @book {MR2978290, AUTHOR = {Horn, R.A. and Johnson, C.R.}, TITLE = {Matrix analysis}, EDITION = {Second}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {2013}, PAGES = {xviii+643}, ISBN = {978-0-521-54823-6}, MRCLASS = {15-01}, MRNUMBER = {2978290}, MRREVIEWER = {Mohammad Sal Moslehian}, } @BOOK{HoJo:91, AUTHOR = "R.A. Horn and C.R. Johnson", TITLE = {Topics in Matrix Analysis}, NOTE = {Corrected reprint of the 1991 original}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {1994}, PAGES = {viii+607}, ISBN = {0-521-46713-6}, MRCLASS = {15-02 (15-01 65-02 65Fxx)}, MRNUMBER = {95c:15001}, } @article {MR1935224, AUTHOR = {Horn, R.A.}, TITLE = {Normal matrices with a dominant eigenvalue and an eigenvector with no zero entries}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {357}, YEAR = {2002}, PAGES = {35--44}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15-XX}, MRNUMBER = {1 935 224}, } @BOOK {HoPa:95, author = "R. HORST and P.M. Pardalos", title = "Handbook of Global Optimization", publisher = "Kluwer Academic Publishers", year = "1995", volume = "2", address = "Dordrecht; Boston", isbn = "0792331206", series = "Nonconvex optimization and its applications" } @ARTICLE {Hosh:72, author = "S. HOSHINO", title = "A formulation of variable metric methods", journal = "Journal Instit. Math. Appl.", year = "1972", volume = "10", pages = "394-403"} @article {MR2587731, AUTHOR = {Vavasis, S.A.}, TITLE = {On the complexity of nonnegative matrix factorization}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {20}, YEAR = {2009}, NUMBER = {3}, PAGES = {1364--1377}, ISSN = {1052-6234}, MRCLASS = {65F05 (15A23 15B48 68T05 90C26 90C60)}, MRNUMBER = {2587731}, MRREVIEWER = {Juan R. Torregrosa}, DOI = {10.1137/070709967}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/070709967}, } @TECHREPORT {HoVav:95, author = "P.D. HOUGH and S.A. Vavasis", title = "Complete orthogonal decomposition for weighted least squares", institution = "Center for Applied Math., Cornell University", location = "Ithaca, NY", keywords = "lsq, nla, interior points", year = "1995"} @ARTICLE{2016arXiv160500320K, author = {{Karimi}, S. and {Vavasis}, S.A.}, title = "{A unified convergence bound for conjugate gradient and accelerated gradient}", journal = {ArXiv e-prints}, archivePrefix = "arXiv", eprint = {1605.00320}, primaryClass = "math.OC", keywords = {Mathematics - Optimization and Control, 90C25, G.1.6}, year = 2016, month = may, adsurl = {http://adsabs.harvard.edu/abs/2016arXiv160500320K}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } @BOOK {Hous:64, author = "A.S. Householder", title = "The Theory of Matrices in Numerical Analysis", publisher = "Blaisdell Publishing Company", year = "1964", address = "New York, NY", note = "Dover edition in 1975"} @ARTICLE {HousBa:60, author = "A.S. Householder and F. L. BAUER", title = "On certain iterative methods for solving linear systems", journal = "Numer. Math.", year = "1960", volume = "2", pages = "55-59"} @book {MR3192933, AUTHOR = {Lu, Y.}, TITLE = {Discrete frenet frame with application to structural biology and kinematics}, NOTE = {Thesis (Ph.D.)--The Florida State University}, PUBLISHER = {ProQuest LLC, Ann Arbor, MI}, YEAR = {2013}, PAGES = {84}, ISBN = {978-1303-43329-0}, MRCLASS = {Thesis}, MRNUMBER = {3192933}, URL = {http://gateway.proquest.com.proxy.lib.uwaterloo.ca/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:3596535}, } @article{PhysRevE.83.061908, title = {Discrete Frenet frame, inflection point solitons, and curve visualization with applications to folded proteins}, author = {Hu, Shuangwei and Lundgren, Martin and Niemi, Antti J.}, journal = {Phys. Rev. E}, volume = {83}, issue = {6}, pages = {061908}, numpages = {13}, year = {2011}, month = {Jun}, publisher = {American Physical Society}, doi = {10.1103/PhysRevE.83.061908}, url = {http://link.aps.org/doi/10.1103/PhysRevE.83.061908} } @article{PhysRevE.88.042709, title = {Topology and structural self-organization in folded proteins}, author = {Lundgren, M. and Krokhotin, Andrey and Niemi, Antti J.}, journal = {Phys. Rev. E}, volume = {88}, issue = {4}, pages = {042709}, numpages = {15}, year = {2013}, month = {Oct}, publisher = {American Physical Society}, doi = {10.1103/PhysRevE.88.042709}, url = {http://link.aps.org/doi/10.1103/PhysRevE.88.042709} } @techreport{HsiaSheu:13, author = "Y. Hsia and R.-L. Sheu", year = "2013", title = "Trust Region Subproblem with a Fixed Number of Additional Linear Inequality Constraints has Polynomial Complexity", institution = "Beihang University", address = "Beijing, China", type = "Report", URL = {http://arxiv.org/abs/1312.1398} } @article{HLN11, title = {Discrete Frenet frame, inflection point solitons, and curve visualization with applications to folded proteins}, author = {Hu, S. and Lundgren, M. and Niemi, A.J.}, journal = {Phys. Rev. E}, volume = {83}, issue = {6}, pages = {061908}, numpages = {13}, year = {2011}, month = {Jun}, publisher = {American Physical Society}, doi = {10.1103/PhysRevE.83.061908}, url = {http://link.aps.org/doi/10.1103/PhysRevE.83.061908} } @TECHREPORT {HuSt:91, author = "Y.F. HU and C. STOREY", title = "A family of optimally conditioned quasi-{N}ewton updates for unconstrained optimization", institution = "Department of Mathematical Sciences, Loughborough University of Technology", location = "Leicestershire", year = "1991"} @article {MR99j:90037, AUTHOR = {Huang, Wanzhen and Zhang, Feng}, TITLE = {An {$O(n\sp 2)$} algorithm for a controllable machine scheduling problem}, JOURNAL = {IMA J. Math. Appl. Bus. Indust.}, FJOURNAL = {IMA Journal of Mathematics Applied in Business and Industry}, VOLUME = {10}, YEAR = {1999}, NUMBER = {1}, PAGES = {15--26}, ISSN = {0953-0061}, MRCLASS = {90B35 (93E20)}, MRNUMBER = {99j:90037}, } @article {MR98m:90072, AUTHOR = {Huang, W. and Li, S.}, TITLE = {A two-stage hybrid flowshop with uniform machines and setup times}, JOURNAL = {Math. Comput. Modelling}, FJOURNAL = {Mathematical and Computer Modelling}, VOLUME = {27}, YEAR = {1998}, NUMBER = {2}, PAGES = {27--45}, ISSN = {0895-7177}, CODEN = {MCMOEG}, MRCLASS = {90B35}, MRNUMBER = {98m:90072}, } @article {MR95k:90122, AUTHOR = {Borwein, J. M. and Huang, W. Z.}, TITLE = {A fast heuristic method for polynomial moment problems with {B}oltzmann-{S}hannon entropy}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {5}, YEAR = {1995}, NUMBER = {1}, PAGES = {68--99}, ISSN = {1052-6234}, CODEN = {SJOPE8}, MRCLASS = {90C45 (44A60 65K05)}, MRNUMBER = {95k:90122}, MRREVIEWER = {Dominikus Noll}, } @article {MR703826, AUTHOR = {Borwein, J.M.}, TITLE = {On the existence of {P}areto efficient points}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {8}, YEAR = {1983}, NUMBER = {1}, PAGES = {64--73}, ISSN = {0364-765X}, MRCLASS = {90C25 (46N05 52A05)}, MRNUMBER = {703826}, MRREVIEWER = {Autorreferat}, DOI = {10.1287/moor.8.1.64}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1287/moor.8.1.64}, } @article {MR1098432, AUTHOR = {Borwein, J.M. and Zhuang, D.}, TITLE = {Super efficiency in vector optimization}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {338}, YEAR = {1993}, NUMBER = {1}, PAGES = {105--122}, ISSN = {0002-9947}, CODEN = {TAMTAM}, MRCLASS = {90C29 (52A41)}, MRNUMBER = {1098432}, MRREVIEWER = {Bernard Lemaire}, DOI = {10.2307/2154446}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.2307/2154446}, } @book {MR2596822, AUTHOR = {Borwein, J.M. and Vanderwerff, J.D.}, TITLE = {Convex functions: constructions, characterizations and counterexamples}, SERIES = {Encyclopedia of Mathematics and its Applications}, VOLUME = {109}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {2010}, PAGES = {x+521}, ISBN = {978-0-521-85005-6}, MRCLASS = {49-02 (46B20 46N10 49J53 52A41 90C25)}, MRNUMBER = {2596822}, MRREVIEWER = {Heinz H. Bauschke}, DOI = {10.1017/CBO9781139087322}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1017/CBO9781139087322}, } @techreport{BorweinJuly:16, author = "J. Borwein", year = "2016", title = "Generalizations, examples and counter-examples in analysis and optimisation", institution = "CARMA, University of Newcastle", address = "NSW, Australia", type = "Report", number = "In honour of Michel Thera at 70" } @article {MR3260973, AUTHOR = {Arag{\'o}n Artacho, F.J. and Borwein, J.M. and Tam, M.K.}, TITLE = {Recent results on {D}ouglas-{R}achford methods for combinatorial optimization problems}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {163}, YEAR = {2014}, NUMBER = {1}, PAGES = {1--30}, ISSN = {0022-3239}, MRCLASS = {47J25 (90C27)}, MRNUMBER = {3260973}, MRREVIEWER = {Heinz H. Bauschke}, DOI = {10.1007/s10957-013-0488-0}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s10957-013-0488-0}, } @article {MR3498569, AUTHOR = {Arag\'{o}n Artacho, Francisco J. and Borwein, Jonathan M. and Tam, Matthew K.}, TITLE = {Global behavior of the {D}ouglas-{R}achford method for a nonconvex feasibility problem}, JOURNAL = {J. Global Optim.}, FJOURNAL = {Journal of Global Optimization. An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering}, VOLUME = {65}, YEAR = {2016}, NUMBER = {2}, PAGES = {309--327}, ISSN = {0925-5001}, MRCLASS = {90C26 (65K05)}, MRNUMBER = {3498569}, MRREVIEWER = {Zhili Ge}, DOI = {10.1007/s10898-015-0380-6}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10898-015-0380-6}, } @article {MR3257300, AUTHOR = {Arag{\'o}n Artacho, F.J. and Borwein, J.M. and Tam, M.K.}, TITLE = {Douglas-{R}achford feasibility methods for matrix completion problems}, JOURNAL = {ANZIAM J.}, FJOURNAL = {The ANZIAM Journal. The Australian \& New Zealand Industrial and Applied Mathematics Journal}, VOLUME = {55}, YEAR = {2014}, NUMBER = {4}, PAGES = {299--326}, ISSN = {1446-1811}, MRCLASS = {47J25 (15A83 65K05 90C59)}, MRNUMBER = {3257300}, MRREVIEWER = {Heinz H. Bauschke}, DOI = {10.1017/S1446181114000145}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1017/S1446181114000145}, } @article {MR4378594, AUTHOR = {Altschuler, J.M. and Boix-Adser\`a, E.}, TITLE = {Wasserstein barycenters are {NP}-hard to compute}, JOURNAL = {SIAM J. Math. Data Sci.}, FJOURNAL = {SIAM Journal on Mathematics of Data Science}, VOLUME = {4}, YEAR = {2022}, NUMBER = {1}, PAGES = {179--203}, MRCLASS = {68Q17 (49Q22)}, MRNUMBER = {4378594}, DOI = {10.1137/21M1390062}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/21M1390062}, } @article {MR4253737, AUTHOR = {Altschuler, J.M. and Boix-Adser\`a, E.}, TITLE = {Wasserstein barycenters can be computed in polynomial time in fixed dimension}, JOURNAL = {J. Mach. Learn. Res.}, FJOURNAL = {Journal of Machine Learning Research (JMLR)}, VOLUME = {22}, YEAR = {2021}, PAGES = {Paper No. 44, 19}, ISSN = {1532-4435}, MRCLASS = {90C05 (49Q22 60A10 68Q25)}, MRNUMBER = {4253737}, } @article{Mulzer_2018, doi = {10.1007/s00454-018-9979-y}, url = {https://doi.org/10.1007%2Fs00454-018-9979-y}, year = 2018, month = {mar}, publisher = {Springer Science and Business Media {LLC} }, volume = {60}, number = {3}, pages = {720--755}, author = {W. Mulzer and Y. Stein}, title = {Computational Aspects of the Colorful Carath{\'{e}}odory Theorem}, journal = {Discrete {\&}amp$\mathsemicolon$ Computational Geometry} } @article{2019_BaoYuWaHuYao, author = {Bao, J. and Yu, C. and Wang, J. and Hu, Y. and Yao, J-C.}, year = {2019}, month = {11}, title = {Modified inexact Levenberg Marquardt methods for solving nonlinear least squares problems}, volume = {74}, journal = {Computational Optimization and Applications}, doi = {10.1007/s10589-019-00111-y} } @article{1996_Ba, title={The Approximation of Fixed Points of Compositions of Nonexpansive Mappings in Hilbert Space}, author={H.H. Bauschke}, journal={Journal of Mathematical Analysis and Applications}, year={1996}, volume={202}, pages={150-159} } @incollection {MR3971968, AUTHOR = {Bauschke, H.H. and Burachik, R.S. and Kaya, C.Y.}, TITLE = {Constraint splitting and projection methods for optimal control of double integrator}, BOOKTITLE = {Splitting algorithms, modern operator theory, and applications}, PAGES = {45--68}, PUBLISHER = {Springer, Cham}, YEAR = {[2019] \copyright 2019}, MRCLASS = {49M27 (49J15 49N10)}, MRNUMBER = {3971968}, MRREVIEWER = {Thomas Haberkorn}, } @misc{bauschke2018projecting, title={Projecting onto the intersection of a cone and a sphere}, author={H.H. Bauschke and M. N. Bui and X. Wang}, year={2018}, eprint={1708.00585}, archivePrefix={arXiv}, primaryClass={math.OC} } @misc{bauschke2021projection, title={The projection onto the cross}, author={H.H. Bauschke and M.Krishan Lal and X. Wang}, year={2021}, eprint={2108.04382}, archivePrefix={arXiv}, primaryClass={math.OC} } @article {MR98f:90045, AUTHOR = {Bauschke, H.H. and Borwein, J.M.}, TITLE = {On projection algorithms for solving convex feasibility problems}, JOURNAL = {SIAM Rev.}, FJOURNAL = {SIAM Review. A Publication of the Society for Industrial and Applied Mathematics}, VOLUME = {38}, YEAR = {1996}, NUMBER = {3}, PAGES = {367--426}, ISSN = {0036-1445}, CODEN = {SIREAD}, MRCLASS = {90C25 (47N10 49M45 65J10)}, MRNUMBER = {98f:90045}, MRREVIEWER = {F. Deutsch}, } @article {MR1191505, AUTHOR = {Borwein, J.M. and Th{\'e}ra, M.}, TITLE = {Sandwich theorems for semicontinuous operators}, JOURNAL = {Canad. Math. Bull.}, FJOURNAL = {Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques}, VOLUME = {35}, YEAR = {1992}, NUMBER = {4}, PAGES = {463--474}, ISSN = {0008-4395}, CODEN = {CMBUA3}, MRCLASS = {54C08 (46A99 54C60 54C65 54F05)}, MRNUMBER = {1191505}, MRREVIEWER = {P. Maritz}, DOI = {10.4153/CMB-1992-061-7}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.4153/CMB-1992-061-7}, } @article {MR755971, AUTHOR = {Borwein, J.M. and Penot, J.-P. and Th{\'e}ra, M.}, TITLE = {Conjugate convex operators}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {102}, YEAR = {1984}, NUMBER = {2}, PAGES = {399--414}, ISSN = {0022-247X}, CODEN = {JMANAK}, MRCLASS = {90C48 (46G99 49A50)}, MRNUMBER = {755971}, MRREVIEWER = {Christian Malivert}, DOI = {10.1016/0022-247X(84)90180-X}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/0022-247X(84)90180-X}, } @article {MR3203237, AUTHOR = {Bailey, D. H. and Borwein, J. M. and L{\'o}pez de Prado, M. and Zhu, Q.J.}, TITLE = {Pseudo-mathematics and financial charlatanism: the effects of backtest overfitting on out-of-sample performance}, JOURNAL = {Notices Amer. Math. Soc.}, FJOURNAL = {Notices of the American Mathematical Society}, VOLUME = {61}, YEAR = {2014}, NUMBER = {5}, PAGES = {458--471}, ISSN = {0002-9920}, MRCLASS = {91G70 (62P05 91G80)}, MRNUMBER = {3203237}, DOI = {10.1090/noti1105}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1090/noti1105}, } @book {MR1641658, AUTHOR = {Borwein, J.M. and Borwein, P.B.}, TITLE = {Pi and the {AGM}}, SERIES = {Canadian Mathematical Society Series of Monographs and Advanced Texts, 4}, NOTE = {A study in analytic number theory and computational complexity, Reprint of the 1987 original, A Wiley-Interscience Publication}, PUBLISHER = {John Wiley \& Sons, Inc., New York}, YEAR = {1998}, PAGES = {xvi+414}, ISBN = {0-471-31515-X}, MRCLASS = {11Y60 (11B65 68Q25)}, MRNUMBER = {1641658}, } @article {ANZS:ANZS018, author = {Hu, X.}, title = {An Exact Algorithm for Projection onto a Polyhedral Cone}, journal = {Australian \& New Zealand Journal of Statistics}, volume = {40}, number = {2}, publisher = {Blackwell Publishers Ltd}, issn = {1467-842X}, url = {http://dx.doi.org/10.1111/1467-842X.00018}, doi = {10.1111/1467-842X.00018}, pages = {165--170}, keywords = {order restriction, polyhedral cone, projection, algorithm}, year = {1998}, } @article {MR95k:90121, AUTHOR = {Borwein, J. M. and Huang, W.}, TITLE = {Uniform convergence for moment problems with {F}ermi-{D}irac type entropies}, JOURNAL = {ZOR---Math. Methods Oper. Res.}, FJOURNAL = {Zeitschrift f\"ur Operations Research. Mathematical Methods of Operations Research}, VOLUME = {40}, YEAR = {1994}, NUMBER = {3}, PAGES = {239--252}, ISSN = {0340-9422}, MRCLASS = {90C45 (44A60)}, MRNUMBER = {95k:90121}, MRREVIEWER = {Dominikus Noll}, } @article {MR90d:65121, AUTHOR = {Huang, Wan Zhen and Zhang, Lian Sheng}, TITLE = {A study on {L}emar\'echal's higher-order algorithm---a conceptual algorithm}, JOURNAL = {J. Math. Res. Exposition}, FJOURNAL = {Journal of Mathematical Research and Exposition}, VOLUME = {9}, YEAR = {1989}, NUMBER = {1}, PAGES = {131--137}, ISSN = {1000-341X}, CODEN = {SYPIET}, MRCLASS = {65K05}, MRNUMBER = {90d:65121}, } @article {MR89e:90124, AUTHOR = {Huang, Wan Zhen}, TITLE = {A new proof of optimality for an algorithm for one-machine scheduling problems}, JOURNAL = {Shanghai Keji Daxue Xuebao}, FJOURNAL = {Shanghai Keji Daxue Xuebao. Journal of Shanghai University of Science and Technology}, YEAR = {1987}, NUMBER = {4}, PAGES = {116--118}, ISSN = {0258-7041}, CODEN = {SKDXDH}, MRCLASS = {90B35}, MRNUMBER = {89e:90124}, } @article {MR1402852, AUTHOR = {Huang, Wanzhen}, TITLE = {Heuristic solutions to polynomial moment problems with some convex entropic objectives}, JOURNAL = {Numer. Algorithms}, FJOURNAL = {Numerical Algorithms}, VOLUME = {12}, YEAR = {1996}, NUMBER = {3-4}, PAGES = {297--308}, ISSN = {1017-1398}, MRCLASS = {90C25 (65K10)}, MRNUMBER = {1 402 852}, } @article {MR1326400, AUTHOR = {Huang, Wan Zhen and Tang, Guo Chun}, TITLE = {A branch and bound approach to minimizing the weighted number of tardy jobs}, JOURNAL = {Acta Math. Appl. Sinica}, FJOURNAL = {Acta Mathematicae Applicatae Sinica. Yingyong Shuxue Xuebao}, VOLUME = {15}, YEAR = {1992}, NUMBER = {2}, PAGES = {194--199}, ISSN = {0254-3079}, CODEN = {YYSPDS}, MRCLASS = {90B35 (90C27)}, MRNUMBER = {1 326 400}, } @mastersthesis{Huang04preprocessingand, author = {X. Huang}, title = {Preprocessing and postprocessing in linear optimization}, school = {McMaster University}, year = {2004} } @TECHREPORT {Hua:72a, author = "P. HUARD", title = "Optimisation dans ${R}^{n}, 1^{ere}$ partie: {E}l\'{e}ments {T}he\'{o}riques", institution = "Laboratoire de Calcul, University of Lille I", year = "1972"} @TECHREPORT {Hua:72b, author = "P. HUARD", title = "Optimisation dans ${R}^{n}, 2^{eme}$ partie: {A}lgorithms {G}\'{e}n\'{e}raux", institution = "Laboratoire de Calcul, University of Lille I", year = "1972"} @ARTICLE {Hua:74, author = "P. HUARD", title = "Tentative de synth\`{e}se dans les m\'{e}thodes de programmation non-lin\'{e}aire", journal = "Cahiers du Centre d'etudes de R.O.", year = "1974", volume = "16", pages = "347-367"} @ARTICLE {Hua:75, author = "P. HUARD", title = "Optimization and point-to-set maps", journal = "Math. Prog.", year = "1975", volume = "8", pages = "308-331"} @INCOLLECTION {Hua:79, author = "P. HUARD", title = "Point-to set maps and mathematical programming", booktitle = "Math. Programming Studies \#10", publisher = "North-Holland", year = "1979", address = "Amsterdam"} @ARTICLE {Hub:72, author = "P.J. HUBER", title = "Robust statistics: a review", journal = "Ann. Statist.", year = "1972", volume = "43", pages = "1041"} @ARTICLE {Hub:73, author = "P.J. HUBER", title = "Robust regression: asymptotics, conjectures, and {M}onte {C}arlo", journal = "Ann. Statist.", year = "1973", volume = "1", pages = "799-821"} @BOOK {Hub:81, author = "P.J. HUBER", title = "Robust Statistics", publisher = "John Wiley \& Sons", year = "1981", address = "New York, NY"} @BOOK {Hubert:87, author = "L.J. HUBERT", title = "Assignment Methods in Combinatorial Data Analysis", publisher = "Marcel Dekker, INC", year = "1987", address = "New York and Basel"} @INCOLLECTION {HuPa:72, author = "D. HUTCHINSON and J.M. PARKINSON", title = "An investigation into the efficiency of variants of the {S}implex {M}ethod", booktitle = "Numerical Methods for Nonlinear Optimization", publisher = "Academic Press", year = "1972", editor = "F.A. Lootsma", pages = "115-135", address = "London and New York"} @article{HUESO200977, title = {Modified {N}ewton's method for systems of nonlinear equations with singular Jacobian}, journal = {Journal of Computational and Applied Mathematics}, volume = {224}, number = {1}, pages = {77-83}, year = {2009}, issn = {0377-0427}, doi = {https://doi.org/10.1016/j.cam.2008.04.013}, url = {https://www.sciencedirect.com/science/article/pii/S0377042708001787}, author = {J.L. Hueso and E. Martinez and J.R. Torregrosa}, keywords = {{N}ewton's method, Jacobian matrix, Order of convergence, Fixed point function}, abstract = {It is well known that {N}ewton's method for a nonlinear system has quadratic convergence when the Jacobian is a nonsingular matrix in a neighborhood of the solution. Here we present a modification of this method for nonlinear systems whose Jacobian matrix is singular. We prove, under certain conditions, that this modified {N}ewton's method has quadratic convergence. Moreover, different numerical tests confirm the theoretical results and allow us to compare this variant with the classical {N}ewton's method.} } %IIIIIIIIIIIII @BOOK{Ichiishi83, author = {T. Ichiishi}, title = {Game theory for Economic Analysis}, series = {}, volume = {}, publisher = {Academic Press}, address = {New York, {NY}}, year = {1983} } @BOOK {Ign:82, author = "J.P. IGNIZIO", title = "Linear Programming in Single- \& Multiple- Objective Systems", publisher = "Prentice-Hall", year = "1982", address = "Englewood Cliffs, NJ"} @ARTICLE {Ingb:89, author = "L. Ingber", title = "Very Fast Simulated re-annealing", journal = "Mathl. Comput. Modeling", year = "1989", volume = "12", pages = "967-973"} @ARTICLE {IofLe:72, author = "A.D. IOFFE and V.L. LEVIN", title = "Subdifferentials of convex functions", journal = "Trans. Moscow Math. Soc.", year = "1972", volume = "26", pages = "1-72"} @BOOK {IoTi:79, author = "A.D. IOFFE and V.M. TIHOMIROV", title = "Theory of Extremum Problems", publisher = "North-Holland", year = "1979", series ="Studies in Mathematics and its Applications", address = "New York, NY"} @article {MR3286678, AUTHOR = {Ipsen, I.C.F. and Wentworth, T.}, TITLE = {The effect of coherence on sampling from matrices with orthonormal columns, and preconditioned least squares problems}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {35}, YEAR = {2014}, NUMBER = {4}, PAGES = {1490--1520}, ISSN = {0895-4798}, MRCLASS = {65F08 (15A12 65F10 65F20 65F25 65F35 68W20)}, MRNUMBER = {3286678}, MRREVIEWER = {Lars Eld\'en}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/120870748}, } @article {MR1656931, AUTHOR = {Ipsen, I.C.F. and Meyer, C.D.}, TITLE = {The idea behind {K}rylov methods}, JOURNAL = {Amer. Math. Monthly}, FJOURNAL = {American Mathematical Monthly}, VOLUME = {105}, YEAR = {1998}, NUMBER = {10}, PAGES = {889--899}, ISSN = {0002-9890}, MRCLASS = {65F10}, MRNUMBER = {1656931}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.2307/2589281}, } @ARTICLE {IpTod:88, author = "C.M. IP and M.J. Todd", title = "Optimal conditioning and convergence in rank one quasi-{N}ewton updates", journal = "SIAM J. Numerical Analysis", year = "1988", volume = "25", pages = "206-221"} @ARTICLE {IsLowRiWil:75, author = "T.L. ISENHOUR and S.R. LOWRY and G.L. RITTER and C.L. WILKINS", title = "Simplex pattern recognition", journal = "Anal. Chem.", year = "1975", volume = "47", number = "12", pages = "1951-1956"} %JJJJJJJJJJJJ @BOOK {Ja:77, author = "D.H. JACOBSON", title = "Extensions of Linear-Quadratic Control, Optimization and Matrix Theory", publisher = "Academic Press", year = "1977", address = "New York"} @BOOK {JaKoPi:72, author = "S.L.S. JACOBY and J.S. KOWALIK and J.T. PIZZO", title = "Iterative Methods for Nonlinear Optimization Problems", publisher = "Prentice-Hall", year = "1972", address = "Englewood Cliffs, NJ"} @INPROCEEDINGS{Jaggi, author = {M. Jaggi}, title = {Revisiting {F}rank-{W}olfe: {P}rojection-free sparse convex optimization}, booktitle = {Proceedings of the 30th International Conference on Machine Learning (ICML-13)}, year = {2013}, pages={427--435} } @BOOK {Ja:86, author = "J. JAHN", title = "Mathematical Vector Optimization in Partially Ordered Linear Spaces", publisher = "Peter Lang", year = "1986", address = "Frankfurt am Main"} @BOOK {Jame:70, author = "G. JAMESON", title = "Ordered linear spaces", publisher = "Springer-Verlag", year = "1970", address = "New York"} @article{JANSEN199715, title = "Sensitivity analysis in linear programming: just be careful!", journal = "European Journal of Operational Research", volume = "101", number = "1", pages = "15 - 28", year = "1997", issn = "0377-2217", doi = "https://doi.org/10.1016/S0377-2217(96)00172-5", url = "http://www.sciencedirect.com/science/article/pii/S0377221796001725", author = "B. Jansen and J.J. de Jong and C. Roos and T. Terlaky", keywords = "Programming linear, Programming parametric, Practice, Sensitivity analysis, Lagrange multipliers" } @article {int:Jansen4, AUTHOR = {JANSEN, B. and ROOS, C. and Terlaky, T.}, TITLE = {The theory of linear programming: skew symmetric self-dual problems and the central path}, JOURNAL = {Optimization}, FJOURNAL = {Optimization. A Journal of Mathematical Programming and Operations Research}, VOLUME = {29}, YEAR = {1994}, NUMBER = {3}, PAGES = {225--233}, ISSN = {0233-1934}, } @TECHREPORT {JaWr:94, author = "F. JARRE and S. Wright", title = "On the role of the objective function in barrier methods", institution = "Mathematics and Computer Science Division, Argonne National Labs", number = "Manuscript No. 94-485", year = "1994", keywords = "barrier methods; interior points", address = "Argonne, Illinois"} @TECHREPORT {LiWr:01, author = "J. LINDEROTH and S. Wright", title = "Computational Grids for Stochastic Programming", institution = "Computer Sciences Department, University of Wisconsin-Madison", number = "Optimization Technical Report 01-01", year = "2001", address = "Madison, Wisconsin"} @TECHREPORT {LiShWr:01, author = "J. LINDEROTH and A. SHAPIRO and S. Wright", title = "The Empirical Behavior of Sampling Methods for Stochastic Programming", institution = "Computer Sciences Department, University of Wisconsin-Madison", number = "Optimization Technical Report 02-01", year = "2002", address = "Madison, Wisconsin"} @ARTICLE {JeYo:80, author = "K.C. JEA and D.M. Young", title = "Generalized conjugate gradient acceleration of iterative methods", journal = laa, year = "1980", volume = "34", pages = "59-194"} @TECHREPORT {JeYo:81, author = "K.C. JEA and D.M. Young", title = "Generalized conjugate gradient acceleration of iterative methods, part {II}: {T}he nonsymmetrizable case", institution = "Center for Numerical Analysis, University of Texas at Austin", year = "1981", number = "163", address = "Austin, TX"} @PHDTHESIS {Jea:82, author = "K.C. JEA", title = "Generalized conjugate gradient acceleration of iterative methods", school = "University of Texas at Austin", year = "1982", address = "Austin, TX", note = "Also available as Center for Numerical Analysis Report \#176"} @TECHREPORT {JeKiYo:83, author = "K.C. JEA and D.R. KINCAID and D.M. Young", title = "Accelerating nonsymmetrizable iterative methods", institution = "Center for Numerical Analysis, University of Texas at Austin", year = "1983", number = "181", address = "Austin, TX"} @article {MR86a:65016, AUTHOR = {JENNINGS, A. and AJIZ, M.A.}, TITLE = {Incomplete methods for solving ${A}^T{A}x=b$}, JOURNAL = {SIAM J. Sci. Statist. Comput.}, FJOURNAL = {Society for Industrial and Applied Mathematics. Journal on Scientific and Statistical Computing}, VOLUME = {5}, YEAR = {1984}, NUMBER = {4}, PAGES = {978--987}, ISSN = {0196-5204}, CODEN = {SIJCD4}, MRCLASS = {65D10 (65F20)}, MRNUMBER = {86a:65016}, MRREVIEWER = {Youcef Saad}, } @article {MR1555027, AUTHOR = {Jensen, J. L. W. V.}, TITLE = {Sur les fonctions convexes et les in\'{e}galit\'{e}s entre les valeurs moyennes}, JOURNAL = {Acta Math.}, FJOURNAL = {Acta Mathematica}, VOLUME = {30}, YEAR = {1906}, NUMBER = {1}, PAGES = {175--193}, ISSN = {0001-5962}, MRCLASS = {DML}, MRNUMBER = {1555027}, DOI = {10.1007/BF02418571}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/BF02418571}, } @article {MR1554908, AUTHOR = {Jensen, J. L. W. V.}, TITLE = {Sur un nouvel et important th\'{e}or\`eme de la th\'{e}orie des fonctions}, JOURNAL = {Acta Math.}, FJOURNAL = {Acta Mathematica}, VOLUME = {22}, YEAR = {1899}, NUMBER = {1}, PAGES = {359--364}, ISSN = {0001-5962}, MRCLASS = {DML}, MRNUMBER = {1554908}, DOI = {10.1007/BF02417878}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/BF02417878}, } @article{citeulike:3819014, abstract = {Abstract\ \ The celebrated S-lemma establishes a powerful equivalent condition for the nonnegativity of a quadratic function over a single quadratic inequality. However, this lemma fails without the technical condition, known as the Slater condition. In this paper, we first show that the Slater condition is indeed necessary for the S-lemma and then establishes a regularized form of the S-lemma in the absence of the Slater condition. Consequently, we present characterizations of global optimality and the Lagrangian duality for quadratic optimization problems with a single quadratic constraint. Our method of proof makes use of Brickman's theorem and conjugate analysis, exploiting the hidden link between the convexity and the S-lemma.}, author = {Jeyakumar, Vaithilingam and Huy, Nguyen and Li, Guoyin}, citeulike-article-id = {3819014}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/s11081-008-9076-9}, citeulike-linkout-1 = {http://www.springerlink.com/content/w04746n057302g0t}, doi = {10.1007/s11081-008-9076-9}, journal = {Optimization and Engineering}, posted-at = {2008-12-22 19:28:10}, title = {Necessary and sufficient conditions for S -lemma and nonconvex quadratic optimization}, url = {http://dx.doi.org/10.1007/s11081-008-9076-9} } @article{jeyakumar:983, author = {V. Jeyakumar and G. M. Lee and G. Y. Li}, collaboration = {}, title = {Alternative Theorems for Quadratic Inequality Systems and Global Quadratic Optimization}, publisher = {SIAM}, year = {2009}, journal = {SIAM Journal on Optimization}, volume = {20}, number = {2}, pages = {983-1001}, keywords = {alternative theorems; quadratic inequality systems; quadratic optimization; global optimality conditions; trust-region problems}, url = {http://link.aip.org/link/?SJE/20/983/1}, doi = {10.1137/080736090} } @ARTICLE{2017arXiv170708706J, author = {{Jiang}, R. and {Li}, D.}, title = "{Novel reformulations and efficient algorithms for the generalized trust region subproblem}", journal = {ArXiv e-prints}, archivePrefix = "arXiv", eprint = {1707.08706}, primaryClass = "math.OC", keywords = {Mathematics - Optimization and Control}, year = 2017, month = jul, adsurl = {http://adsabs.harvard.edu/abs/2017arXiv170708706J}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } @article {JinFangXing10, AUTHOR = {Jin, Q. and Fang, S.C. and Xing, W.}, TITLE = {On the global optimality of generalized trust region subproblems}, JOURNAL = {Optimization}, FJOURNAL = {Optimization. A Journal of Mathematical Programming and Operations Research}, VOLUME = {59}, YEAR = {2010}, NUMBER = {8}, PAGES = {1139--1151}, ISSN = {0233-1934}, MRCLASS = {90C20 (90C46)}, MRNUMBER = {2738598 (2011j:90118)}, MRREVIEWER = {Magdalena Nockowska-Rosiak}, DOI = {10.1080/02331930902995236}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1080/02331930902995236}, } @INCOLLECTION {FJOHN:48, author = "F. John", title = "Extremum problems with inequalities as subsidiary conditions", booktitle = "Sudies and Essays, Courant Anniversary Volume", publisher = "Interscience", address = "New York", year = "1948", pages = "187-204"} @INPROCEEDINGS {Jo:85, author = "C.R. Johnson", title = "Matrix optimization and completion problems", booktitle = "NSF-CBMS Regional Conference on: Optimization in Operator Theory, Analytic Function Theory and Electrical Engineering", year = "1985", pages = "9.1-9.20"} @article {MR4198728, AUTHOR = {Johnstone, P.R. and Eckstein, J.}, TITLE = {Single-forward-step projective splitting: exploiting cocoercivity}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {78}, YEAR = {2021}, NUMBER = {1}, PAGES = {125--166}, ISSN = {0926-6003}, MRCLASS = {90C25 (47J22 49J40 90C48)}, MRNUMBER = {4198728}, MRREVIEWER = {Bing Tan}, DOI = {10.1007/s10589-020-00238-3}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10589-020-00238-3}, } @book {MR896034, AUTHOR = {Helton, J.W. and Ball, J.A. and Johnson, C.R. and Palmer, J.N.}, TITLE = {Operator theory, analytic functions, matrices, and electrical engineering}, SERIES = {CBMS Regional Conference Series in Mathematics}, VOLUME = {68}, PUBLISHER = {Published for the Conference Board of the Mathematical Sciences, Washington, DC}, YEAR = {1987}, PAGES = {xvi+134}, ISBN = {0-8218-0718-8}, MRCLASS = {47-02 (46J15 46N05 47A15 47A68 47B50 93B25 93B28)}, MRNUMBER = {896034 (89f:47001)}, MRREVIEWER = {T. Ando}, } @article {Whitney, AUTHOR = {Whitney, H.}, TITLE = {Analytic extensions of differentiable functions defined in closed sets}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {36}, YEAR = {1934}, NUMBER = {1}, PAGES = {63--89}, ISSN = {0002-9947}, MRCLASS = {26B05}, MRNUMBER = {1501735}, DOI = {10.2307/1989708}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.2307/1989708}, } @article {MR91k:15014, AUTHOR = {Johnson, C.R. and WHITNEY, G.T.}, TITLE = {Minimum rank completions}, JOURNAL = {Linear and Multilinear Algebra}, FJOURNAL = {Linear and Multilinear Algebra}, VOLUME = {28}, YEAR = {1991}, NUMBER = {4}, PAGES = {271--273}, ISSN = {0308-1087}, CODEN = {LNMLAZ}, MRCLASS = {15A15}, MRNUMBER = {91k:15014}, MRREVIEWER = {Shao Kuan Li}, } @ARTICLE {Joh74, author = "D.S. Johnson", title = "Approximation algorithms for combinatorial problems", journal = "Journal of Computer and System Sciences", year = "1974", volume = "9", pages = "256--278"} @ARTICLE {JoArMcSc:89, author = "D.S. Johnson and C.R.ARAGON and L.A. MCGEOCH and C. SCHEVON", title = "Optimization by simulated annealing: an experimental evaluation; part 1, graph partitioning", journal = "Operations Research", year = "1989", volume = "37", pages = "865-892"} @INPROCEEDINGS {JoSchn:86, author = "B.A. JONES and R.B. Schnabel", title = "A comparison of two sphere fitting methods", booktitle = "Proceedings of the Instrumentation and Measurement Technology Subgroup of the IEEE, Boulder, CO", year = "1986"} @techreport{JongStei:95, author = "H. TH. JONGEN and O. STEIN", year = "1995", title = "On generic one-parametric semi-infinite optimization", institution = "Universitat Trier, Mathematik/Informatik", type = "Report", number = "Nr. 95-06" } @ARTICLE {JM:92, author = "M. JUVAN and B. MOHAR", title = "Optimal linear labelings and eigenvalues of graphs", journal = "Discrete Applied Mathematics", year = "1992", volume = "36", pages = "153-168" } %KKKKKKKKKKKK @article {MR0007812, AUTHOR = {Kac, M.}, TITLE = {On the average number of real roots of a random algebraic equation}, JOURNAL = {Bull. Amer. Math. Soc.}, FJOURNAL = {Bulletin of the American Mathematical Society}, VOLUME = {49}, YEAR = {1943}, PAGES = {314--320}, ISSN = {0002-9904}, MRCLASS = {41.1X}, MRNUMBER = {0007812 (4,196d)}, MRREVIEWER = {P. Erd{\"o}s}, } @techreport{kags:84, author = "B. KAGSTR{\"O}M", year = "1984", title = "The generalized singular value decomposition and the general $(A - \lambda B)$ - problem", institution = "Institute of Information Processing, University of Umea", type = "Report", number = "UMINF-118.84", kwds = "nla, geig, matrix pencil" } @article {MR656462, AUTHOR = {Davis, Chandler and Kahan, W. M. and Weinberger, H. F.}, TITLE = {Norm-preserving dilations and their applications to optimal error bounds}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {19}, YEAR = {1982}, NUMBER = {3}, PAGES = {445--469}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {47A20 (65J10)}, MRNUMBER = {656462 (84b:47010)}, MRREVIEWER = {Peter Lancaster}, DOI = {10.1137/0719029}, URL = {http://dx.doi.org/10.1137/0719029}, } @article {MR0264450, AUTHOR = {Davis, C. and Kahan, W.M.}, TITLE = {The rotation of eigenvectors by a perturbation. {III}}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {7}, YEAR = {1970}, PAGES = {1--46}, ISSN = {0036-1429}, MRCLASS = {47.48}, MRNUMBER = {0264450 (41 \#9044)}, MRREVIEWER = {C. A. Hall}, } @article {MR0246155, AUTHOR = {Davis, C. and Kahan, W. M.}, TITLE = {Some new bounds on perturbation of subspaces}, JOURNAL = {Bull. Amer. Math. Soc.}, FJOURNAL = {Bulletin of the American Mathematical Society}, VOLUME = {75}, YEAR = {1969}, PAGES = {863--868}, ISSN = {0002-9904}, MRCLASS = {47.48}, MRNUMBER = {0246155 (39 \#7460)}, MRREVIEWER = {A. McIntosh}, } @article{KAYKOBAD198727, title = {On nonnegative factorization of matrices}, journal = {Linear Algebra and its Applications}, volume = {96}, pages = {27-33}, year = {1987}, issn = {0024-3795}, doi = {https://doi.org/10.1016/0024-3795(87)90334-X}, url = {https://www.sciencedirect.com/science/article/pii/002437958790334X}, author = {M. Kaykobad}, abstract = {It is shown that a sufficient condition for a nonnegative real symmetric matrix to be completely positive is that the matrix is diagonally dominant.} } @article {MR0180852, AUTHOR = {Davis, C.}, TITLE = {The rotation of eigenvectors by a perturbation. {II}}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {11}, YEAR = {1965}, PAGES = {20--27}, ISSN = {0022-247x}, MRCLASS = {47.48}, MRNUMBER = {0180852 (31 \#5082)}, MRREVIEWER = {J. Rovnyak}, } @article {MR1286566, AUTHOR = {Boley, Daniel L. and Van Dooren, Paul}, TITLE = {Placing zeroes and the {K}ronecker canonical form}, JOURNAL = {Circuits Systems Signal Process.}, FJOURNAL = {Circuits, Systems, and Signal Processing}, VOLUME = {13}, YEAR = {1994}, NUMBER = {6}, PAGES = {783--802}, ISSN = {0278-081X}, MRCLASS = {93B55 (93B10)}, MRNUMBER = {MR1286566 (95m:93037)}, MRREVIEWER = {K. B. Datta}, } @article {MR945626, AUTHOR = {Beelen, Th. and Van Dooren, P.}, TITLE = {An improved algorithm for the computation of {K}ronecker's canonical form of a singular pencil}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {105}, YEAR = {1988}, PAGES = {9--65}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {65F30}, MRNUMBER = {MR945626 (89h:65056)}, MRREVIEWER = {Hans-J{\"u}rgen Albrand}, } @article {MR533501, AUTHOR = {Kailath, T. and Kung, S.Y. and Morf, M.}, TITLE = {Displacement ranks of matrices and linear equations}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {68}, YEAR = {1979}, NUMBER = {2}, PAGES = {395--407}, ISSN = {0022-247X}, MRCLASS = {65F05 (68C25)}, MRNUMBER = {533501}, MRREVIEWER = {S. F. McCormick}, DOI = {10.1016/0022-247X(79)90124-0}, URL = {https://doi.org/10.1016/0022-247X(79)90124-0}, } @incollection {MR1038316, AUTHOR = {Kailath, T. and Chun, J.}, TITLE = {Generalized {G}ohberg-{S}emencul formulas for matrix inversion}, BOOKTITLE = {The {G}ohberg anniversary collection, {V}ol.\ {I} ({C}algary, {AB}, 1988)}, SERIES = {Oper. Theory Adv. Appl.}, VOLUME = {40}, PAGES = {231--246}, PUBLISHER = {Birkh\"auser, Basel}, YEAR = {1989}, MRCLASS = {15A09 (15A30)}, MRNUMBER = {1038316}, MRREVIEWER = {L. Rodman}, } @techreport{Santos:10, author = "F. Santos", year = "2010", title = "A counter-example to the Hirsch conjecture", type = "research report, arXiv:1006.2814", } @article {MR0206823, AUTHOR = {Klee, V. and Walkup, D.W.}, TITLE = {The {$d$}-step conjecture for polyhedra of dimension {$d<6$}}, JOURNAL = {Acta Math.}, FJOURNAL = {Acta Mathematica}, VOLUME = {117}, YEAR = {1967}, PAGES = {53--78}, ISSN = {0001-5962}, MRCLASS = {52.40 (52.10)}, MRNUMBER = {0206823 (34 \#6639)}, MRREVIEWER = {G. T. Sallee}, } @article {MR1130448, AUTHOR = {Kalai, G. and Kleitman, D.J.}, TITLE = {A quasi-polynomial bound for the diameter of graphs of polyhedra}, JOURNAL = {Bull. Amer. Math. Soc. (N.S.)}, FJOURNAL = {American Mathematical Society. Bulletin. New Series}, VOLUME = {26}, YEAR = {1992}, NUMBER = {2}, PAGES = {315--316}, ISSN = {0273-0979}, CODEN = {BAMOAD}, MRCLASS = {52B55}, MRNUMBER = {1130448 (92h:52017)}, MRREVIEWER = {W. J. Firey}, DOI = {10.1090/S0273-0979-1992-00285-9}, URL = {http://dx.doi.org/10.1090/S0273-0979-1992-00285-9}, } @article {MR1626691, AUTHOR = {Holt, F.B. and Klee, V.}, TITLE = {Many polytopes meeting the conjectured {H}irsch bound}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {20}, YEAR = {1998}, NUMBER = {1}, PAGES = {1--17}, ISSN = {0179-5376}, CODEN = {DCGEER}, MRCLASS = {52B05 (52B11)}, MRNUMBER = {1626691 (99e:52015)}, MRREVIEWER = {P. R. Goodey}, DOI = {10.1007/PL00009372}, URL = {http://dx.doi.org/10.1007/PL00009372}, } @article{kags:86, author = "B. KAGSTR{\"O}M", year = "1986", title = "{RGSVD}---An Algorithm for Computing the {Kronecker} Structure and Reducing Subspaces of Singular {$A-\lambda B$} Pencils", journal = "SIAM Journal on Scientific and Statistical Computing", volume = "7", pages = "185--211", kwds = "nla, geig, Kronecker form, reducing subspace, matrix pencil" } @article {MR0129016, author = "L.V. KANTOROVICH", TITLE = {Mathematical methods of organizing and planning production}, JOURNAL = {Management Sci.}, FJOURNAL = {Management Science. Journal of the Institute of Management Science. Application and Theory Series}, VOLUME = {6}, YEAR = {1959/1960}, PAGES = {366--422}, ISSN = {0025-1909}, MRCLASS = {90.30}, MRNUMBER = {MR0129016 (23 \#B2053)}, MRREVIEWER = {M. M. Flood}, } @ARTICLE {Kan:48, author = "L.V. KANTOROVICH", title = "Functional analysis and applied mathematics", journal = "Uspekhi Mat. Nauk.", year = "1948", volume = "3", pages = "89-185", note = "Transl. by C. Benster as N.B.S. Rept. 1509, Washington D.C., 1952"} @book {MR83h:46002, AUTHOR = {KANTOROVICH, L.V. and AKILOV, G.P.}, TITLE = {Functional analysis}, EDITION = {Second}, NOTE = {Translated from the Russian by Howard L. Silcock}, PUBLISHER = {Pergamon Press}, ADDRESS = {Oxford}, YEAR = {1982}, PAGES = {xiv+589}, ISBN = {0-08-023036-9; 0-08-026486-7}, MRCLASS = {46-01 (47-01 65-01)}, MRNUMBER = {83h:46002}, } @INPROCEEDINGS {KaVa:86, author = "S. KAPOOR and P.M. VAIDYA", title = "Fast algorithms for convex quadratic programming and multicommodity flows", booktitle = "Proceedings of the 18th ACM Symp. on Theory of Computing", year = "1986", pages = "147-159"} @ARTICLE {KaRe:94, author = "S. Karisch and F. Rendl", title = "Lower bounds for the quadratic assignment problem via triangle decompositions", journal = mprog, year = "1995", volume = "To appear"} @ARTICLE {Kar:84, author = "N.K. KARMARKAR", title = "A new polynomial-time algorithm for linear programming", journal = "Combinatorica", year = "1984", volume = "4", pages = "373-395"} @techreport{Kar:89, author = "N.K. KARMARKAR", year = "1989", title = "An interior-point approach to {NP}-complete problems", type = "Lecture, 3rd {SIAM} {C}onference on {O}ptimization, {B}oston", kwds = "ipg, trg" } @article {MR91g:90099, AUTHOR = {KARMARKAR, N.K. and LAGARIAS, J.C. and SLUTSMAN, L. and WANG, P.}, TITLE = {Power series variants of {K}armarkar-type algorithms}, JOURNAL = {AT\&T Tech. J.}, FJOURNAL = {AT\&T Technical Journal}, VOLUME = {68}, YEAR = {1989}, NUMBER = {3}, PAGES = {20--36}, ISSN = {8576-2324}, MRCLASS = {90C05}, MRNUMBER = {91g:90099}, } @ARTICLE {KarResRam:91, author = "N.K. KARMARKAR and M.G.C. RESENDE and K.G. RAMAKRISHNAN", title = "An interior point algorithm to solve computationally difficult set covering problems", journal = mprog, year = "1991", volume = "52", pages = "597-618"} @article {MR86h:90076, AUTHOR = {KARNEY, D.F.}, TITLE = {In a semi-infinite program only a countable subset of the constraints is essential}, JOURNAL = {J. Approx. Theory}, FJOURNAL = {Journal of Approximation Theory}, VOLUME = {44}, YEAR = {1985}, NUMBER = {1}, PAGES = {69--72}, ISSN = {0021-9045}, CODEN = {JAXTAZ}, MRCLASS = {90C25}, MRNUMBER = {86h:90076}, MRREVIEWER = {Jong Shi Pang}, } @article {MR84i:90117, AUTHOR = {KARNEY, D.F.}, TITLE = {A duality theorem for semi-infinite convex programs and their finite subprograms}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {27}, YEAR = {1983}, NUMBER = {1}, PAGES = {75--82}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C25 (49D39)}, MRNUMBER = {84i:90117}, MRREVIEWER = {J. Borwein}, } @article {MR83c:90095, AUTHOR = {KARNEY, D.F.}, TITLE = {Duality gaps in semi-infinite linear programming---an approximation problem}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {20}, YEAR = {1981}, NUMBER = {2}, PAGES = {129--143}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C05 (49D39)}, MRNUMBER = {83c:90095}, MRREVIEWER = {H. Voigt}, } @mastersthesis{Karush:39, author = "W. KARUSH", year = 1939, title = "Minima of Functions of Several Variables with Inequalities as Side Constraints", school = {University of Chicago, Illiois} } @BOOK {KaLoTeZi:83, author = "M.H. Karwan and V. Lotfi and J. Telgen and S. Zionts", title = "Redundancy in mathematical programming", publisher = "Springer-Verlag", year = "1983", address = "New York, NY"} @ARTICLE {Kauf:75, author = "L.C. KAUFMAN", title = "A variable projection method for solving separable nonlinear least squares problems", journal = "BIT", year = "1975", volume = "15", pages = "49-57"} @article {MR2195758, AUTHOR = {KEARSLEY, A.J.}, TITLE = {Matrix-free algorithm for the large-scale constrained trust-region subproblem}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods \& Software}, VOLUME = {21}, YEAR = {2006}, NUMBER = {2}, PAGES = {233--245}, ISSN = {1055-6788}, MRCLASS = {90C20 (65K10)}, MRNUMBER = {MR2195758}, } @article {MR2252741, AUTHOR = {KEIL, C. and JANSSON, C.}, TITLE = {Computational experience with rigorous error bounds for the {N}etlib linear programming library}, JOURNAL = {Reliab. Comput.}, FJOURNAL = {Reliable Computing. An International Journal Devoted to Reliable Mathematical Computations Based on Finite Representations and Guaranteed Accuracy}, VOLUME = {12}, YEAR = {2006}, NUMBER = {4}, PAGES = {303--321}, ISSN = {1385-3139}, CODEN = {RCOMF8}, MRCLASS = {65G30 (90C05)}, URL = {http://www.ti3.tu-harburg.de/paper/jansson/netlib5.pdf}, MRNUMBER = {MR2252741}, } @article{doi:10.1080/10556789308805545, author = {C.T. Kelley and Z.Q. Xue}, title = {Inexact Newton Methods for singular problems}, journal = {Optimization Methods and Software}, volume = {2}, number = {3-4}, pages = {249-267}, year = {1993}, publisher = {Taylor & Francis}, doi = {10.1080/10556789308805545}, URL = {https://doi.org/10.1080/10556789308805545}, eprint = {https://doi.org/10.1080/10556789308805545} } @book {MR2000h:90003, AUTHOR = {Kelley, C.T.}, TITLE = {Iterative methods for optimization}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {1999}, PAGES = {xvi+180}, ISBN = {0-89871-433-8}, MRCLASS = {90-02 (65K05 90-01 90C30)}, MRNUMBER = {2000h:90003}, MRREVIEWER = {William W. Hager}, } @ARTICLE {Kelr:65, author = "H.B. KELLER", title = "On the solution of singular and semidefinite linear systems by iteration", journal = "SIAM J. of Numer. Math.", year = "1965", volume = "2", pages = "281-290"} @book {MR96d:65002, AUTHOR = {Kelley, C.T.}, TITLE = {Iterative methods for linear and nonlinear equations}, NOTE = {With separately available software}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {1995}, PAGES = {iv+165}, ISBN = {0-89871-352-8}, MRCLASS = {65-02 (65Fxx 65Hxx)}, MRNUMBER = {96d:65002}, MRREVR = {W. Govaerts}, } @TECHREPORT {KelSa:85, author = "C.T. Kelley and E.W. SACHS", title = "A new quasi-{N}ewton method for some differential equations", institution = "Department of Mathematics, North Carolina State University", year = "1985"} @ARTICLE {KelWri:91, author = "C.T. Kelley and S.J. Wright", title = "Sequential quadratic programming for certain parameter identification problems", journal = "Math. Prog. Series A", volume = "51", pages = "281-305", year = "1991"} @article {MR1643348, AUTHOR = {Argyros, Ioannis K.}, TITLE = {A local convergence theorem for the inexact {N}ewton method at singular points}, JOURNAL = {Southwest J. Pure Appl. Math.}, FJOURNAL = {Southwest Journal of Pure and Applied Mathematics}, YEAR = {1997}, NUMBER = {1}, PAGES = {30--36 (electronic)}, ISSN = {1083-0464}, MRCLASS = {65J15 (47H17)}, MRNUMBER = {1643348}, } @article {MR985481, AUTHOR = {Xi, Shao Lin and Gu, Ming}, TITLE = {Quasi-{N}ewton methods at singular points}, JOURNAL = {Math. Numer. Sinica}, FJOURNAL = {Mathematica Numerica Sinica. Jisuan Shuxue}, VOLUME = {10}, YEAR = {1988}, NUMBER = {3}, PAGES = {291--298}, ISSN = {0254-7791}, MRCLASS = {65H05}, MRNUMBER = {985481}, } @article {MR714695, AUTHOR = {Kelley, C.T. and Suresh, R.}, TITLE = {A new acceleration method for {N}ewton's method at singular points}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {20}, YEAR = {1983}, NUMBER = {5}, PAGES = {1001--1009}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {65H10 (58C15)}, MRNUMBER = {714695}, MRREVIEWER = {L. B. Rall}, DOI = {10.1137/0720070}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/0720070}, } @article {MR694520, AUTHOR = {Decker, D.W. and Keller, H.B. and Kelley, C.T.}, TITLE = {Convergence rates for {N}ewton's method at singular points}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {20}, YEAR = {1983}, NUMBER = {2}, PAGES = {296--314}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {65J15 (47H17)}, MRNUMBER = {694520}, MRREVIEWER = {Simeon Reich}, DOI = {10.1137/0720020}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/0720020}, } @article {MR646604, AUTHOR = {Decker, D.W. and Kelley, C.T.}, TITLE = {Convergence acceleration for {N}ewton's method at singular points}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {19}, YEAR = {1982}, NUMBER = {1}, PAGES = {219--229}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {65H05 (58E07 65J15)}, MRNUMBER = {646604}, MRREVIEWER = {Michael Pr{\"u}fer}, DOI = {10.1137/0719012}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/0719012}, } @article {MR581492, AUTHOR = {Decker, D.W. and Kelley, C.T.}, TITLE = {{N}ewton's method at singular points. {II}}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {17}, YEAR = {1980}, NUMBER = {3}, PAGES = {465--471}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {65J15}, MRNUMBER = {581492}, MRREVIEWER = {A. A. Fonarev}, DOI = {10.1137/0717039}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/0717039}, } @article {MR3339847, AUTHOR = {Kempe, D. and Kleinberg, J. and Tardos, \'E.}, TITLE = {Maximizing the spread of influence through a social network}, JOURNAL = {Theory Comput.}, FJOURNAL = {Theory of Computing. An Open Access Journal}, VOLUME = {11}, YEAR = {2015}, PAGES = {105--147}, ISSN = {1557-2862}, MRCLASS = {91D30 (68Q17 68Q25 68W25)}, MRNUMBER = {3339847}, DOI = {10.4086/toc.2015.v011a004}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.4086/toc.2015.v011a004}, } @incollection {MR2184706, AUTHOR = {Kempe, D. and Kleinberg, J. and Tardos, \'E.}, TITLE = {Influential nodes in a diffusion model for social networks}, BOOKTITLE = {Automata, languages and programming}, SERIES = {Lecture Notes in Comput. Sci.}, VOLUME = {3580}, PAGES = {1127--1138}, PUBLISHER = {Springer, Berlin}, YEAR = {2005}, MRCLASS = {91D30 (05C90)}, MRNUMBER = {2184706}, MRREVIEWER = {Sandra L. Arlinghaus}, DOI = {10.1007/11523468_91}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/11523468_91}, } @article {MR559463, AUTHOR = {Decker, D.W. and Kelley, C.T.}, TITLE = {{N}ewton's method at singular points. {I}}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {17}, YEAR = {1980}, NUMBER = {1}, PAGES = {66--70}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {65J15}, MRNUMBER = {559463}, MRREVIEWER = {A. A. Fonarev}, DOI = {10.1137/0717009}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/0717009}, } @ARTICLE {KeLi:70, author = "B.W. Kernighan and S. Lin", title = "An efficient heuristic procedure for partitioning graphs", journal = "Bell Syst. Tech. J.", year = "1970", volume = "49", pages = "291-307"} @phdthesis{Homadi:17, title = {Progress on the Marcus-de Oliveira Determinantal Conjecture}, school = {Department Mathematics and Statistics, Auburn University}, author = {Homadi, K.}, year = {2017}, } @article {MR1319053, AUTHOR = {Khachiyan, L.}, TITLE = {On the complexity of approximating extremal determinants in matrices}, JOURNAL = {J. Complexity}, FJOURNAL = {Journal of Complexity}, VOLUME = {11}, YEAR = {1995}, NUMBER = {1}, PAGES = {138--153}, ISSN = {0885-064X}, MRCLASS = {65F40 (15A15 65Y20 68Q25 90C60)}, MRNUMBER = {1319053}, MRREVIEWER = {Shinji Mizuno}, DOI = {10.1006/jcom.1995.1005}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1006/jcom.1995.1005}, } @ARTICLE {Khac:79, author = "L.G. Khachian", title = "A polynomial algorithm in linear programming", journal = "Doklady Akademiia Nauk SSSR", year = "1979", volume = "244", pages = "1093-1096"} @PHDTHESIS {Kha:89, author = "H.F.H. KHALFAN", title = "Topics in quasi-{N}ewton methods for unconstrained optimization", school = "University of Colorado", year = "1989"} @article {kim2, author = "S.-J. KIM and K. KOH and M. LUSTIG and S. Boyd and D. GORINEVSKY", title = "A method for large-scale $\ell_1$-regularized least squares problems with applications in signal processing and statistics", journal = {IEEE Journal of Selected Topics in Signal Processing}, volume = {1}, pages= "606-617", year = "2007"} @article {MR2017763, AUTHOR = {Koch, T.}, TITLE = {The final {NETLIB}-{LP} results}, JOURNAL = {Oper. Res. Lett.}, FJOURNAL = {Operations Research Letters}, VOLUME = {32}, YEAR = {2004}, NUMBER = {2}, PAGES = {138--142}, ISSN = {0167-6377}, MRCLASS = {90-04 (90C05)}, MRNUMBER = {2017763}, DOI = {10.1016/S0167-6377(03)00094-4}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1016/S0167-6377(03)00094-4}, } @article{doi:10.1080/03081087.2016.1267104, author = {N. Kishore Kumar and J. Schneider}, title = {Literature survey on low rank approximation of matrices}, journal = {Linear and Multilinear Algebra}, volume = {65}, number = {11}, pages = {2212-2244}, year = {2017}, publisher = {Taylor & Francis}, doi = {10.1080/03081087.2016.1267104}, URL = { https://doi.org/10.1080/03081087.2016.1267104 }, eprint = { https://doi.org/10.1080/03081087.2016.1267104 } } @article {MR3417786, AUTHOR = {Kir{\'a}ly, F.J. and Theran, L. and Tomioka, R.}, TITLE = {The algebraic combinatorial approach for low-rank matrix completion}, JOURNAL = {J. Mach. Learn. Res.}, FJOURNAL = {Journal of Machine Learning Research (JMLR)}, VOLUME = {16}, YEAR = {2015}, PAGES = {1391--1436}, ISSN = {1532-4435}, MRCLASS = {15A83 (05C50 05E99 14A10 62F99)}, MRNUMBER = {3417786}, } @INCOLLECTION {KlMi:72, author = "V. KLEE and G.J. MINTY", title = "How good is the simplex algorithm", booktitle = "Inequalities - III", publisher = "Academic Press Inc.", address = "New York and London", year = "1972", editor = "O. Shisha"} @article {MR1654578, AUTHOR = {KLYACHKO, A.A.}, TITLE = {Stable bundles, representation theory and {H}ermitian operators}, JOURNAL = {Selecta Math. (N.S.)}, FJOURNAL = {Selecta Mathematica. New Series}, VOLUME = {4}, YEAR = {1998}, NUMBER = {3}, PAGES = {419--445}, ISSN = {1022-1824}, CODEN = {SMATF6}, MRCLASS = {14J60 (14D20 14M25 14N15 15A42 20G05 47B15)}, MRNUMBER = {MR1654578 (2000b:14054)}, MRREVIEWER = {Alexey N. Rudakov}, } @article {MR1923723, AUTHOR = {KNYAZEV, A.V. and ARGENTATI, M.E.}, TITLE = {Principal angles between subspaces in an {$A$}-based scalar product: algorithms and perturbation estimates}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {23}, YEAR = {2002}, NUMBER = {6}, PAGES = {2008--2040 (electronic)}, ISSN = {1095-7197}, MRCLASS = {65F30 (68P20)}, MRNUMBER = {1 923 723}, } @BOOK {Knu:73, author = "D.E. Knuth", title = "The Art of Computer Programming, Vol. 3: Sorting and Searching", publisher = "Addison-Wesley", year = "1973", series = "Reading", address = "Massachusetts"} @ARTICLE {Kn:94, author = "D.E. Knuth", title = "The Sandwich Theorem", journal = electjc, volume = "1", pages = "48pp", year = "1994"} @article {MR2150161, AUTHOR = {Kolotilina, L.Y.}, TITLE = {Bounds for the eigenvalues of block {$2\times2$} {H}ermitian positive-definite matrices}, JOURNAL = {Numer. Linear Algebra Appl.}, FJOURNAL = {Numerical Linear Algebra with Applications}, VOLUME = {12}, YEAR = {2005}, NUMBER = {5-6}, PAGES = {393--417}, ISSN = {1070-5325}, MRCLASS = {15A42}, MRNUMBER = {2150161}, MRREVIEWER = {Fumio Hiai}, DOI = {10.1002/nla.434}, URL = {https://doi.org/10.1002/nla.434}, } @article {MR2312378, AUTHOR = {Koberstein, A. and Suhl, U.H.}, TITLE = {Progress in the dual simplex method for large scale {LP} problems: practical dual phase 1 algorithms}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {37}, YEAR = {2007}, NUMBER = {1}, PAGES = {49--65}, ISSN = {0926-6003}, MRCLASS = {90C06}, MRNUMBER = {MR2312378 (2007m:90045)}, DOI = {10.1007/s10589-007-9022-3}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s10589-007-9022-3}, } @incollection{int:Kojima4, author = "M. Kojima and S. MIZUNO and A. YOSHISE", title = "A primal--dual interior point algorithm for linear programming", booktitle = "Progress in Mathematical Programming~: Interior Point and Related Methods", publisher = "Springer Verlag", address = "New York", editor = "N.~Megiddo", year = "1989", pages = "29--47" } @ARTICLE {KMM93, author = "M. Kojima and N. MEGIDDO and S. MIZUNO", title = "A primal-dual infeasible-interior-point algorithm for linear programming", journal = mprog, volume = "61", pages = "263-280", year = "1993"} @ARTICLE {KokLoo:85, author = "M. KOK and F.A. LOOTSMA", title = "Pairwise-comparison methods in multi-objective programming, with applications in a long-term energy model", journal = "European J. Oper. Res.", year = "1985"} @ARTICLE {KooSchnaWe:85, author = "J.E. KOONTZ and R.B. Schnabel and B.E. WEISS", title = "A modular system of algorithms for unconstrained minimization", journal = "ACM Transactions on Mathematical Software", year = "1985", volume = "11", pages = "419-440", note = "Also available as Technical Report CU-CS-240-82, Department of Computer Science, University of Colorado, Boulder, CO"} @ARTICLE {Koop:75, author = "T.C. Koopmans", title = "Concepts of optimality and their uses", journal = "Nobel Memorial Lecture", year = "1975", volume = "Yale University", pages = ""} @ARTICLE {Ko:92, author = "F. K{\"{O}}RNER", title = "Remarks on a difficult test problem for quadratic {B}oolean programming", journal = "Optimization", year = "1992", volume = "26", pages = "355-357"} @misc{kostyukova2020strong, title={Strong duality for a problem of linear copositive programming}, author={O. Kostyukova and T. Tchemisova}, year={2020}, eprint={2004.09865}, archivePrefix={arXiv}, primaryClass={math.OC} } @ARTICLE {Kova:95, author = "V.V. KOVACEVIC-VUJCIC", title = "A view of interior point methods for linear programming", journal = "Yugoslav J. of Operations Research", year = "1995", volume = "5", number = "2", pages = "173-194"} @ARTICLE {KoTaHa:79, author = "M.K. KOZLOV and S.P. TARASOV and L.G. KHACHIYAN", title = "Polynomial solvability of convex quadratic programming", journal = "Soviet Math. Doklady", year = "1979", volume = "20", pages = "1108-1111"} @book{kran93, author = "Steven G. Krantz", title = "How To Teach Mathematics: {A} Personal Perspective", publisher = "American Mathematical Society", address = "Providence, RI", year = 1993, isbn = "0-8218-0197-X" } @ARTICLE {KraLo:74, author = "R.D. KRAUSE and J.A. LOTT", title = "Use of the {S}implex {M}ethod to optimize analytical conditions in {C}linical {C}hemistry", journal = "Clinical Chemistry", year = "1974", volume = "20", number = "7", pages = "775-782"} @ARTICLE {KR, author = "J. KREIMER and R. Y. RUBINSTEIN", title = "Nondifferentiable optimization via smooth approximation: General analytical approach", journal = "Annals of Operations Research", year = "1992", volume = "39", pages = "97--119"} @ARTICLE {Kr:61, author = "K. KRETSCHMER", title = "Programming in paired spaces", journal = "Canad. J. Math.", year = "1961", volume = "13", pages = "221-238"} @article{KrislockMalickRoupin:2017, author = {Krislock, N. and Malick, J. and Roupin, F.}, title = {Biq{C}runch: {A} Semidefinite Branch-and-Bound Method for Solving Binary Quadratic Problems}, journal = {ACM Trans. Math. Softw.}, issue_date = {March 2017}, volume = {43}, number = {4}, month = jan, year = {2017}, issn = {0098-3500}, pages = {32:1--32:23}, articleno = {32}, numpages = {23}, url = {http://doi.acm.org/10.1145/3005345}, doi = {10.1145/3005345}, acmid = {3005345}, publisher = {ACM}, address = {New York, NY, USA}, keywords = {Binary quadratic programming, NP-hard, exact resolution, quasi-{N}ewton, semidefinite relaxations}, } @ARTICLE {krislocklangvarahpaiseidel:04, Author = {Krislock, N. and Lang, J. and Varah, J.M. and Pai, D.K. and Seidel, H.-P.}, Journal = {IEEE Transactions on Robotics and Automation}, Number = {6}, Pages = {1007--1011}, Title = {Local Compliance Estimation via Positive Semidefinite Constrained Least Squares}, Volume = {20}, Year = {2004}} @ARTICLE {KuWo:94, author = "J. KUCZYNSKI and H. WOZNIAKOWSKI", title = "Pobabilistic bounds on the extremal eigenvalues and condition number by the Lanczos algorithm", journal = simax, year = "1994", volume = "15", keywords = "eig,iter", number = "2", pages = "672-691"} @article {MR2496064, AUTHOR = {Seeger, A. and Torki, M.}, TITLE = {Local minima of quadratic forms on convex cones}, JOURNAL = {J. Global Optim.}, FJOURNAL = {Journal of Global Optimization. An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering}, VOLUME = {44}, YEAR = {2009}, NUMBER = {1}, PAGES = {1--28}, ISSN = {0925-5001}, CODEN = {JGOPEO}, MRCLASS = {90C20 (90C33)}, MRNUMBER = {MR2496064}, DOI = {10.1007/s10898-007-9225-2}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s10898-007-9225-2}, } @Article{GourionSeeger:10, title = "Critical angles in polyhedral convex cones: numerical and statistical considerations", author = "D. Gourion and A. Seeger", journal = mprog, year = "2010", NUMBER = {1}, volume = "123", pages = "173-198" } @article {MR1999147, AUTHOR = {Seeger, A. and Torki, M.}, TITLE = {On eigenvalues induced by a cone constraint}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {372}, YEAR = {2003}, PAGES = {181--206}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A18 (58C40)}, MRNUMBER = {MR1999147 (2004g:15014)}, MRREVIEWER = {Jiu Ding}, DOI = {10.1016/S0024-3795(03)00553-6}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/S0024-3795(03)00553-6}, } @article {MR2101850, AUTHOR = {MONGEAU, M. and Torki, M.}, TITLE = {Computing eigenelements of real symmetric matrices via optimization}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {29}, YEAR = {2004}, NUMBER = {3}, PAGES = {263--287}, ISSN = {0926-6003}, CODEN = {CPPPEF}, MRCLASS = {65F15 (49K10 49M37)}, MRNUMBER = {MR2101850 (2005h:65061)}, MRREVIEWER = {Daniel Kressner}, } @article {MR1773908, AUTHOR = {Dai, Hua and Lancaster, Peter}, TITLE = {Preconditioning block {L}anczos algorithm for solving symmetric eigenvalue problems}, JOURNAL = {J. Comput. Math.}, FJOURNAL = {Journal of Computational Mathematics. An International Journal on Numerical Methods, Analysis and Applications}, VOLUME = {18}, YEAR = {2000}, NUMBER = {4}, PAGES = {365--374}, ISSN = {0254-9409}, CODEN = {JCMMEB}, MRCLASS = {65F15 (15A12 65F30)}, MRNUMBER = {MR1773908 (2001c:65042)}, } @article {MR1410088, AUTHOR = {Baglama, J. and Calvetti, D. and Reichel, L.}, TITLE = {Iterative methods for the computation of a few eigenvalues of a large symmetric matrix}, NOTE = {International Linear Algebra Year (Toulouse, 1995)}, JOURNAL = {BIT}, FJOURNAL = {BIT. Numerical Mathematics}, VOLUME = {36}, YEAR = {1996}, NUMBER = {3}, PAGES = {400--421}, ISSN = {0006-3835}, CODEN = {NBITAB}, MRCLASS = {65F15 (65F50)}, MRNUMBER = {MR1410088 (97g:65075)}, } @article {MR1142296, AUTHOR = {Zhang, Guo Dong}, TITLE = {The bisection-{N}ewton iterative method for finding extreme eigenvalues of symmetric matrices}, JOURNAL = {Numer. Math. J. Chinese Univ.}, FJOURNAL = {Numerical Mathematics. A Journal of Chinese Universities. Gaodeng Xuexiao Jisuan Shuxue Xuebao}, VOLUME = {13}, YEAR = {1991}, NUMBER = {2}, PAGES = {114--121}, ISSN = {1000-081X}, MRCLASS = {65F15}, MRNUMBER = {MR1142296 (92j:65055)}, } @book {MR808963, AUTHOR = {Cullum, Jane K. and Willoughby, Ralph A.}, TITLE = {L\'anczos algorithms for large symmetric eigenvalue computations. {V}ol. {II}}, SERIES = {Progress in Scientific Computing}, VOLUME = {4}, NOTE = {Programs}, PUBLISHER = {Birkh\"auser Boston Inc.}, ADDRESS = {Boston, MA}, YEAR = {1985}, PAGES = {vii+500}, ISBN = {0-8176-3294-8}, MRCLASS = {65F15 (49G10 65F50)}, MRNUMBER = {MR808963 (87h:65064b)}, MRREVIEWER = {Alan L. Andrew}, } @article {MR677870, AUTHOR = {Evans, D. J. and Shanehchi, J.}, TITLE = {Preconditioned iterative methods for the large sparse symmetric eigenvalue problem}, JOURNAL = {Comput. Methods Appl. Mech. Engrg.}, FJOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {31}, YEAR = {1982}, NUMBER = {3}, PAGES = {251--264}, ISSN = {0045-7825}, CODEN = {CMMECC}, MRCLASS = {65F15 (65F50)}, MRNUMBER = {MR677870 (84c:65064)}, MRREVIEWER = {H. G. Miller}, } @INPROCEEDINGS {Kuhn:76, author = "H.W. Kuhn", title = "Nonlinear programming: a historical view", booktitle = "Nonlinear Programming", publisher = "AMS", year = "1976", editor = "R.W. Cottle and C.E. Lemke", pages = "1-26", address = "Providence, R.I."} @inproceedings {MR13:855f, AUTHOR = {Kuhn, H.W. and Tucker, A.W.}, TITLE = {Nonlinear programming}, BOOKTITLE = {Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950}, PAGES = {481--492}, PUBLISHER = {University of California Press}, ADDRESS = {Berkeley and Los Angeles}, YEAR = {1951}, MRCLASS = {90.0X}, MRNUMBER = {13,855f}, MRREVR = {D. Gale}, } @article{kur76, author={S. Kurcyusz}, title={On the existence and nonexistence of {L}agrange multipliers in {B}anach spaces}, journal={Journal of Optimization Theory and Applications}, year={1976}, volume={20}, pages={81-110}} @article{LOBOS201640, title = "On optimal zeroth-order bounds of linear elastic properties of multiphase materials and application in materials design", journal = "International Journal of Solids and Structures", volume = "84", pages = "40 - 48", year = "2016", issn = "0020-7683", doi = "https://doi.org/10.1016/j.ijsolstr.2015.12.015", url = "http://www.sciencedirect.com/science/article/pii/S0020768315005077", author = "M. Lobos and T. Böhlke", keywords = "Materials design, Effective anisotropic linear elastic properties, Optimal bounds, Material data bases" } @article{NADEAU20017945, title = "On optimal zeroth-order bounds with application to {H}ashin–{S}htrikman bounds and anisotropy parameters", journal = "International Journal of Solids and Structures", volume = "38", number = "44", pages = "7945 - 7965", year = "2001", issn = "0020-7683", doi = "https://doi.org/10.1016/S0020-7683(00)00393-0", url = "http://www.sciencedirect.com/science/article/pii/S0020768300003930", author = "J.C. Nadeau and M. Ferrari", keywords = "Zeroth-order bounds, Hashin–Shtrikman bounds, Material anisotropy parameters" } @article{KRONER1977137, title = "Bounds for effective elastic moduli of disordered materials", journal = "Journal of the Mechanics and Physics of Solids", volume = "25", number = "2", pages = "137 - 155", year = "1977", issn = "0022-5096", doi = "https://doi.org/10.1016/0022-5096(77)90009-6", url = "http://www.sciencedirect.com/science/article/pii/0022509677900096", author = "E. Kröner" } @article {KuangGhaddaretalAlternLPSOCPACOPF16, AUTHOR = "X. Kuang and B. Ghaddar and J. Naoum-Sawaya and L.F. Zuluaga", TITLE = "Alternative LP and SOCP hierarchies for ACOPF problems", JOURNAL = {IEEE Trans. Power Systems}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Power Systems}, VOLUME = {32}, YEAR = {2016}, NUMBER = {4}, PAGES = {2826--2836} } @article{Kurdyka-1998, author = {Kurdyka, K.}, title = {On gradients of functions definable in o-minimal structures}, journal = {Annales de l'institut Fourier}, year = {1998}, volume = {146}, pages = {769-783}, } @book {MR2000f:37060, AUTHOR = {Kuznetsov, Yuri A.}, TITLE = {Elements of applied bifurcation theory}, SERIES = {Applied Mathematical Sciences}, VOLUME = {112}, EDITION = {Second}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1998}, PAGES = {xx+591}, ISBN = {0-387-98382-1}, MRCLASS = {37Gxx (34-04 34C23 37-04 37M20)}, MRNUMBER = {2000f:37060}, } %LLLLLLLLLLLL @incollection {MR775351, AUTHOR = {LASDON, L. S.}, TITLE = {Reduced gradient methods}, BOOKTITLE = {Nonlinear optimization, 1981 (Cambridge, 1981)}, PAGES = {243--250}, PUBLISHER = {Academic Press}, ADDRESS = {London}, YEAR = {1982}, } @TECHREPORT {La:95, author = "M. Lasserre", title = "A {F}arkas lemma without a standard closure condition", institution = "LAAS-CNRS", year = "1995", type = "Report de Recherche", address = "Toulouse,, France"} @article {MR3246296, AUTHOR = {Liberti, L. and Lavor, C. and Maculan, N. and Mucherino, A.}, TITLE = {Euclidean distance geometry and applications}, JOURNAL = {SIAM Rev.}, FJOURNAL = {SIAM Review}, VOLUME = {56}, YEAR = {2014}, NUMBER = {1}, PAGES = {3--69}, ISSN = {0036-1445}, MRCLASS = {51K05 (51F15)}, MRNUMBER = {3246296}, DOI = {10.1137/120875909}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/120875909}, } @article {MR2996476, AUTHOR = {Mucherino, A. and Lavor, C. and Liberti, L.}, TITLE = {The discretizable distance geometry problem}, JOURNAL = {Optim. Lett.}, FJOURNAL = {Optimization Letters}, VOLUME = {6}, YEAR = {2012}, NUMBER = {8}, PAGES = {1671--1686}, ISSN = {1862-4472}, MRCLASS = {52C10 (05C62 90C35)}, MRNUMBER = {2996476}, DOI = {10.1007/s11590-011-0358-3}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s11590-011-0358-3}, } @article {MR2925767, AUTHOR = {Lavor, Carlile and Liberti, Leo and Maculan, Nelson and Mucherino, Antonio}, TITLE = {The discretizable molecular distance geometry problem}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {52}, YEAR = {2012}, NUMBER = {1}, PAGES = {115--146}, ISSN = {0926-6003}, MRCLASS = {92E10 (51K05)}, MRNUMBER = {2925767}, DOI = {10.1007/s10589-011-9402-6}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s10589-011-9402-6}, } @article {MR2898950, AUTHOR = {Lavor, Carlile and Liberti, Leo and Maculan, Nelson and Mucherino, Antonio}, TITLE = {Recent advances on the discretizable molecular distance geometry problem}, JOURNAL = {European J. Oper. Res.}, FJOURNAL = {European Journal of Operational Research}, VOLUME = {219}, YEAR = {2012}, NUMBER = {3}, PAGES = {698--706}, ISSN = {0377-2217}, CODEN = {EJORDT}, MRCLASS = {92E10 (05C62)}, MRNUMBER = {2898950}, DOI = {10.1016/j.ejor.2011.11.007}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/j.ejor.2011.11.007}, } @article {MR2902263, AUTHOR = {Lavor, Carlile and Lee, Jon and Lee-St. John, Audrey and Liberti, Leo and Mucherino, Antonio and Sviridenko, Maxim}, TITLE = {Discretization orders for distance geometry problems}, JOURNAL = {Optim. Lett.}, FJOURNAL = {Optimization Letters}, VOLUME = {6}, YEAR = {2012}, NUMBER = {4}, PAGES = {783--796}, ISSN = {1862-4472}, MRCLASS = {05C22 (05C62 05C85)}, MRNUMBER = {2902263}, DOI = {10.1007/s11590-011-0302-6}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s11590-011-0302-6}, } @techreport{RHLewis:14, author = {R.H. Lewis}, title = {Yet Another Graph Partitioning Problem is {NP}-Hard}, journal = {CoRR}, volume = {abs/1403.5544}, year = {2014}, url = {http://arxiv.org/abs/1403.5544}, archivePrefix = {arXiv}, eprint = {1403.5544}, timestamp = {Mon, 13 Aug 2018 16:46:00 +0200}, biburl = {https://dblp.org/rec/bib/journals/corr/Lewis14}, bibsource = {dblp computer science bibliography, https://dblp.org} } @article {MR1168771, AUTHOR = {Bui, T.N. and Jones, C.}, TITLE = {Finding good approximate vertex and edge partitions is {NP}-hard}, JOURNAL = {Inform. Process. Lett.}, FJOURNAL = {Information Processing Letters}, VOLUME = {42}, YEAR = {1992}, NUMBER = {3}, PAGES = {153--159}, ISSN = {0020-0190}, MRCLASS = {68R10 (05C85 68Q15 68Q25)}, MRNUMBER = {1168771}, MRREVIEWER = {Etsuro Moriya}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1016/0020-0190(92)90140-Q}, } @incollection {MR2878447, AUTHOR = {Liberti, Leo and Masson, Beno{\^{\i}}t and Lee, Jon and Lavor, Carlile and Mucherino, Antonio}, TITLE = {On the number of solutions of the discretizable molecular distance geometry problem}, BOOKTITLE = {Combinatorial optimization and applications}, SERIES = {Lecture Notes in Comput. Sci.}, VOLUME = {6831}, PAGES = {322--342}, PUBLISHER = {Springer}, ADDRESS = {Heidelberg}, YEAR = {2011}, MRCLASS = {05A15 (90C35)}, MRNUMBER = {2878447}, DOI = {10.1007/978-3-642-22616-8_26}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/978-3-642-22616-8_26}, } @article {MR2853996, AUTHOR = {Lavor, Carlile and Liberti, Leo and Maculan, Nelson}, TITLE = {A note on ``{A} branch-and-prune algorithm for the molecular distance geometry problem'' [MR2387010]}, JOURNAL = {Int. Trans. Oper. Res.}, FJOURNAL = {International Transactions in Operational Research}, VOLUME = {18}, YEAR = {2011}, NUMBER = {6}, PAGES = {751--752}, ISSN = {0969-6016}, MRCLASS = {92E10 (05C05 51M25 90C27)}, MRNUMBER = {2853996}, DOI = {10.1111/j.1475-3995.2011.00807.x}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1111/j.1475-3995.2011.00807.x}, } @Article{LNN:95, author = "C. LEMAR\'ECHAL and A.S. Nemirovski and Y.E. Nesterov", title = "New variants of bundle methods", journal = mprog, year = "1995", volume = "69", pages = "111-147" } @INPROCEEDINGS {Lemar:78a, author = "C. LEMARECHAL", title = "Bundle methods in nonsmooth optimization", booktitle = "Proceedings of the IIASA Workshop, vol. 3, Nonsmooth Optimization, March 28-April 8, 1977", editor = "Claude Lemarechal and Robert Mifflin", pages = "79-102", publisher = "Pergamon Press, 1978"} @article{LempMaur:80, author = "F. LEMPIO and H. MAURER", year = "1980", title = "Differential stability in infinite-dimensional nonlinear programming", journal = "Appl. Math. Optim.", volume = "6", pages = "139--152" } @incollection {MR83m:49013, AUTHOR = {LEMPIO, F. and ZOWE, J.}, TITLE = {Higher order optimality conditions}, BOOKTITLE = {Modern applied mathematics (Bonn, 1979)}, PAGES = {147--193}, PUBLISHER = {North-Holland}, ADDRESS = {Amsterdam}, YEAR = {1982}, } @book {MR88m:90090, AUTHOR = {SCHRIJVER, A.}, TITLE = {Theory of linear and integer programming}, SERIES = {Wiley-Interscience Series in Discrete Mathematics}, NOTE = {A Wiley-Interscience Publication}, PUBLISHER = {John Wiley \& Sons Ltd.}, ADDRESS = {Chichester}, YEAR = {1986}, PAGES = {xii+471}, ISBN = {0-471-90854-1}, MRCLASS = {90C05 (90C10)}, MRNUMBER = {88m:90090}, MRREVIEWER = {J{\"u}rgen K{\"o}hler}, } @BOOK {LeKaSc:90, author = "J.K. LENSTRA and A.H.G. RINNOY KAN and A. SCHRIJVER", title = "History of Mathematical Programming: A Collection of Personal Reminiscences", publisher = "CWI North-Holland", year = "1991", address = "Amsterdam"} @article {LevinBen-Israel01, AUTHOR = {Levin, Y. and Ben-Israel, A.}, TITLE = {Directional {N}ewton Methods in $n$ Variables}, JOURNAL = {Mathematics of Computations}, VOLUME = {}, YEAR = {2001}, NUMBER = {}, PAGES = {}, MRCLASS = {}, MRNUMBER = {}, URL = {http://rutcor.rutgers.edu/~bisrael/NEWTON-DIR.ps}, } @article {LevinBen-Israel01a, AUTHOR = {Levin, Y. and Ben-Israel, A.}, TITLE = {A {N}ewton Method for Systems of $m$ Equations in $n$ Variables}, JOURNAL = {Nonlinear Analysis}, VOLUME = {47}, YEAR = {2001}, NUMBER = {}, PAGES = {1961--1971}, MRCLASS = {}, MRNUMBER = {}, URL = {ftp://rutcor.rutgers.edu/pub/rrr/reports2000/26.ps}, } @inproceedings {LevinBen-Israel01b, AUTHOR = {Levin, Y. and Ben-Israel, A.}, TITLE = {Directional {H}alley and Quasi-{H}alley Methods in $n$ Variables}, BOOKTITLE = {Inherently {P}arallel {A}lgorithms in {F}easibility and {O}ptimization and their {A}pplications}, EDITOR = {Butnariu, D. and Censor, Y. and Reich, S.}, PAGES = {}, PUBLISHER = {Elsevier Science}, ADDRESS = {Amsterdam}, YEAR = {2001}, MRNUMBER = {}, URL = {ftp://rutcor.rutgers.edu/pub/rrr/reports2000/28.ps}, } @article {LevinBen-Israel01c, AUTHOR = {Levin, Y. and Ben-Israel, A.}, TITLE = {The {N}ewton Bracketing Method for Convex Minimization}, JOURNAL = {Computational Optimization and Applications}, VOLUME = {}, YEAR = {2001}, NUMBER = {}, PAGES = {}, MRCLASS = {}, MRNUMBER = {}, URL = {ftp://rutcor.rutgers.edu/pub/rrr/reports2000/33.ps}, } @TECHREPORT{LevinBen-Israel02, author = {Levin, Y. and Ben-Israel, A.}, title = {Inverse-free Methods for Systems of Nonlinear Equations}, institution = {Rutgers University}, year = {2000}, type = {RUTCOR--Rutgers Ctr. Oper. Res.}, number = {58-2000}, address = {Piscataway, NJ}, URL = {ftp://rutcor.rutgers.edu/pub/rrr/reports2000/58.ps}, } @article {LevinEtAl01, AUTHOR = {Levin, Y. and Nediak, M. and Ben-Israel, A.}, TITLE = {A Direct Approach to Calculus of Variations via {N}ewton-{R}aphson Method}, JOURNAL = {Comput. \& Appl. Math.}, VOLUME = {139}, YEAR = {2001}, NUMBER = {}, PAGES = {197--213}, MRCLASS = {}, MRNUMBER = {}, } @article{Le:66, author = "N. LEVINSON", year = "1966", title = "A class of continuous linear programming problems", journal = "J. Math. Anal. Appl.", volume = "16", pages = "73--83" } @TECHREPORT {Lemar:78b, author = "C. LEMARECHAL", title = "Nonlinear programming and nonsmooth optimization", institution = "INRIA", year = "1978", type = "Report de Recherche", number = "332", address = "Le Chesnay, France"} @ARTICLE {Lemk:54, author = "C.E. LEMKE", title = "The dual method of solving the linear programming problem", journal = "Naval Res. Logist. Quart.", year = "1954", volume = "1", pages = "36"} @BOOK {Le:90, author = "T. Lengauer", TITLE = {Combinatorial algorithms for integrated circuit layout}, NOTE = {With a foreword by Bryan Preas}, PUBLISHER = {John Wiley \& Sons Ltd.}, ADDRESS = {Chichester}, YEAR = {1990}, PAGES = {xxviii+697}, ISBN = {0-471-92838-0}, MRCLASS = {68Q35 (52B55 68R10 90C27)}, MRNUMBER = {91h:68089}, MRREVR = {Lukas P. P. P. van Ginneken}, } @ARTICLE {Leve:44, Author = "K. Levenberg", title = "A method for the solution of certain problems in least squares", journal = "Quart. Appl. Math.", year = "1944", volume = "2", pages = "164-168"} @article {MR96h:90122, AUTHOR = {Lewis, A.S.. and PHILPOTT, A.B.}, TITLE = {Experiments with affine scaling and semi-infinite programming}, JOURNAL = {New Zealand J. Math.}, FJOURNAL = {New Zealand Journal of Mathematics}, VOLUME = {24}, YEAR = {1995}, NUMBER = {2}, PAGES = {49--71}, ISSN = {1171-6096}, MRCLASS = {90C34 (90-04)}, MRNUMBER = {96h:90122}, } @article {MR91c:90118, AUTHOR = {ANDERSON, E.J. and Lewis, A.S..}, TITLE = {An extension of the simplex algorithm for semi-infinite linear programming}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {44}, YEAR = {1989}, NUMBER = {3, (Ser. A)}, PAGES = {247--269}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C48 (49M39 90C05)}, MRNUMBER = {91c:90118}, MRREVIEWER = {Sven-{\AA}ke Gustafson}, } @incollection {MR87k:90173, AUTHOR = {Lewis, A.S.}, TITLE = {Extreme points of infinite transportation problems}, BOOKTITLE = {X symposium on operations research, Part I, Sections 1--5 (Munich, 1985)}, PAGES = {115--126}, PUBLISHER = {Athen\"aum/Hain/Hanstein}, ADDRESS = {K\"onigstein}, YEAR = {1986}, MRCLASS = {90C08}, MRNUMBER = {87k:90173}, MRREVIEWER = {K. G. Murty}, } @book {Lewco663:94, author = "A.S. Lewis", title = "Take-home final exam, {C}ourse {CO}663 in {C}onvex {A}nalysis", publisher = "University of Waterloo", address = "Ontario, Canada", year = "1994"} @Article{Lewis2013, author="Lewis, A.S. and Overton, M.L.", title="Nonsmooth optimization via quasi-{N}ewton methods", journal="Mathematical Programming", year="2013", month="Oct", day="01", volume="141", number="1", pages="135--163", abstract="We investigate the behavior of quasi-{N}ewton algorithms applied to minimize a nonsmooth function f, not necessarily convex. We introduce an inexact line search that generates a sequence of nested intervals containing a set of points of nonzero measure that satisfy the Armijo and Wolfe conditions if f is absolutely continuous along the line. Furthermore, the line search is guaranteed to terminate if f is semi-algebraic. It seems quite difficult to establish a convergence theorem for quasi-{N}ewton methods applied to such general classes of functions, so we give a careful analysis of a special but illuminating case, the Euclidean norm, in one variable using the inexact line search and in two variables assuming that the line search is exact. In practice, we find that when f is locally Lipschitz and semi-algebraic with bounded sublevel sets, the BFGS (Broyden--Fletcher--Goldfarb--Shanno) method with the inexact line search almost always generates sequences whose cluster points are Clarke stationary and with function values converging R-linearly to a Clarke stationary value. We give references documenting the successful use of BFGS in a variety of nonsmooth applications, particularly the design of low-order controllers for linear dynamical systems. We conclude with a challenging open question.", issn="1436-4646", doi="10.1007/s10107-012-0514-2", url="https://doi.org/10.1007/s10107-012-0514-2" } @article{yamashita2008sparse, title={Sparse quasi-{N}ewton updates with positive definite matrix completion}, author={Yamashita, N.}, journal={Mathematical programming}, volume={115}, number={1}, pages={1--30}, year={2008}, publisher={Springer} } @article {MR3097282, AUTHOR = {Lewis, A.S. and Overton, M.L.}, TITLE = {Nonsmooth optimization via quasi-{N}ewton methods}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming}, VOLUME = {141}, YEAR = {2013}, NUMBER = {1-2, Ser. A}, PAGES = {135--163}, ISSN = {0025-5610}, MRCLASS = {49J52 (90C30 90C53)}, MRNUMBER = {3097282}, MRREVIEWER = {Russell Luke}, DOI = {10.1007/s10107-012-0514-2}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10107-012-0514-2}, } @ARTICLE {LewOve96, Author = "A.S. Lewis and M.L. Overton", title = "Eigenvalue Optimization", journal = "Acta Numerica", year = "1996", volume = "5", pages = "149-190"} } @phdthesis{XinxinLi:93, author= {X. Li}, title= {Some operator splitting methods for convex optimization}, url = {https://repository.hkbu.edu.hk/etd_oa/43/}, school= {Hong Kong Baptist University, Hong Kong}, year= {2014}, advisor = {Yuan, Xiaoming}, } @article {MR96c:90083, AUTHOR = {Li, D.}, TITLE = {Zero duality gap for a class of nonconvex optimization problems}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {85}, YEAR = {1995}, NUMBER = {2}, PAGES = {309--324}, ISSN = {0022-3239}, CODEN = {JOTABN}, } @article {MR2886307, AUTHOR = {Zheng, X.J. and Sun, X.L. and Li, D. and Xu, Y.F.}, TITLE = {On zero duality gap in nonconvex quadratic programming problems}, JOURNAL = {J. Global Optim.}, FJOURNAL = {Journal of Global Optimization. An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering}, VOLUME = {52}, YEAR = {2012}, NUMBER = {2}, PAGES = {229--242}, ISSN = {0925-5001}, MRCLASS = {90C46 (90C20 90C26)}, MRNUMBER = {2886307}, MRREVIEWER = {Riccardo Cambini}, DOI = {10.1007/s10898-011-9660-y}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10898-011-9660-y}, } @article{Ao, author = "A. LI and L. TUN\c{C}EL", title = "Some Applications of Symmetric Cone Programming in Financial Mathematics", JOURNAL = {Transactions on Operational Research}, VOLUME = {17}, YEAR = {2006}, PAGES = {1--19}, } @mastersthesis{Aothesis, author = "A. LI", year = 2005, title = "Some Applications of Symmetric Cone Programming in Financial Mathematics", school = { University of Waterloo, Canada}, URL= "www.math.uwaterloo.ca/CandO\_Dept/program\_of\_studies/graduate/MMathEssays.shtml" } @TECHREPORT {LiPaRe:93, author = "Y. Li and P.M. Pardalos and M.G.C. RESENDE", title = "A greedy randomized adaptive search procedure for the quadratic assignment problem", institution = "DIMACS Series in Discrete Mathematics and Theoretical Computer Science", year = "1993"} @article {MR2047426, AUTHOR = {LI, R-C and YE, Q.}, TITLE = {A {K}rylov subspace method for quadratic matrix polynomials with application to constrained least squares problems}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {25}, YEAR = {2003}, NUMBER = {2}, PAGES = {405--428 (electronic)}, ISSN = {0895-4798}, MRCLASS = {15A18 (15A24 65H17)}, MRNUMBER = {MR2047426 (2005a:15009)}, } @article{GM75, title={Approximation par $\acute{e}$l$\acute{e}$ments finis d'ordre un et r$\acute{e}$solution par p$\acute{e}$nalisation-dualit$\acute{e}$ d'une classe de probl$\grave{e}$mes non lin$\acute{e}$aires}, author={R. Glowinski and A. Marrocco}, journal={R.A.I.R.O.}, volume={R2}, pages={41--76}, year={1975} } @ARTICLE{2018arXiv180512344L, author = {{Lin}, T. and {Ma}, S. and {Ye}, Y. and {Zhang}, S.}, title = "{An ADMM-Based Interior-Point Method for Large-Scale Linear Programming}", journal = {ArXiv e-prints}, archivePrefix = "arXiv", eprint = {1805.12344}, primaryClass = "math.OC", keywords = {Mathematics - Optimization and Control}, year = 2018, month = may, adsurl = {http://adsabs.harvard.edu/abs/2018arXiv180512344L}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } @article {MR943994, AUTHOR = {Lin, W.W.}, TITLE = {The computation of the {K}ronecker canonical form of an arbitrary symmetric pencil}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {103}, YEAR = {1988}, PAGES = {41--71}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A21 (15A22)}, MRNUMBER = {943994 (89k:15017)}, MRREVIEWER = {Lajos L{\'a}szl{\'o}}, DOI = {10.1016/0024-3795(88)90220-0}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/0024-3795(88)90220-0}, } @ARTICLE {Lo:34, Author = "K. L{\"{O}}WNER", title = "Uber monotone matrixfunctionen", journal = "Math. Z.", year = "1934", volume = "49", pages = "375-392"} @article{VaBoWu:98, Author = {L. Vandenberghe and S. Boyd and S-P. Wu}, Date-Added = {2008-06-01 13:45:22 -0400}, Date-Modified = {2008-06-03 11:13:38 -0400}, Doi = {10.1137/S0895479896303430}, Fjournal = {SIAM Journal on Matrix Analysis and Applications}, Journal = {SIAM J. Matrix Anal. Appl.}, Keywords = {SDP; interior-point methods; linear matrix inequalities; determinant maximization}, Number = {2}, Pages = {499-533}, Publisher = {SIAM}, Title = {Determinant Maximization with Linear Matrix Inequality Constraints}, Url = {http://link.aip.org/link/?SML/19/499/1}, Volume = {19}, Year = {1998}, Bdsk-File-1 = {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}, Bdsk-Url-1 = {http://link.aip.org/link/?SML/19/499/1}} @article {Lobo1998, AUTHOR = {Lobo, M.S. and Vandenberghe, L. and Boyd, S. and Lebret, H.}, TITLE = {Applications of second-order cone programming}, NOTE = {ILAS Symposium on Fast Algorithms for Control, Signals and Image Processing (Winnipeg, MB, 1997)}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {284}, YEAR = {1998}, NUMBER = {1-3}, PAGES = {193--228}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {90C08 (90C20 90C90 93B40)}, MRNUMBER = {1655138 (99k:90103)}, MRREVIEWER = {Jos F. Sturm}, DOI = {10.1016/S0024-3795(98)10032-0}, URL = {http://dx.doi.org/10.1016/S0024-3795(98)10032-0}, } @phdthesis{Lobo1, author = "M.S. LOBO", year = 2000, title = "Convex and Robust Optimization with Applications in Finance", school = {Stanford University, USA}, } @article {Lobo, AUTHOR = {M.S. LOBO and M. FAZEL and S. Boyd}, TITLE = {Portfolio optimization with linear and fixed transaction costs}, JOURNAL = {Ann. Oper. Res.}, FJOURNAL = {Annals of Operations Research}, VOLUME = {157}, YEAR = {2007}, PAGES = {341--365}, } @article {MR1974470, AUTHOR = {FALIKMAN, D. and FRIEDLAND, S. and LOEWY, Raphael}, TITLE = {On spaces of matrices containing a nonzero matrix of bounded rank}, JOURNAL = {Pacific J. Math.}, FJOURNAL = {Pacific Journal of Mathematics}, VOLUME = {207}, YEAR = {2002}, NUMBER = {1}, PAGES = {157--176}, ISSN = {0030-8730}, CODEN = {PJMAAI}, MRCLASS = {15A03}, MRNUMBER = {MR1974470 (2004d:15001)}, MRREVIEWER = {Donald W. Robinson}, } @article {MR1662865, AUTHOR = {FRIEDLAND, S. and LOEWY, R.}, TITLE = {Spaces of symmetric matrices containing a nonzero matrix of bounded rank}, NOTE = {Special issue celebrating the 60th birthday of Ludwig Elsner}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {287}, YEAR = {1999}, NUMBER = {1-3}, PAGES = {161--170}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A30}, MRNUMBER = {MR1662865 (99j:15024)}, MRREVIEWER = {R. Piziak}, } @ARTICLE {LoSc:75, Author = "R. LOEWY and H. Schneider", title = "Positive operators on the n-dimensional ice cream cone", journal = "J. Math. Anal. Appl.", year = "1975", volume = "49", pages = "375-392"} @INCOLLECTION {Loot:81, author = "F.A. LOOTSMA", title = "Performance evaluation of nonlinear optimization methods via multi-criteria decision analysis and via linear model analysis", booktitle = "Nonlinear Optimization", publisher = "Academic Press", year = "1981", editor = "M.J.D. Powell", address = "New York, NY"} @ARTICLE {Loot:85, author = "F.A. LOOTSMA", title = "Performance evaluation of nonlinear optimization methods via pairwise comparison and fuzzy numbers", journal = "Math. Prog.", year = "1985"} @Book{Lojasiewicz-1963, title = {Une propri$\acute{e}$t$\acute{e}$ topologique des sous-ensembles analytiques r$\acute{e}$els, Les $\acute{E}$quations aux D$\acute{e}$riv$\acute{e}$es Partielles}, publisher = {$\acute{E}$ditions du centre National de la Recherche Scientifique}, year = {1963}, author = {{\L}ojasiewicz, S.}, address = {Paris}, owner = {BoJiang}, pages = {87-89}, } @BOOK {Lovasz:79, author = "L. Lov{\'{a}}sz", title = "Combinatorial Problems and Exercises", publisher = "North-Holland", year = "1979", address = "Amsterdam"} @article {MR81g:05095, AUTHOR = {Lov{\'a}sz, L.}, TITLE = {On the {S}hannon capacity of a graph}, JOURNAL = {IEEE Trans. Inform. Theory}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Information Theory}, VOLUME = {25}, YEAR = {1979}, NUMBER = {1}, PAGES = {1--7}, ISSN = {0018-9448}, CODEN = {IETTAW}, MRCLASS = {05C99 (94A17)}, MRNUMBER = {81g:05095}, } @article {MR97g:65103, AUTHOR = {LU, S. and BARLOW, J.L.}, TITLE = {Multifrontal computation with the orthogonal factors of sparse matrices}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {17}, YEAR = {1996}, NUMBER = {3}, PAGES = {658--679}, ISSN = {0895-4798}, CODEN = {SJMAEL}, MRCLASS = {65F50 (15A23)}, MRNUMBER = {97g:65103}, } @BOOK {Luen:73, author = "D.G. Luenberger", title = "Introduction to Linear and Nonlinear Programming", publisher = "Addison-Wesley", year = "1973", series = "Reading", address = "Massachusetts"} @BOOK {Luen:84, author = "D.G. Luenberger", title = "Linear and Nonlinear Programming", publisher = "Addison-Wesley", year = "1984", series = "Reading", edition = "second", address = "Massachusetts"} @BOOK {Lu:69, author = "D.G. Luenberger", title = "Optimization by Vector Space Methods", publisher = "John Wiley", year = "1969"} @inproceedings {Lu2, AUTHOR = {Luenberger, D.G.}, TITLE = {Algorithmic analysis in constrained optimization}, BOOKTITLE = {Nonlinear programming (Proc. Sympos., New York, 1975)}, PAGES = {39--51. SIAM-AMS Proc., Vol. IX}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, R. I.}, YEAR = {1976}, MRCLASS = {90C30 (65K05)}, MRNUMBER = {53 #4989}, MRREVR = {J. A. Tomlin}, } @ARTICLE {Luk:92, author = "L. LUKSAN", title = "Variationally derived scaling and the variable metric updates from the preconvex part of the {B}royden family", journal = "JOTA", year = "1992"} @article {MR21:2927, AUTHOR = {LUMER, G. and ROSENBLUM, M.}, TITLE = {Linear operator equations}, JOURNAL = {Proc. Amer. Math. Soc.}, VOLUME = {10}, YEAR = {1959}, PAGES = {32--41}, MRCLASS = {46.00}, MRNUMBER = {21 \#2927}, MRREVIEWER = {F. H. Brownell}, } @TECHREPORT {Luo:94, author = "Z. LUO", title = "Analysis of a cutting plane method that uses weighted analytic center and multiple cuts", institution = "Department of Electrical and Computer Engineering, McMaster University", year = "1994", address = "Hamilton, Ontario"} @article {MR96m:90032, AUTHOR = {LUSTIG, I. J. and ROTHBERG, E.}, TITLE = {Gigaflops in linear programming}, JOURNAL = {Oper. Res. Lett.}, FJOURNAL = {Operations Research Letters}, VOLUME = {18}, YEAR = {1996}, NUMBER = {4}, PAGES = {157--165}, ISSN = {0167-6377}, CODEN = {ORLED5}, MRCLASS = {90C05}, MRNUMBER = {96m:90032}, } @ARTICLE {LuMaSh:92, author = "I. J. LUSTIG and R.E. MARSTEN and D. F. SHANNO", title = "On implementing {M}ehrotra's predictor--corrector interior point method for linear programming", year = "1992", volume = "2", journal = siopt, number = "3", pages = "435-449"} @article{int:Lustig7, author = "I. J. LUSTIG and R.E. MARSTEN and D. F. SHANNO", title = "Computational experience with a primal--dual interior point method for linear programming", journal = laa, volume = "152", year = "1991", pages = "191--222" } @article{int:Lustig:94, author = "I. J. LUSTIG and R.E. MARSTEN and D. F. SHANNO", title = "Interior Point Methods for Linear Programming: Computational State of the Art", journal = "ORSA Journal on Computing", volume = "6", year = "1994", pages = "1--14" } @article {MR2496900, AUTHOR = {LUCET, Y.}, TITLE = {What shape is your conjugate? {A} survey of computational convex analysis and its applications}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {20}, YEAR = {2009}, NUMBER = {1}, PAGES = {216--250}, ISSN = {1052-6234}, MRCLASS = {52B55 (52-02 65Dxx 90C25)}, MRNUMBER = {MR2496900}, } @book {MR1433592, AUTHOR = {L{\"U}TKEPOHL, H.}, TITLE = {Handbook of matrices}, PUBLISHER = {John Wiley \& Sons Ltd.}, ADDRESS = {Chichester}, YEAR = {1996}, PAGES = {xvi+304}, ISBN = {0-471-97015-8}, MRCLASS = {15-00}, MRNUMBER = {MR1433592 (97i:15001)}, } @TECHREPORT {Lyne:81, author = "J.N. LYNESS", title = "Remarks about performance profiles", institution = "Applied Mathematics Division, Argonne National Labs", year = "1981", type = "Technical Memorandum", number = "369", address = "Argonne, IL"} %MMMMMMMMMMMM @article{McCormick-1976, author={McCormick, G.P.}, title={Computability of global solutions to factorable nonconvex programs: part I Convex underestimating problems}, journal={Mathematical Programming}, volume={10}, year=1976, pages={147--175} } @book{MansiniRenata2015Lami, series = {EURO Advanced Tutorials on Operational Research}, publisher = {Springer}, isbn = {9783319184821}, year = {2015}, title = {Linear and mixed integer programming for portfolio optimization}, language = {eng}, address = {Cham}, author = {Mansini, R.}, keywords = {Portfolio management -- Mathematical models; Linear programming; Integer programming}, } @phdthesis{MA12, author = {Ma, Y.}, advisor = {Zhi, L.}, title = {Polynomial Optimization via Low-rank Matrix Completion and Semidefinite Programming}, year = {2012}, publisher = {Academy of Mathematics and Systems Science, Chinese Academy of Science}, } @TECHREPORT {Maa:85, author = " Z.A. MAANY", title = "A new algorithm for highly curved constrained optimization", institution = "The Hatfield Polytechnic Numerical Optimization Centre", year = "1985", number = "T.R. 161"} @book {MR84d:49001, AUTHOR = {Macki, Jack W. and Strauss, Aaron}, TITLE = {Introduction to optimal control theory}, NOTE = {Undergraduate Texts in Mathematics}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1982}, PAGES = {xiii+165}, ISBN = {0-387-90624-X}, MRCLASS = {49-01 (93-01)}, MRNUMBER = {84d:49001}, MRREVIEWER = {E. O. Roxin}, } @ARTICLE {Mad:75, author = "K. MADSEN", title = "An algorithm for minimax solution of overdetermined systems of non-linear equations", journal = "IMA J. Numer. Anal.", year = "1975", volume = "16", pages = "321-328"} @ARTICLE {MadSch:78, author = "K. MADSEN and H. SCHJAER-JACOBSEN", title = "Linearly constrained minimax optimization", journal = "Math. Prog.", year = "1978", volume = "14", pages = "208-223"} @article {MR0368771, AUTHOR = {MAGNANTI, T.L.}, TITLE = {Fenchel and {L}agrange duality are equivalent}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {7}, YEAR = {1974}, PAGES = {253--258}, ISSN = {0025-5610}, MRCLASS = {90C25}, MRNUMBER = {MR0368771 (51 \#5012)}, MRREVIEWER = {J. Stoer}, } @BOOK {MagNeu:88, author = "J.R. MAGNUS and H. NEUDECKER", title = "Matrix Differential Calculus", publisher = "Wiley", year = "1988", address = "New York, NY"} @article {MR2062967, AUTHOR = {Mangasarian, O.L.}, TITLE = {A {N}ewton method for linear programming}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {121}, YEAR = {2004}, NUMBER = {1}, PAGES = {1--18}, ISSN = {0022-3239}, MRCLASS = {90C05 (65C05 90C06 90C53)}, MRNUMBER = {2062967}, DOI = {10.1023/B:JOTA.0000026128.34294.77}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1023/B:JOTA.0000026128.34294.77}, } @incollection {MR774243, AUTHOR = {Mangasarian, O.L.}, TITLE = {Normal solutions of linear programs}, NOTE = {Mathematical programming at Oberwolfach, II (Oberwolfach, 1983)}, JOURNAL = {Math. Programming Stud.}, FJOURNAL = {Mathematical Programming Study}, NUMBER = {22}, YEAR = {1984}, PAGES = {206--216}, ISSN = {0303-3929}, MRCLASS = {90C05}, MRNUMBER = {774243}, DOI = {10.1007/bfb0121017}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/bfb0121017}, } @article {MR83c:90098, AUTHOR = {Mangasarian, O.L.}, TITLE = {Iterative solution of linear programs}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {18}, YEAR = {1981}, NUMBER = {4}, PAGES = {606--614}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {90C05 (65K05)}, MRNUMBER = {83c:90098}, MRREVIEWER = {Jacques A. Ferland}, } @article {MR528716, AUTHOR = {MAJINDAR, K.N.}, TITLE = {Linear combinations of {H}ermitian and real symmetric matrices}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {25}, YEAR = {1979}, PAGES = {95--105}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A63 (15A57)}, MRNUMBER = {MR528716 (80b:15033)}, MRREVIEWER = {Yik-Hoi Au-Yeung}, DOI = {10.1016/0024-3795(79)90009-0}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/0024-3795(79)90009-0}, } @article{doi:10.1080/01630563.2014.912056, author = { A. Maugeri and D. Puglisi}, title = {Non-Convex Strong Duality Via Subdifferential}, journal = {Numerical Functional Analysis and Optimization}, volume = {35}, number = {7-9}, pages = {1095-1112}, year = {2014}, publisher = {Taylor & Francis}, doi = {10.1080/01630563.2014.912056}, URL = { https://doi.org/10.1080/01630563.2014.912056 }, eprint = { https://doi.org/10.1080/01630563.2014.912056 } } @incollection {MR1120094, AUTHOR = {DE LEONE, R. and Mangasarian, O.L.}, TITLE = {Serial and parallel solution of large scale linear programs by augmented {L}agrangian successive overrelaxation}, BOOKTITLE = {Optimization, parallel processing and applications (Oberwolfach, 1987 and Karlsruhe, 1987)}, SERIES = {Lecture Notes in Econom. and Math. Systems}, VOLUME = {304}, PAGES = {103--124}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1988}, MRCLASS = {90C05}, MRNUMBER = {1 120 094}, } @BOOK {Mang:69, author = "O.L. Mangasarian", title = "Nonlinear Programming", publisher = "McGraw-Hill", year = "1969", address = "New York, NY"} @article {MR89d:90164, AUTHOR = {Mangasarian, O. L.}, TITLE = {A simple characterization of solution sets of convex programs}, JOURNAL = {Oper. Res. Lett.}, FJOURNAL = {Operations Research Letters}, VOLUME = {7}, YEAR = {1988}, NUMBER = {1}, PAGES = {21--26}, ISSN = {0167-6377}, CODEN = {ORLED5}, } @article {MR86m:90092, AUTHOR = {Mangasarian, O. L.}, TITLE = {A condition number for differentiable convex inequalities}, JOURNAL = mor, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {10}, YEAR = {1985}, NUMBER = {2}, PAGES = {175--179}, ISSN = {0364-765X}, } @incollection {MR84f:65034, AUTHOR = {Mangasarian, O. L.}, TITLE = {A condition number for linear inequalities and linear programs}, BOOKTITLE = {6. Symposium \"uber Operations Research, Part 1 (Augsburg, 1981)}, PAGES = {3--15}, SERIES = {Methods Oper. Res.}, VOLUME = {43}, PUBLISHER = {Athen\"aum/Hain/Hanstein}, ADDRESS = {K\"onigstein/Ts.}, YEAR = {1981}, } @article {MR4212357, AUTHOR = {Grabiner, J.V.}, TITLE = {``{I}t's all for the best'': optimization in the history of science}, JOURNAL = {J. Humanist. Math.}, FJOURNAL = {Journal of Humanistic Mathematics}, VOLUME = {11}, YEAR = {2021}, NUMBER = {1}, PAGES = {54--80}, MRCLASS = {01-02 (49-03 90-03)}, MRNUMBER = {4212357}, DOI = {10.5642/jhummath.202101.05}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.5642/jhummath.202101.05}, } @article {MR34:7263, AUTHOR = {Mangasarian, O.L. and Fromovitz, S.}, TITLE = {The {F}ritz {J}ohn necessary optimality conditions in the presence of equality and inequality constraints}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {17}, YEAR = {1967}, PAGES = {37--47}, } @PHDTHESIS {Mara:78, author = "N. MARATOS", title = "Exact penalty function algorithms for finite-dimensional and control optimization problems", school = "University of London", year = "1978"} @TECHREPORT {MarNoc:00, author = "M. MARAZZI and J. Nocedal", title = "Feasibility Control in Nonlinear Optimization", institution = "Department of Electrical Engineering and Computer Science, Northwestern University", year = "2000", number = "OTC 2000/04"} @book {marminc:64, AUTHOR = {MARCUS, M. and MINC, H.}, TITLE = {A Survey of Matrix Theory and Matrix Inequalities}, NOTE = {Reprint of the 1969 edition}, PUBLISHER = {Dover Publications Inc.}, ADDRESS = {New York}, YEAR = {1992}, PAGES = {xii+180}, ISBN = {0-486-67102-X}, } @book {MR0225972, AUTHOR = {Marden, M.}, TITLE = {Geometry of polynomials}, SERIES = {Second edition. Mathematical Surveys, No. 3}, PUBLISHER = {American Mathematical Society, Providence, R.I.}, YEAR = {1966}, PAGES = {xiii+243}, MRCLASS = {30.11}, MRNUMBER = {0225972}, MRREVIEWER = {O. Shisha}, } @article {JOFI:JOFI1525, author = {Markowitz, H.}, title = {PORTFOLIO SELECTION*}, journal = {The Journal of Finance}, volume = {7}, number = {1}, publisher = {Blackwell Publishing Ltd}, issn = {1540-6261}, url = {http://dx.doi.org/10.1111/j.1540-6261.1952.tb01525.x}, doi = {10.1111/j.1540-6261.1952.tb01525.x}, pages = {77--91}, year = {1952}, } @book {MR2547483, AUTHOR = {Markowitz, H.M.}, TITLE = {Harry {M}arkowitz. {S}elected works}, SERIES = {Nobel Laureate Series}, VOLUME = {1}, PUBLISHER = {World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ}, YEAR = {2008}, PAGES = {xvi+700}, ISBN = {978-981-283-364-8; 981-283-364-1}, MRCLASS = {01A75}, MRNUMBER = {MR2547483}, } @book {MR1094565, AUTHOR = {Markowitz, H.M.}, TITLE = {Mean-variance analysis in portfolio choice and capital markets}, PUBLISHER = {Basil Blackwell}, ADDRESS = {Oxford}, YEAR = {1987}, PAGES = {xii+387}, ISBN = {0-631-15381-0}, MRCLASS = {90A09 (90-02)}, MRNUMBER = {MR1094565 (91k:90024)}, } @book {MR0103768, AUTHOR = {Markowitz, H.M.}, TITLE = {Portfolio selection: {E}fficient diversification of investments}, SERIES = {Cowles Foundation for Research in Economics at Yale University, Monograph 16}, PUBLISHER = {John Wiley \& Sons Inc.}, ADDRESS = {New York}, YEAR = {1959}, PAGES = {x+344}, MRCLASS = {90.00}, MRNUMBER = {MR0103768 (21 \#2532)}, MRREVIEWER = {T. Haavelmo}, } @article {MR2363705, AUTHOR = {Mart{\'{\i}}, R. and Campos, V. and Pi{\~n}ana, E.}, TITLE = {A branch and bound algorithm for the matrix bandwidth minimization}, JOURNAL = {European J. Oper. Res.}, FJOURNAL = {European Journal of Operational Research}, VOLUME = {186}, YEAR = {2008}, NUMBER = {2}, PAGES = {513--528}, ISSN = {0377-2217}, CODEN = {EJORDT}, MRCLASS = {90C35 (05C62 05C85 90C57)}, MRNUMBER = {2363705 (2008h:90117)}, DOI = {10.1016/j.ejor.2007.02.004}, URL = {http://dx.doi.org/10.1016/j.ejor.2007.02.004}, } @book{MATLAB:2018a, year = {2018}, author = {MATLAB}, title = {version 9.4.0.813654 (R2018a)}, publisher = {The MathWorks Inc.}, address = {Natick, Massachusetts} } @article {MR0247866, AUTHOR = {Maybee, J. and Quirk, J.}, TITLE = {Qualitative problems in matrix theory}, JOURNAL = {SIAM Rev.}, FJOURNAL = {SIAM Review}, VOLUME = {11}, YEAR = {1969}, PAGES = {30--51}, ISSN = {0036-1445}, MRCLASS = {90.10 (15.00)}, MRNUMBER = {0247866}, MRREVIEWER = {W. F. Tyndall}, } @ARTICLE{5387455, author={Forrest, J. J. H. and Tomlin, J. A.}, journal={IBM Systems Journal}, title={Implementing the simplex method for the Optimization Subroutine Library}, year={1992}, month= { }, volume={31}, number={1}, pages={11 -25}, keywords={}, doi={10.1147/sj.311.0011}, ISSN={0018-8670}} @book {michaud:98, AUTHOR = {MICHAUD, R.O.}, TITLE = { Efficient Asset Management: A Practical Guide to Stock Portfolio Optimization and Asset Allocation}, PUBLISHER = {HBS Press}, ADDRESS = {Boston}, YEAR = {1998}, } @article {MR2131468, AUTHOR = {SERBAN, R. and KOON, W.S. and L0, M.W. and MARSDEN, J.E. and PETZOLD, L.R. and ROSS, S. D. and WILSON, R.S.}, TITLE = {Halo orbit mission correction maneuvers using optimal control}, JOURNAL = {Automatica J. IFAC}, FJOURNAL = {Automatica. A Journal of IFAC, the International Federation of Automatic Control}, VOLUME = {38}, YEAR = {2002}, NUMBER = {4}, PAGES = {571--583}, ISSN = {0005-1098}, CODEN = {ATCAA9}, MRCLASS = {70M20 (49N90 70F15 70Q05 93C85 93C95)}, MRNUMBER = {MR2131468 (2005m:70084)}, MRREVIEWER = {Josep J. Masdemont}, } @ARTICLE{Mar:94, author = "J.M. Mart\'{i}nez", title = "Local minimizers of quadratic functions on {E}uclidean balls and spheres", journal = siopt, keywords = "trust regions; ; trg; cdtprob", volume = "4", number = "1", pages = "159-176", year = "1994", } @ARTICLE{Mar:87, author = "J.M. Mart\'{i}nez", title = "An algorithm for solving sparse nonlinear least squares problems", journal = "Computing", volume = "39", number = "4", keywords = "sparse nonlinear least squares problems; Jacobian matrix; {G}auss-{N}ewton equation; iteration; preconditioned conjugate gradient algorithm; convergence results", pages = "307-325", year = "1987", } @article {MR89d:65066, AUTHOR = {Mart{\'\i}nez, J. M.}, TITLE = {An algorithm for solving sparse nonlinear least squares problems}, JOURNAL = {Computing}, FJOURNAL = {Computing. Archives for Scientific Computing}, VOLUME = {39}, YEAR = {1987}, NUMBER = {4}, PAGES = {307--325}, ISSN = {0010-485X}, CODEN = {CMPTA2}, MRCLASS = {65K10}, MRNUMBER = {89d:65066}, MRREVIEWER = {Viorel Arnautu}, } @TECHREPORT{MarKrej:98, author = "N. KREJI\'C and J.M. Mart\'{i}nez", title = "A globally convergent Inexact-{N}ewton method for solving reducible nonlinear systems of equations", institution = "State University of Campinas", year = "1998", } @ARTICLE{MarPowJac:81, author = "MARTIN, D. H. and Powell, M. J. D. and JACOBSON, D. H.", title = "On a decomposition of conditionally positive-semidefinite matrices", journal = laa, keywords = "copositivity", volume = "39", pages = "51-59", year = "1981", } @article {MR3649544, AUTHOR = {Mart\'\i nez, J.M. and Raydan, M.}, TITLE = {Cubic-regularization counterpart of a variable-norm trust-region method for unconstrained minimization}, JOURNAL = {J. Global Optim.}, FJOURNAL = {Journal of Global Optimization. An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering}, VOLUME = {68}, YEAR = {2017}, NUMBER = {2}, PAGES = {367--385}, ISSN = {0925-5001}, MRCLASS = {90C26 (49M15 90C55)}, MRNUMBER = {3649544}, MRREVIEWER = {Stefan M. Stefanov}, DOI = {10.1007/s10898-016-0475-8}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10898-016-0475-8}, } @TECHREPORT{MarSant:92, author = "J.M. Mart\'{i}nez and S.A. Santos", title = "A trust region strategy for minimization on arbitrary domains", institution = "State University of Campinas", keywords = "trust regions; ; trg", year = "1992", } @ARTICLE {Marq:63, author = "D. MARQUARDT", title = "An algorithm for least-squares estimation of nonlinear parameters", journal = "SIAM J. Appl. Math.", year = "1963", volume = "11", pages = "431-441"} @BOOK {MarshOlk:79, author = "A.W. Marshall and I. Olkin", title = "Inequalities: Theory of Majorization and its Applications", publisher = "Academic Press", year = "1979", address = "New York, NY"} @book {MR2759813, AUTHOR = {Marshall, A.W. and Olkin, I. and Arnold, B.C.}, TITLE = {Inequalities: theory of majorization and its applications}, SERIES = {Springer Series in Statistics}, EDITION = {Second}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {2011}, PAGES = {xxviii+909}, ISBN = {978-0-387-40087-7}, MRCLASS = {26-02 (05-02 26D15 26D20 60E15)}, MRNUMBER = {2759813}, } @PHDTHESIS {Marw:78, author = "E.S. MARWIL", title = "Exploiting sparsity in {N}ewton-type methods", school = "Department of Mathematical Sciences, Cornell University", year = "1978", address = "Ithaca, NY"} @ARTICLE {Marw:79, author = "E.S. MARWIL", title = "Convergence results for {S}chubert's method for solving sparse nonlinear equations", journal = "SIAM J. Numer. Anal.", year = "1979", volume = "16", pages = "588-604"} @ARTICLE {MatMey:94, author = "R. MATHAR and R. MEYER ", title = "Algorithms in convex analysis to fit $\ell_p$-distance matrices", journal = "Multivariate Analysis", year = "1994", volume = "51", keywords = "distance matrices", pages = "102-120"} @ARTICLE {MATLAB:97, author = "The MathWorks, Inc", title = "MATLAB 5", journal = "URL: http://144.212.100.10/ ", year = "1997", volume = " ", pages = " "} @article {MR95a:01021, AUTHOR = {MATROSOV, V.M. and MALIKOV, A.I.}, TITLE = {The development of the ideas of {A}. {M}. {L}yapunov over one hundred years: 1892--1992}, JOURNAL = {Izv. Vyssh. Uchebn. Zaved. Mat.}, FJOURNAL = {Izvestiya Vysshikh Uchebnykh Zavedeni\u\i. Matematika}, VOLUME = {4}, year = {1993}, PAGES = {3--47}, ISSN = {0021-3446}, MRCLASS = {01A70 (34-03)}, MRNUMBER = {95a:01021}, MRREVR = {Krzysztof Ciesielski}, } @phdthesis{matstons:94, author = "P. MATSTOMS", year = 1994, title = "Sparse QR Factorization with Applications to Linear Least Squares Problems", school = { Link{\"o}ping University, Sweden}, URL= "http://www.nsc.liu.se/\~{ }pomat/research.html" } @ARTICLE {MatStr:79, author = "H. MATTHIES and G. STRANG ", title = "The solution of nonlinear finite element equations", journal = "Internat. J. Numer. Methods Engrg.", year = "1979", volume = "14", pages = "1613-1626"} @article {MR81e:90093, AUTHOR = {MAURER, H. and ZOWE, J.}, TITLE = {First and second order necessary and sufficient optimality conditions for infinite-dimensional programming problems}, JOURNAL = mprog, FJOURNAL = {Mathematical Programming}, VOLUME = {16}, YEAR = {1979}, NUMBER = {1}, PAGES = {98--110}, ISSN = {0025-5610}, CODEN = {MHPGA4}, } @incollection {MR80a:90131, AUTHOR = {ZOWE, J. and MAURER, H.}, TITLE = {Optimality conditions for the programming problem in infinite dimensions}, BOOKTITLE = {Optimization and operations research (Proc. Workshop, Univ. Bonn, Bonn, 1977)}, PAGES = {261--270}, SERIES = {Lecture Notes in Econom. and Math. Systems}, VOLUME = {157}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1978}, } @incollection {MR58:15182, AUTHOR = {MAURER, H. and ZOWE, J.}, TITLE = {Second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems}, BOOKTITLE = {Optimization techniques (Proc. 8th IFIP Conf., W\"urzburg, 1977), Part 2}, PAGES = {13--21. Lecture Notes in Control and Information Sci., Vol. 7}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1978}, } @ARTICLE {MaRo:94, author = "T. MAUTOR and C. Roucairol", title = "A new exact algorithm for the solution of quadratic assignment problems", journal = "Discrete Applied Mathematics", year = "1994", volume = "55", pages = "281-293"} @article {MR1735350, AUTHOR = {Mays, M.E. and Wojciechowski, J.}, TITLE = {A determinant property of {C}atalan numbers}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {211}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {125--133}, ISSN = {0012-365X}, CODEN = {DSMHA4}, MRCLASS = {05A10 (05A19 05C20)}, MRNUMBER = {MR1735350 (2000k:05018)}, MRREVIEWER = {Louis Shapiro}, } @BOOK {McC:83, author = "G.P. McCORMICK", title = "Nonlinear Programming: Theory, Algorithms, and Applications", publisher = "Wiley-Interscience", year = "1983", address = "New York, NY"} @ARTICLE {MeNe:65, author = "R. MEAD and J.A. NELDER", title = "A simplex method for function minimization", journal = "Comput. J.", year = "1965", volume = "7", number = "4", pages = "308-313"} @article {MR850380, AUTHOR = {Megiddo, N.}, TITLE = {A note on degeneracy in linear programming}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {35}, YEAR = {1986}, NUMBER = {3}, PAGES = {365--367}, ISSN = {0025-5610}, MRCLASS = {90C05}, MRNUMBER = {850380}, DOI = {10.1007/BF01580886}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/BF01580886}, } @article {MR731036, AUTHOR = {Megiddo, N. and Supowit, K.J.}, TITLE = {On the complexity of some common geometric location problems}, JOURNAL = {SIAM J. Comput.}, FJOURNAL = {SIAM Journal on Computing}, VOLUME = {13}, YEAR = {1984}, NUMBER = {1}, PAGES = {182--196}, ISSN = {0097-5397}, CODEN = {SMJCAT}, MRCLASS = {68Q25 (90B05)}, MRNUMBER = {731036 (85c:68028)}, DOI = {10.1137/0213014}, URL = {http://dx.doi.org/10.1137/0213014}, } @incollection{int:Megiddo11, author = "N. MEGIDDO", title = "Pathways to the optimal set in linear programming", booktitle = "Progress in Mathematical Programming~: Interior Point and Related Methods", editor = "N. Megiddo", year = "1989", pages = "131--158", publisher = "Springer Verlag", address = "New York", note = "Identical version in~: {\em Proceedings of the 6th Mathematical Programming Symposium of Japan, Nagoya, Japan}, pages 1--35, 1986" } @article {MR93g:90047, AUTHOR = {Mehrotra, S.}, TITLE = {On the implementation of a primal-dual interior point method}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {2}, YEAR = {1992}, NUMBER = {4}, PAGES = {575--601}, ISSN = {1052-6234}, CODEN = {SJOPE8}, MRCLASS = {90C05 (90-08)}, MRNUMBER = {93g:90047}, } @incollection {MR1446302, AUTHOR = {Mehrotra, S. and WANG, J.-S.}, TITLE = {Conjugate gradient based implementation of interior point methods for network flow problems}, BOOKTITLE = {Linear and nonlinear conjugate gradient-related methods (Seattle, WA, 1995)}, PAGES = {124--142}, PUBLISHER = {SIAM}, ADDRESS = {Philadelphia, PA}, YEAR = {1996}, MRCLASS = {90C35 (65K05 90B10)}, MRNUMBER = {MR1446302}, } @article {MR1179576, AUTHOR = {Mehrotra, S.}, TITLE = {Implementations of affine scaling methods: approximate solutions of systems of linear equations using preconditioned conjugate gradient methods}, JOURNAL = {ORSA J. Comput.}, FJOURNAL = {ORSA Journal on Computing}, VOLUME = {4}, YEAR = {1992}, NUMBER = {2}, PAGES = {103--118}, ISSN = {0899-1499}, MRCLASS = {65F10 (65F35)}, MRNUMBER = {MR1179576}, } @article {MR94k:90043, AUTHOR = {Mehrotra, S. and YE, Y.}, TITLE = {Finding an interior point in the optimal face of linear programs}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {62}, YEAR = {1993}, NUMBER = {3, Ser. A}, PAGES = {497--515}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C05}, MRNUMBER = {94k:90043}, MRREVIEWER = {Vanita Verma}, } @techreport {Mehrozev:2005, AUTHOR = {Mehrotra, S. and OZEVIN, G.}, title = "On the Implementation of Interior Point Decomposition Algorithms for Two-Stage Stochastic Conic", institution = "Northwestern University", address = "", URL="www.optimization-online.org/DB\_HTML/2005/10/1237.html", year = "2005"} @ARTICLE {MeMi:79, author = "A.A. MELKMAN and C.A. MICCHELLI", title = "Optimal estimation of linear operators in Hilbert spaces from inaccurate data", journal = "SIAM J. Numer. Anal.", year = "1979", volume = "16", number = "1", pages = "87-105"} @article {MR2511660, AUTHOR = {Mendl, C.B. and Wolf, M.M.}, TITLE = {Unital quantum channels---convex structure and revivals of {B}irkhoff's theorem}, JOURNAL = {Comm. Math. Phys.}, FJOURNAL = {Communications in Mathematical Physics}, VOLUME = {289}, YEAR = {2009}, NUMBER = {3}, PAGES = {1057--1086}, ISSN = {0010-3616}, CODEN = {CMPHAY}, MRCLASS = {81P45 (81R15)}, MRNUMBER = {2511660 (2010i:81093)}, DOI = {10.1007/s00220-009-0824-2}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s00220-009-0824-2}, } @PHDTHESIS {Mesz:97, author = "C. M\'{e}sz\'{a}ros", title = "An efficient implementation of interior point methods for linear programming and their applications", school = "Eotvos Lorand University of Sciences", keywords = "linear programming, interior-points", year = "1997"} @article {MR2020137, AUTHOR = {M\'{e}sz\'{a}ros, Cs. and Suhl, U.H.}, TITLE = {Advanced preprocessing techniques for linear and quadratic programming}, JOURNAL = {OR Spectrum}, FJOURNAL = {OR Spectrum. Quantitative Approaches in Management}, VOLUME = {25}, YEAR = {2003}, NUMBER = {4}, PAGES = {575--595}, ISSN = {0171-6468}, MRCLASS = {90C05 (90-04 90C20 90C51)}, MRNUMBER = {2020137}, MRREVIEWER = {K. Schittkowski}, DOI = {10.1007/s00291-003-0130-x}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s00291-003-0130-x}, } @article {springerlink:10.1007/s00291-003-0130-x, author = {M{\'e}sz{\'a}ros, C. and Suhl, U.H.}, affiliation = {Computer and Automation Research Institute Hungarian Academy of Sciences L�gym�nyosi u. 11 1111 Budapest Hungary}, title = {Advanced preprocessing techniques for linear and quadratic programming}, journal = {OR Spectrum}, publisher = {Springer Berlin / Heidelberg}, issn = {0171-6468}, keyword = {Business and Economics}, pages = {575-595}, volume = {25}, issue = {4}, url = {http://dx.doi.org/10.1007/s00291-003-0130-x}, note = {10.1007/s00291-003-0130-x}, year = {2003} } @techreport {Mesz:98, author = "C. M�sz�ros", title = "On the sparsity issues of interior point methods for quadratic programming", institution = "Laboratory of Operations Research and Decision Systems", address = "Hungarian Academy of Sciences", keywords = "quadratic programming, interior-points", year = "1998"} @ARTICLE {Mey:70, author = "R.R. MEYER", title = "The validity of a family of optimization methods", journal = "SIAM Journal Control", year = "1970", volume = "1", pages = "41-54"} @article {MR1922763, AUTHOR = {Li, C. and Jin, X.Q.}, TITLE = {Nonlinearly constrained best approximation in {H}ilbert spaces: the strong chip and the basic constraint qualification}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {13}, YEAR = {2002}, NUMBER = {1}, PAGES = {228--239}, ISSN = {1052-6234}, MRCLASS = {41A65 (90C46)}, MRNUMBER = {1922763}, MRREVIEWER = {Wu Li}, DOI = {10.1137/S1052623401385600}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/S1052623401385600}, } @article {MR1346302, AUTHOR = {Andersson, L.E. and Elfving, T.}, TITLE = {Best constrained approximation in {H}ilbert space and interpolation by cubic splines subject to obstacles}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {16}, YEAR = {1995}, NUMBER = {5}, PAGES = {1209--1232}, ISSN = {1064-8275}, MRCLASS = {41A05 (41A15 41A29 65D05 65D07)}, MRNUMBER = {1346302}, DOI = {10.1137/0916070}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/0916070}, } @article {MR1186970, AUTHOR = {Chui, C.K. and Deutsch, F. and Ward, J.D.}, TITLE = {Constrained best approximation in {H}ilbert space. {II}}, JOURNAL = {J. Approx. Theory}, FJOURNAL = {Journal of Approximation Theory}, VOLUME = {71}, YEAR = {1992}, NUMBER = {2}, PAGES = {213--238}, ISSN = {0021-9045}, MRCLASS = {41A29 (41A50 41A65)}, MRNUMBER = {1186970}, MRREVIEWER = {C. Dierieck}, DOI = {10.1016/0021-9045(92)90117-7}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1016/0021-9045(92)90117-7}, } @article {MR1027508, AUTHOR = {Chui, C.K. and Deutsch, F. and Ward, J.D.}, TITLE = {Constrained best approximation in {H}ilbert space}, JOURNAL = {Constr. Approx.}, FJOURNAL = {Constructive Approximation. An International Journal for Approximations and Expansions}, VOLUME = {6}, YEAR = {1990}, NUMBER = {1}, PAGES = {35--64}, ISSN = {0176-4276}, MRCLASS = {41A29 (41A50 41A65)}, MRNUMBER = {1027508}, MRREVIEWER = {C. Dierieck}, DOI = {10.1007/BF01891408}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/BF01891408}, } @ARTICLE {MiSmSwWa:85, author = "C.A. Micchelli and P.W. Smith and J. Swetits and J.D. Ward", title = "Constrained $L_p$ approximation", journal = "Journal of Constructive Approximation", year = "1985", volume = "1", pages = "93-102"} @ARTICLE {Mif:77a, author = "R. Mifflin", title = "An algorithm for constrained optimization with semi-smooth functions", journal = "Math. Oper. Res.", year = "1977", volume = "2", number = "2", pages = "191-207"} @ARTICLE {Mif:77b, author = "R. Mifflin", title = "Semismooth and semi-convex functions in constrained optimization", journal = "SIAM J. Cont. Optim.", year = "1977", volume = "15", pages = "959-972"} @TECHREPORT {Mitchell-Braun, author= "J.E. MITCHELL and S. BRAUN", title = "Rebalancing an investment portfolio in the presence of convex transaction costs", year = "2004", Institution = "Rensselaer Polytechnic", address = "Troy, NY"} @TECHREPORT {Mi:94a, author = "J. MITCHELL", title = "Interior point algorithm for integer programming", institution = "RPI", keywords = "ilp", year = "1994", address = "Troy, NY"} @TECHREPORT {Mi:94b, author = "J. MITCHELL", title = "Fixing Variables and Generating Classical Cutting Planes when using an Interior Point Branch and Cut Method to solve Integer Programming Problems", institution = "RPI", keywords = "ilp", year = "1994", address = "Troy, NY"} @article {MR1976487, AUTHOR = {Mittelmann, H.D.}, TITLE = {An independent benchmarking of {SDP} and {SOCP} solvers}, NOTE = {Computational semidefinite and second order cone programming: the state of the art}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {95}, YEAR = {2003}, NUMBER = {2, Ser. B}, PAGES = {407--430}, ISSN = {0025-5610}, MRCLASS = {90C22 (90C25)}, MRNUMBER = {MR1976487 (2004c:90033)}, } @misc{MittelmannBenchmark, title = "Decision Tree for Optimization Software", author = "H. Mittelmann", note = "{http://plato.asu.edu/bench.html}", year = "2019 (accessed May 2019)" } @misc{MittelmannBenchmarkInforms:17, title = "Latest Benchmarks of Optimization Software", author = "H. Mittelmann", note = "INFORMS Annual Meeting 2017", year = "2017", } @misc{DavisBenchmark, title = "LPnetlib", author = "T. Davis", note = "{https://www.cise.ufl.edu/research/sparse/matrices/LPnetlib/}", year = "2018 (accessed October 2018)" } @article {MR1778434, AUTHOR = {Mittelmann, H.D.}, TITLE = {Benchmarking interior point {LP}/{QP} solvers}, NOTE = {Interior point methods}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods and Software}, VOLUME = {11/12}, YEAR = {1999}, NUMBER = {1-4}, PAGES = {655--670}, ISSN = {1055-6788}, CODEN = {OMSOE2}, MRCLASS = {90C51 (90C05)}, MRNUMBER = {MR1778434}, } @ARTICLE {MiToYe:94, author = "S. MIZUNO and M.J. Todd and Y. YE", title = "On adaptive-step primal-dual interior-point algorithms for linear programming", journal = mor, volume = "18", number = "4", pages = "964-981", year = "1993"} @TECHREPORT {MoPo:92t, author = "B. MOHAR and S. POLJAK", title = "Eigenvalues in combinatorial optimization", institution = "Charles University", year = "1992", number = "92752", address = "Praha, Czechoslovakia"} @incollection {MoPo:92, author = "B. MOHAR and S. POLJAK", title = "Eigenvalues in combinatorial optimization", booktitle = "Combinatorial Graph-Theoretical Problems in Linear Algebra", year = "1993", publisher = "Springer-Verlag", series = "IMA Vol. 50"} @Article{Morales:2001:APF, author = "Jos\'{e} Luis Morales and Jorge Nocedal", title = "Algorithm 809: {PREQN}: {Fortran} 77 Subroutines for Preconditioning Preconditioning the Conjugate Gradient Method", journal = "{ACM} Transactions on Mathematical Software", volume = "27", number = "1", month = mar, year = "2001", pages = "83--91", accepted = "26 October 2000", URL = "http://www.acm.org/pubs/citations/journals/toms/2001-27-1/p83-morales/", URL = "http://www.acm.org/pubs/articles/journals/toms/2001-27-1/p83-morales/p83-morales.pdf", } @ARTICLE {Moran:95, author = "G. MORAN", title = " On the period-two-property of the majority operator in infinite graphs", journal = " Trans. Amer. Math. Soc.", volume = " 347 ", year = "1995", number = "no. 5", pages = "1649--1667"} @INCOLLECTION {More:77, author = "J.J. Mor\'{e}", title = "The {L}evenberg-{M}arquardt algorithm: implementation and theory. ", booktitle = "Lecture Notes in Mathematics \#630, Numerical Analysis", publisher = "Springer-Verlag", year = "1977", editor = "G.A. Watson", pages = "105-116", address = "Berlin, Heidelberg and New York"} @TECHREPORT {More:82, author = "J.J. Mor\'{e}", title = "Recent developments in algorithms and software for trust region methods", institution = "Argonne National Labs", year = "1982", number = "ANL/MCS-TM-2", address = "Argonne, IL"} @INCOLLECTION {More:83, author = "J.J. Mor\'{e}", title = "Recent developments in algorithms and software for trust region methods", booktitle = "Mathematical Programming, the State of the Art", editor = "Bachem and Grotschel and Korte", publisher = "\ \ ", year = "1983", pages = "268-285"} @article {More:93, author = {J.J. Mor\'{e}}, title = {Generalizations of the trust region problem}, journal = {Optim. Methods Software}, volume = {2}, pages = {189--209}, year = {1993} } @article {MR2100573, AUTHOR = {OLIVEIRA, A.R.L. and Sorensen, D.C.}, TITLE = {A new class of preconditioners for large-scale linear systems from interior point methods for linear programming}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {394}, YEAR = {2005}, PAGES = {1--24}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {65F10 (90C05 90C51)}, MRNUMBER = {MR2100573}, } @ARTICLE {MoSo:79, author = "J.J. Mor\'{e} and D.C. Sorensen", title = "On the use of directions of negative curvature in a modified {N}ewton method", journal = mprog, year = "1979", volume = "16", pages = "1-20"} @TECHREPORT {MoSo:82, author = "J.J. Mor\'{e} and D.C. Sorensen", title = "{N}ewton's method", institution = "Applied Mathematics Division, Argonne National Labs", year = "1982", number = "ANL-82-8", address = "Argonne, IL"} @INCOLLECTION {MoSo:82b, author = "J.J. Mor\'{e} and D.C. Sorensen", title = "{N}ewton's method", booktitle = "Studies in Numerical Analysis", publisher = "The Mathematical Association of America", year = "1984", volume = "24", series = "MAA Studies in Mathematics", editor = "Gene H. Golub"} @ARTICLE {MoSo:83, author = "J.J. Mor\'{e} and D.C. Sorensen", title = "Computing a trust region step", journal = "SIAM J. Sci. Statist. Comput.", year = "1983", volume = "4", pages = "553-572"} @ARTICLE {Mor:62, author = "J.J. MOREAU", title = "D\'ecomposition orthogonale d'un espace hilbertien selon deux co\^nes mutuellement polaires", journal = "C.R. Acad.Sci Paris", year = "1962", volume = "255", pages = "238-240"} @TECHREPORT {MoTa:87, author = "A.M. MORSHEDI and R.A. Tapia", title = "Karmarkar as a classical method", institution = "Department of Mathematical Sciences, Rice University", year = "1987", number = "TR87-7", address = "Houston, TX"} @article {MulveyRosenbaumaShettyp:97, AUTHOR = {J.M. Mulvey, D.P. Rosenbauma and B. Shettyb}, TITLE = {Strategic financial risk management and operations research}, JOURNAL = {European J. Oper. Res.}, FJOURNAL = {European Journal of Operational Research}, VOLUME = {97}, YEAR = {1979}, NUMBER = {1}, PAGES = {1--16} } @article {MR0093429, AUTHOR = {MUNKRES, J.}, TITLE = {Algorithms for the assignment and transportation problems}, JOURNAL = {J. Soc. Indust. Appl. Math.}, VOLUME = {5}, YEAR = {1957}, PAGES = {32--38}, MRCLASS = {90.0X}, MRNUMBER = {MR0093429 (19,1244f)}, MRREVIEWER = {P. Wolfe}, } @article {MR97m:90055, AUTHOR = {MURAMATSU, M. and TSUCHIYA, T.}, TITLE = {An affine scaling method with an infeasible starting point: convergence analysis under nondegeneracy assumption}, NOTE = {Interior point methods in mathematical programming}, JOURNAL = {Ann. Oper. Res.}, FJOURNAL = {Annals of Operations Research}, VOLUME = {62}, YEAR = {1996}, PAGES = {325--355}, ISSN = {0254-5330}, MRCLASS = {90C05}, MRNUMBER = {97m:90055}, } @article {MR96c:90049, AUTHOR = {TSUCHIYA, T. and MURAMATSU, M.}, TITLE = {Global convergence of a long-step affine scaling algorithm for degenerate linear programming problems}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {5}, YEAR = {1995}, NUMBER = {3}, PAGES = {525--551}, ISSN = {1052-6234}, CODEN = {SJOPE8}, MRCLASS = {90C05 (90C08)}, MRNUMBER = {96c:90049}, MRREVIEWER = {Florian Jarre}, } @BOOK {Murr:72, author = "W. MURRAY", title = "Numerical Methods for Unconstrained Optimization", publisher = "Academic Press", year = "1972", address = "London"} @ARTICLE {MuOv:80, author = "W. MURRAY and M.L. Overton", title = "A projected {L}agrangian algorithm for nonlinear minimax optimization", journal = "SIAM J. Sci. Statist. Comput.", year = "1980", volume = "1", pages = "345-370"} @ARTICLE {MuOv:81, author = "W. MURRAY and M.L. Overton", title = "A projected {L}agrangian algorithm for nonlinear $l_{1}$ optimization", journal = "SIAM J. Sci. Statist. Comput.", year = "1981", volume = "2", pages = "207-224"} @BOOK {Murt:76, author = "K.G. MURTY", title = "Linear and Combinatorial Programming", publisher = "John Wiley \& Sons", year = "1976", address = "New York, NY"} @BOOK {Murt:88, author = "K.G. MURTY", title = "Linear Complementarity, Linear and Nonlinear Programming", publisher = "Heldermann Verlag", year = "1988", address = "Berlin"} @BOOK {Murty, author = "K.G. MURTY", title = "Linear Complementarity, Linear and Nonlinear Programming", publisher = "Heldermann Verlag", year = "1988", address = "Berlin"} @article {MR941464, AUTHOR = {Mukherjee, B.N. and Maiti, S.S.}, TITLE = {On some properties of positive definite {T}oeplitz matrices and their possible applications}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {102}, YEAR = {1988}, PAGES = {211--240}, ISSN = {0024-3795}, MRCLASS = {15A15 (15A18 15A48 62M99)}, MRNUMBER = {941464}, MRREVIEWER = {A. B\"ottcher}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1016/0024-3795(88)90326-6}, } %NNNNNNNNNNNNNNNNNNNNN @book {NagurneyQiang:09, AUTHOR = {Nagurney, A. and Qiang, Q.}, TITLE = {Fragile Networks: Identifying Vulnerabilities and Synergies in an Uncertain World}, PUBLISHER = {John Wiley}, ADDRESS = {}, YEAR = {2009} } @TECHREPORT {Nag:94, author = "I. NAJFELD", title = "Derivatives of the matrix exponential and their computation", institution = "Biological Chemistry and Molecular Pharmacology", address = "Harvard Medical School, Boston, MA 02115-5718", year = "1994", keywords = "matrix exponential, matrix derivatives", number = "TR-33-94"} @ARTICLE {Naz:80, author = "L. NAZARETH", title = "Some recent approaches to solving large residual nonlinear least squares problems", journal = "SIAM Rev.", year = "1980", volume = "22", pages = "1-11"} @TECHREPORT {Naz:83, author = "L. NAZARETH", title = "An adaptive method of minimizing a sum of squares of nonlinear functions", institution = "International Institute for Applied Systems Analysis", year = "1983", number = "WP-83-99"} @TECHREPORT {Naz:84, author = "L. NAZARETH", title = "Some approaches to making conjugate gradient methods for nonlinear minimization less dependent on notions of conjugacy", institution = "Center for Pure and Applied Mathematics, University of California, Berkeley", year = "1984"} @ARTICLE {Naz:86, author = "L. NAZARETH", title = "The method of successive affine reduction for nonlinear minimization", journal = "Math. Prog.", year = "1986", volume = "35", pages = "97-109"} @TECHREPORT {Naz:93, author = "L. NAZARETH", title = "A reformulation of the central path equations and its algorithmic implications", institution = "Dept. of Pure and Applied Mathematics, Washington State University, Pullman", year = "1993"} @article {MR1444091, AUTHOR = {Na\!evdal, G.}, TITLE = {On a generalization of the trigonometric moment problem}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {258}, YEAR = {1997}, PAGES = {1--18}, ISSN = {0024-3795}, MRCLASS = {44A60 (42A70)}, MRNUMBER = {1444091}, MRREVIEWER = {Tiberiu Constantinescu}, URL = {https://doi.org/10.1016/S0024-3795(96)00151-6}, } @TECHREPORT {Naz:96, author = "L. NAZARETH", title = "Computer solution of linear programs: non-simplex algorithms {II}", institution = "Dept. of Pure and Applied Mathematics, Washington State University, Pullman", year = "1996"} @article {MR95b:90119, AUTHOR = {Nazareth, J. L.}, TITLE = {The {N}ewton and {C}auchy perspectives on computational nonlinear optimization}, JOURNAL = {SIAM Rev.}, FJOURNAL = {SIAM Review. A Publication of the Society for Industrial and Applied Mathematics}, VOLUME = {36}, YEAR = {1994}, NUMBER = {2}, PAGES = {215--225}, ISSN = {0036-1445}, CODEN = {SIREAD}, } @book {MR95i:90003, AUTHOR = {Nazareth, J. L.}, TITLE = {The {N}ewton-{C}auchy framework}, NOTE = {A unified approach to unconstrained nonlinear minimization}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {769}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1994}, PAGES = {xii+101}, ISBN = {3-540-57671-1}, } @book {Nazareth:03, AUTHOR = {NAZARETH, J.L.}, TITLE = {Differentiable Optimization and Equation Solving}, NOTE = {A unified approach to unconstrained nonlinear minimization}, SERIES = {CMS Books in Mathematics}, VOLUME = {13}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {2003}, PAGES = {350}, ISBN = {0-387-95572-0} } @book {NemKanTodd:89, TITLE = {Optimization}, EDITOR = {NEMHAUSER, G. L. and RINNOOY KAN, A. H. G. and Todd, M.J.}, SERIES = {Handbooks in Operations Research and Management Science}, VOLUME = {1}, PUBLISHER = {North-Holland Publishing Co.}, ADDRESS = {Amsterdam}, YEAR = {1989}, PAGES = {xiv+709}, ISBN = {0-444-87284-1}, } @article{nem_cond, author={Harchaoui, Z. and Juditsky, A. and Nemirovski, A.}, year={2014}, issn={0025-5610}, journal={Mathematical Programming}, doi={10.1007/s10107-014-0778-9}, title={Conditional gradient algorithms for norm-regularized smooth convex optimization}, url={http://dx.doi.org/10.1007/s10107-014-0778-9}, publisher={Springer Berlin Heidelberg}, pages={1-38}, language={English} } @article {MR2436012, AUTHOR = {Nemirovski, A.S. and Todd, M.J.}, TITLE = {Interior-point methods for optimization}, JOURNAL = {Acta Numer.}, FJOURNAL = {Acta Numerica}, VOLUME = {17}, YEAR = {2008}, PAGES = {191--234}, ISSN = {0962-4929}, ISBN = {978-0-521-51642-6}, MRCLASS = {90C51 (90C30)}, MRNUMBER = {2436012 (2009j:90141)}, MRREVIEWER = {Warren L. Hare}, DOI = {10.1017/S0962492906370018}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1017/S0962492906370018}, } @article {Nemir:86, AUTHOR = {Nemirovski, A.}, TITLE = {The regularization properties of the adjoint gradient method in ill-posed problems}, JOURNAL = {USSR Comput. Math. and Math. Phys.}, VOLUME = {26}, YEAR = {1986}, NUMBER = {2}, PAGES = {7--16}, } @book {MR702836, AUTHOR = {Nemirovsky, A.S. and Yudin, D.B.}, TITLE = {Problem complexity and method efficiency in optimization}, SERIES = {A Wiley-Interscience Publication}, NOTE = {Translated from the Russian and with a preface by E. R. Dawson, Wiley-Interscience Series in Discrete Mathematics}, PUBLISHER = {John Wiley \&\ Sons, Inc., New York}, YEAR = {1983}, PAGES = {xv+388}, ISBN = {0-471-10345-4}, MRCLASS = {90C25 (68C25)}, MRNUMBER = {702836}, } @article {MR2327005, AUTHOR = {Nesterov, Y.}, TITLE = {Accelerating the cubic regularization of {N}ewton's method on convex problems}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {112}, YEAR = {2008}, NUMBER = {1, Ser. B}, PAGES = {159--181}, ISSN = {0025-5610}, MRCLASS = {90C25 (49M37 90C53)}, MRNUMBER = {2327005}, MRREVIEWER = {Anhua Lin}, DOI = {10.1007/s10107-006-0089-x}, URL = {http://dx.doi.org/10.1007/s10107-006-0089-x}, } @article {MR2229459, AUTHOR = {Nesterov, Y. and Polyak, B.T.}, TITLE = {Cubic regularization of {N}ewton method and its global performance}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {108}, YEAR = {2006}, NUMBER = {1, Ser. A}, PAGES = {177--205}, ISSN = {0025-5610}, MRCLASS = {90C53 (90C30)}, MRNUMBER = {2229459}, MRREVIEWER = {Michel H. Geoffroy}, DOI = {10.1007/s10107-006-0706-8}, URL = {http://dx.doi.org/10.1007/s10107-006-0706-8}, } @article {MR2313779, AUTHOR = {Nesterov, Yurii}, TITLE = {Smoothing technique and its applications in semidefinite optimization}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {110}, YEAR = {2007}, NUMBER = {2, Ser. A}, PAGES = {245--259}, ISSN = {0025-5610}, MRCLASS = {90C06 (90C22 90C25 90C60)}, MRNUMBER = {2313779 (2008e:90051)}, MRREVIEWER = {Marina Alex Epelman}, DOI = {10.1007/s10107-006-0001-8}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s10107-006-0001-8}, } @article {MR2166537, AUTHOR = {Nesterov, Y.}, TITLE = {Smooth minimization of non-smooth functions}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {103}, YEAR = {2005}, NUMBER = {1, Ser. A}, PAGES = {127--152}, ISSN = {0025-5610}, MRCLASS = {90C47 (90C60)}, MRNUMBER = {2166537 (2006g:90174)}, MRREVIEWER = {Marko M. M{\"a}kel{\"a}}, DOI = {10.1007/s10107-004-0552-5}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s10107-004-0552-5}, } @techreport{Nest:94, author = "Y.E. Nesterov", title = "Infeasible start interior point primal-dual methods in nonlinear programming", year = "1994", institution = "CORE", address = "Belgium", } @book {MR2142598, AUTHOR = {Nesterov, Y.}, TITLE = {Introductory lectures on convex optimization}, SERIES = {Applied Optimization}, VOLUME = {87}, NOTE = {A basic course}, PUBLISHER = {Kluwer Academic Publishers}, ADDRESS = {Boston, MA}, YEAR = {2004}, PAGES = {xviii+236}, ISBN = {1-4020-7553-7}, MRCLASS = {90-02 (90-01 90C25)}, MRNUMBER = {MR2142598 (2005k:90001)}, } @article {NesterovmodGN:07, AUTHOR = {Nesterov, Y.}, TITLE = {Modified {G}auss-{N}ewton scheme with worst case guarantees for global performance}, JOURNAL = {oms}, VOLUME = {22}, YEAR = {2007}, NUMBER = {3}, PAGES = {469--483}, } @article{NestToddYe:96, author = "Y.E. Nesterov and M.J. Todd and Y. Ye", TITLE = {Infeasible-start primal-dual methods and infeasibility detectors for nonlinear programming problems}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {84}, YEAR = {1999}, NUMBER = {2, Ser. A}, PAGES = {227--267}, ISSN = {0025-5610}, MRCLASS = {90C25 (90C51 90C60)}, MRNUMBER = {2000d:90055}, MRREVIEWER = {Yin Zhang}, } @book {MR0157871, AUTHOR = {von Neumann, John}, TITLE = {Collected works. {V}ol. {I}: {L}ogic, theory of sets and quantum mechanics}, SERIES = {General editor: A. H. Taub}, PUBLISHER = {Pergamon Press}, ADDRESS = {New York}, YEAR = {1961}, PAGES = {x+654 pp. (1 plate)}, MRCLASS = {01.60 (00.00)}, MRNUMBER = {0157871 (28 \#1100)}, } @book{neu, AUTHOR = "Neumann, J. von", TITLE = "Collected Works", NOTE = "A.H.\ Traub, ed.", PUBLISHER = "Pergamon Press", ADDRESS = "New York", YEAR = "1962", } @book {MR0034514, AUTHOR = {von Neumann, John}, TITLE = {Functional {O}perators. {II}. {T}he {G}eometry of {O}rthogonal {S}paces}, SERIES = {Annals of Mathematics Studies, no. 22}, PUBLISHER = {Princeton University Press}, ADDRESS = {Princeton, N. J.}, YEAR = {1950}, PAGES = {iii+107}, MRCLASS = {46.3X}, MRNUMBER = {MR0034514 (11,599e)}, MRREVIEWER = {P. R. Halmos}, } @INCOLLECTION {vonNeum:63, author = "J. von Neumann", title = "Discussion of a maximum problem", booktitle = "Jon von Neumann, Collected Works", publisher = "Pergamon", year = "1963", editor = "A.H. Taub", pages = "89-95", address = "New York"} @article {MR99f:65066, AUTHOR = {neumaier, A.}, TITLE = {Solving ill-conditioned and singular linear systems: a tutorial on regularization}, JOURNAL = {SIAM Rev.}, FJOURNAL = {SIAM Review}, VOLUME = {40}, YEAR = {1998}, NUMBER = {3}, PAGES = {636--666 (electronic)}, ISSN = {1095-7200}, MRCLASS = {65F30}, MRNUMBER = {99f:65066}, MRREVIEWER = {Andreas Rieder}, } @book {MR55:13315, AUTHOR = {NEUSTADT, L.W.}, TITLE = {Optimization}, NOTE = {A Theory of Necessary Conditions, With a chapter by H. T. Banks}, PUBLISHER = {Princeton University Press}, ADDRESS = {Princeton, N. J.}, YEAR = {1976}, PAGES = {xiii+424}, MRCLASS = {49BXX}, MRNUMBER = {55 #13315}, MRREVR = {J. Warga}, } @article {MR1777081, AUTHOR = {MORALES, J.L. and Nocedal, J.}, TITLE = {Automatic preconditioning by limited memory quasi-{N}ewton updating}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {10}, YEAR = {2000}, NUMBER = {4}, PAGES = {1079--1096 (electronic)}, ISSN = {1095-7189}, MRCLASS = {}, MRNUMBER = {1 777 081}, } @article {MR2002j:90078, AUTHOR = {Morales, Jos{\'e} Luis and Nocedal, Jorge}, TITLE = {Enriched methods for large-scale unconstrained optimization}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {21}, YEAR = {2002}, NUMBER = {2}, PAGES = {143--154}, ISSN = {0926-6003}, CODEN = {CPPPEF}, MRCLASS = {90C30 (90C52)}, MRNUMBER = {2002j:90078}, } @article {MR92d:65112, AUTHOR = {NASH, S.G. and Nocedal, J.}, TITLE = {A numerical study of the limited memory {B}{F}{G}{S} method and the truncated-{N}ewton method for large scale optimization}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {1}, YEAR = {1991}, NUMBER = {3}, PAGES = {358--372}, ISSN = {1052-6234}, CODEN = {SJOPE8}, MRCLASS = {}, MRNUMBER = {92d:65112}, MRREVIEWER = {Marco Gaviano}, } @article {sp1, AUTHOR = {NASH, S.G. and SOFER, A.}, TITLE = {Preconditioning Reduced Matrices}, JOURNAL = simax, FJOURNAL = {SIAM Journal on Matrix Analysis Applications}, VOLUME = {17}, YEAR = {1996}, NUMBER = {1}, PAGES = {47--68}, ISSN = {1052-6234}, } @article {MR1159043, AUTHOR = {Bartels, S.G. and Higham, D.J.}, TITLE = {The structured sensitivity of {V}andermonde-like systems}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {62}, YEAR = {1992}, NUMBER = {1}, PAGES = {17--33}, ISSN = {0029-599X}, CODEN = {NUMMA7}, MRCLASS = {65F35 (65F05)}, MRNUMBER = {MR1159043 (93e:65071)}, MRREVIEWER = {George D. Poole}, } @incollection {MR1772884, AUTHOR = {BARYAMUREEBA, V. and Steihaug, T.}, TITLE = {Computational issues for a new class of preconditioners}, BOOKTITLE = {Large-scale scientific computations of engineering and environmental problems, II (Sozopol, 1999)}, SERIES = {Notes Numer. Fluid Mech.}, VOLUME = {73}, PAGES = {128--135}, PUBLISHER = {Vieweg}, ADDRESS = {Braunschweig}, YEAR = {2000}, MRCLASS = {65F35}, MRNUMBER = {1 772 884}, } @incollection {sp2, AUTHOR = {BARYAMUREEBA, V. and Steihaug, T. and ZHANG, Y.}, TITLE = {Application of a New Class of Preconditioners to Large Linear Programming Problems}, BOOKTITLE = {Euro-Par 1999}, SERIES = {LNCS 1685}, VOLUME = {}, PAGES = {1044--1048}, PUBLISHER = {Springer-Verlag Berlin Heidelberg}, YEAR = {1999}, } @article {MR1842569, AUTHOR = {Liu, Guanghui and Han, Lixing}, TITLE = {A study of the {D}ennis-{W}olkowicz method on convex functions}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {19}, YEAR = {2001}, NUMBER = {3}, PAGES = {297--317}, ISSN = {0926-6003}, CODEN = {CPPPEF}, MRCLASS = {90C25 (90C53)}, MRNUMBER = {1842569 (2002c:90051)}, MRREVIEWER = {K. Schittkowski}, DOI = {10.1023/A:1011212022308}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1023/A:1011212022308}, } @incollection {MR3536565, AUTHOR = {Nikolov, A. and Singh, M.}, TITLE = {Maximizing determinants under partition constraints}, BOOKTITLE = {S{TOC}'16---{P}roceedings of the 48th {A}nnual {ACM} {SIGACT} {S}ymposium on {T}heory of {C}omputing}, PAGES = {192--201}, PUBLISHER = {ACM, New York}, YEAR = {2016}, MRCLASS = {90C27 (15B48 68W25)}, MRNUMBER = {3536565}, } @article {MR90m:90253, AUTHOR = {Liu, D.C. and Nocedal, J.}, TITLE = {On the limited memory {B}{F}{G}{S} method for large scale optimization}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {45}, YEAR = {1989}, NUMBER = {3, (Ser. B)}, PAGES = {503--528}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {}, MRNUMBER = {90m:90253}, } @incollection {MR88g:90131, author = "J. Nocedal", TITLE = {Viewing the conjugate gradient method as a trust region algorithm}, BOOKTITLE = {Numerical analysis (Guanajuato, 1984)}, PAGES = {118--126}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1986}, MRCLASS = {}, MRNUMBER = {88g:90131}, MRREVIEWER = {A. G. Azpeitia}, } @incollection {MR1446295, author = "J. Nocedal", TITLE = {Conjugate gradient methods and nonlinear optimization}, BOOKTITLE = {Linear and nonlinear conjugate gradient-related methods (Seattle, WA, 1995)}, PAGES = {9--23}, PUBLISHER = {SIAM}, ADDRESS = {Philadelphia, PA}, YEAR = {1996}, MRCLASS = {}, MRNUMBER = {1 446 295}, } @misc{NikkeiYahooMM, title = {Nikkei 225 (\^N225)}, howpublished = {\url{https://finance.yahoo.com/quote/%5EN225/history/}}, note = {Accessed: 2020-05-24} } @TECHREPORT {Noc:85, author = "J. Nocedal", title = "Viewing the conjugate gradient methods as a trust region algorithm", institution = "Department of Electrical Engineering and Computer Science, Northwestern University", year = "1985", number = "85-01-NAM-01"} @INCOLLECTION {Nocedal:90, author = "J. Nocedal", title = "The performance of several algorithms for large scale unconstrained optimization", editor = "Thomas F. Coleman and Yuying Li", booktitle = "Large-{S}cale {N}umerical {O}ptimization", publisher = "SIAM", year = "1990", address = "Philadelphia"} @TECHREPORT {NoOv:83, author = "J. Nocedal and M.L. Overton", title = "Projected {H}essian updating algorithms for nonlinearly constrained optimization", institution = "Department of Computer Science, Courant Institute of Mathematical Sciences", year = "1983", number = "95", address = "New York, NY"} @TECHREPORT {NoYu:91, author = "J. Nocedal and Y. YUAN", title = "Analysis of a self-scaling quasi-{N}ewton method", institution = "Department of Electrical Engineering and Computer Science, Northwestern University", year = "1991", address = "Chicago, Ill"} @incollection {MR1628351, AUTHOR = {Nocedal, Jorge}, TITLE = {Large scale unconstrained optimization}, BOOKTITLE = {The state of the art in numerical analysis (York, 1996)}, SERIES = {Inst. Math. Appl. Conf. Ser. New Ser.}, VOLUME = {63}, PAGES = {311--338}, PUBLISHER = {Oxford Univ. Press}, ADDRESS = {New York}, YEAR = {1997}, MRCLASS = {90-02 (65K05 90C06 90C30)}, MRNUMBER = {MR1628351 (99b:90003)}, } @article {MR95b:90146, AUTHOR = {NOZAWA, R.}, TITLE = {Examples of max-flow and min-cut problems with duality gaps in continuous networks}, JOURNAL = mprog, FJOURNAL = {Mathematical Programming}, VOLUME = {63}, YEAR = {1994}, NUMBER = {2, Ser. A}, PAGES = {213--234}, ISSN = {0025-5610}, CODEN = {MHPGA4}, } %OOOOO @article {MR3911719, AUTHOR = {Estrin, Ron and Orban, Dominique and Saunders, Michael A.}, TITLE = {L{SLQ}: an iterative method for linear least-squares with an error minimization property}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {40}, YEAR = {2019}, NUMBER = {1}, PAGES = {254--275}, ISSN = {0895-4798}, MRCLASS = {65F10 (15A06 65F20 65F22 65F25 65F35 65F50 93E24)}, MRNUMBER = {3911719}, DOI = {10.1137/17M1113552}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/17M1113552}, } @article {MR3911718, AUTHOR = {Estrin, Ron and Orban, Dominique and Saunders, Michael}, TITLE = {Euclidean-norm error bounds for {SYMMLQ} and {CG}}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {40}, YEAR = {2019}, NUMBER = {1}, PAGES = {235--253}, ISSN = {0895-4798}, MRCLASS = {65F10 (15A06 15A60 65F50)}, MRNUMBER = {3911718}, DOI = {10.1137/16M1094816}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/16M1094816}, } @incollection {MR3811386, AUTHOR = {Ma, Ding and Judd, Kenneth L. and Orban, Dominique and Saunders, Michael A.}, TITLE = {Stabilized optimization via an {NCL} algorithm}, BOOKTITLE = {Numerical analysis and optimization}, SERIES = {Springer Proc. Math. Stat.}, VOLUME = {235}, PAGES = {173--191}, PUBLISHER = {Springer, Cham}, YEAR = {2018}, MRCLASS = {65K05 (49M37 90-04 90C30)}, MRNUMBER = {3811386}, } @article {MR3806606, AUTHOR = {Orban, Dominique}, TITLE = {{\it {I}ntroduction to computation and programming using python. {S}econd edition, with application to understanding data} [book review, {MIT} {P}ress, {C}ambridge, {MA}, 2016]}, JOURNAL = {SIAM Rev.}, FJOURNAL = {SIAM Review}, VOLUME = {60}, YEAR = {2018}, NUMBER = {2}, PAGES = {483--485}, ISSN = {0036-1445}, MRCLASS = {00A17}, MRNUMBER = {3806606}, } @article {MR3800240, AUTHOR = {Arreckx, Sylvain and Orban, Dominique}, TITLE = {A regularized factorization-free method for equality-constrained optimization}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {28}, YEAR = {2018}, NUMBER = {2}, PAGES = {1613--1639}, ISSN = {1052-6234}, MRCLASS = {90C55 (65F50 65K05 90C06 90C20 90C30 90C51 90C53)}, MRNUMBER = {3800240}, MRREVIEWER = {Hiroshi Yabe}, DOI = {10.1137/16M1088570}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/16M1088570}, } @book {MR3660695, AUTHOR = {Orban, Dominique and Arioli, Mario}, TITLE = {Iterative solution of symmetric quasi-definite linear systems}, SERIES = {SIAM Spotlights}, VOLUME = {3}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA}, YEAR = {2017}, PAGES = {xiv+93}, ISBN = {978-1-611974-72-0}, MRCLASS = {65F10 (15A06)}, MRNUMBER = {3660695}, MRREVIEWER = {Jos\'{e} E. Rom\'{a}n}, } @article {MR3579750, AUTHOR = {Dehghani, A. and Goffin, J.-L. and Orban, D.}, TITLE = {A primal-dual regularized interior-point method for semidefinite programming}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods \& Software}, VOLUME = {32}, YEAR = {2017}, NUMBER = {1}, PAGES = {193--219}, ISSN = {1055-6788}, MRCLASS = {90C22 (90C25 90C46 90C51)}, MRNUMBER = {3579750}, DOI = {10.1080/10556788.2016.1235708}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1080/10556788.2016.1235708}, } @article {MR3566236, AUTHOR = {Towhidi, Mehdi and Orban, Dominique}, TITLE = {Customizing the solution process of {COIN}-{OR}'s linear solvers with {P}ython}, JOURNAL = {Math. Program. Comput.}, FJOURNAL = {Mathematical Programming Computation}, VOLUME = {8}, YEAR = {2016}, NUMBER = {4}, PAGES = {377--391}, ISSN = {1867-2949}, MRCLASS = {90C05 (90-04 90C10 90C11)}, MRNUMBER = {3566236}, DOI = {10.1007/s12532-015-0094-2}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s12532-015-0094-2}, } @article {MR3511448, AUTHOR = {Arreckx, Sylvain and Lambe, Andrew and Martins, Joaquim R. R. A. and Orban, Dominique}, TITLE = {A matrix-free augmented lagrangian algorithm with application to large-scale structural design optimization}, JOURNAL = {Optim. Eng.}, FJOURNAL = {Optimization and Engineering. International Multidisciplinary Journal to Promote Optimization Theory \& Applications in Engineering Sciences}, VOLUME = {17}, YEAR = {2016}, NUMBER = {2}, PAGES = {359--384}, ISSN = {1389-4420}, MRCLASS = {90C06 (74P10 90-04)}, MRNUMBER = {3511448}, DOI = {10.1007/s11081-015-9287-9}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s11081-015-9287-9}, } @incollection {MR3446845, AUTHOR = {Gould, Nick I. M. and Orban, Dominique and Toint, Philippe L.}, TITLE = {An interior-point {$\ell_1$}-penalty method for nonlinear optimization}, BOOKTITLE = {Numerical analysis and optimization}, SERIES = {Springer Proc. Math. Stat.}, VOLUME = {134}, PAGES = {117--150}, PUBLISHER = {Springer, Cham}, YEAR = {2015}, MRCLASS = {90C51 (65K05 90C26)}, MRNUMBER = {3446845}, DOI = {10.1007/978-3-319-17689-5_6}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/978-3-319-17689-5_6}, } @article {MR3391157, AUTHOR = {Orban, Dominique}, TITLE = {Limited-memory {LDL{$^\top$}} factorization of symmetric quasi-definite matrices with application to constrained optimization}, JOURNAL = {Numer. Algorithms}, FJOURNAL = {Numerical Algorithms}, VOLUME = {70}, YEAR = {2015}, NUMBER = {1}, PAGES = {9--41}, ISSN = {1017-1398}, MRCLASS = {65F08 (15A06 15A23 15B57 65F10 90C20)}, MRNUMBER = {3391157}, MRREVIEWER = {Miroslav T\ocirc{u}ma}, DOI = {10.1007/s11075-014-9933-x}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s11075-014-9933-x}, } @article {MR3320935, AUTHOR = {Gould, N.I.M. and Orban, D. and Toint, P.L.}, TITLE = {{$\sf{CUTEst}$}: a constrained and unconstrained testing environment with safe threads for mathematical optimization}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {60}, YEAR = {2015}, NUMBER = {3}, PAGES = {545--557}, ISSN = {0926-6003}, MRCLASS = {90-04 (68W40)}, MRNUMBER = {3320935}, DOI = {10.1007/s10589-014-9687-3}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10589-014-9687-3}, } @article {MR3274367, AUTHOR = {Gould, Nick and Orban, Dominique and Rees, Tyrone}, TITLE = {Projected {K}rylov methods for saddle-point systems}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {35}, YEAR = {2014}, NUMBER = {4}, PAGES = {1329--1343}, ISSN = {0895-4798}, MRCLASS = {65F10 (15A06 65F08 65F50 90C20)}, MRNUMBER = {3274367}, MRREVIEWER = {Vladimir B. Larin}, DOI = {10.1137/130916394}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/130916394}, } @article {MR3252847, AUTHOR = {Audet, Charles and Dang, Kien-Cong and Orban, Dominique}, TITLE = {Optimization of algorithms with {OPAL}}, JOURNAL = {Math. Program. Comput.}, FJOURNAL = {Mathematical Programming Computation}, VOLUME = {6}, YEAR = {2014}, NUMBER = {3}, PAGES = {233--254}, ISSN = {1867-2949}, MRCLASS = {65K05 (65Y15 90C90)}, MRNUMBER = {3252847}, DOI = {10.1007/s12532-014-0067-x}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s12532-014-0067-x}, } @article {MR3148649, AUTHOR = {Greif, Chen and Moulding, Erin and Orban, Dominique}, TITLE = {Bounds on eigenvalues of matrices arising from interior-point methods}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {24}, YEAR = {2014}, NUMBER = {1}, PAGES = {49--83}, ISSN = {1052-6234}, MRCLASS = {15A42 (15A06 65F22 90C20 90C51)}, MRNUMBER = {3148649}, MRREVIEWER = {Chee-Khian Sim}, DOI = {10.1137/120890600}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/120890600}, } @article {MR3175458, AUTHOR = {Armand, Paul and Benoist, Jo\"{e}l and Orban, Dominique}, TITLE = {From global to local convergence of interior methods for nonlinear optimization}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods \& Software}, VOLUME = {28}, YEAR = {2013}, NUMBER = {5}, PAGES = {1051--1080}, ISSN = {1055-6788}, MRCLASS = {90C51 (90C06 90C30)}, MRNUMBER = {3175458}, MRREVIEWER = {Jiu Ding}, DOI = {10.1080/10556788.2012.668905}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1080/10556788.2012.668905}, } @article {MR3069876, AUTHOR = {Gould, Nicholas I. M. and Orban, Dominique and Robinson, Daniel P.}, TITLE = {Trajectory-following methods for large-scale degenerate convex quadratic programming}, JOURNAL = {Math. Program. Comput.}, FJOURNAL = {Mathematical Programming Computation}, VOLUME = {5}, YEAR = {2013}, NUMBER = {2}, PAGES = {113--142}, ISSN = {1867-2949}, MRCLASS = {90C20 (90-04 90C51)}, MRNUMBER = {3069876}, DOI = {10.1007/s12532-012-0050-3}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s12532-012-0050-3}, } @article {MR3022781, AUTHOR = {Audet, C. and Dang, C.-K. and Orban, D.}, TITLE = {Efficient use of parallelism in algorithmic parameter optimization applications}, JOURNAL = {Optim. Lett.}, FJOURNAL = {Optimization Letters}, VOLUME = {7}, YEAR = {2013}, NUMBER = {3}, PAGES = {421--433}, ISSN = {1862-4472}, MRCLASS = {90C60 (65K10)}, MRNUMBER = {3022781}, DOI = {10.1007/s11590-011-0428-6}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s11590-011-0428-6}, } @article {MR2902690, AUTHOR = {Coulibaly, Z. and Orban, D.}, TITLE = {An {$\ell_1$} elastic interior-point method for mathematical programs with complementarity constraints}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {22}, YEAR = {2012}, NUMBER = {1}, PAGES = {187--211}, ISSN = {1052-6234}, MRCLASS = {90C51 (65K05 90C30)}, MRNUMBER = {2902690}, MRREVIEWER = {Thierry Champion}, DOI = {10.1137/090777232}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/090777232}, } @article {MR2373304, AUTHOR = {Friedlander, M.P. and Tseng, P.}, TITLE = {Exact regularization of convex programs}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {18}, YEAR = {2007}, NUMBER = {4}, PAGES = {1326--1350}, ISSN = {1052-6234}, MRCLASS = {90C25 (65K05 90C46 90C51)}, MRNUMBER = {2373304}, MRREVIEWER = {Heinz H. Bauschke}, DOI = {10.1137/060675320}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/060675320}, } @article {MR2899152, AUTHOR = {Friedlander, M. P. and Orban, D.}, TITLE = {A primal-dual regularized interior-point method for convex quadratic programs}, JOURNAL = {Math. Program. Comput.}, FJOURNAL = {Mathematical Programming Computation}, VOLUME = {4}, YEAR = {2012}, NUMBER = {1}, PAGES = {71--107}, ISSN = {1867-2949}, MRCLASS = {90C20 (65K05 90C51)}, MRNUMBER = {2899152}, MRREVIEWER = {Javier F. Pe\~{n}a}, DOI = {10.1007/s12532-012-0035-2}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s12532-012-0035-2}, } @article {MR2830333, AUTHOR = {Orban, Dominique}, TITLE = {{\it {I}ntroduction to derivative-free optimization} [book review of MR2487816]}, JOURNAL = {SIAM Rev.}, FJOURNAL = {SIAM Review}, VOLUME = {53}, YEAR = {2011}, NUMBER = {2}, PAGES = {395--396}, ISSN = {0036-1445}, MRCLASS = {00A17}, MRNUMBER = {2830333}, } @article {MR2721290, AUTHOR = {Fourer, R. and Orban, Dominique}, TITLE = {Dr{A}mpl: a meta solver for optimization problem analysis}, JOURNAL = {Comput. Manag. Sci.}, FJOURNAL = {Computational Management Science}, VOLUME = {7}, YEAR = {2010}, NUMBER = {4}, PAGES = {437--463}, ISSN = {1619-697X}, MRCLASS = {90-04 (90C25 90C26 90C30)}, MRNUMBER = {2721290}, DOI = {10.1007/s10287-009-0101-z}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10287-009-0101-z}, } @article {MR2663505, AUTHOR = {Fourer, Robert and Maheshwari, Chandrakant and Neumaier, Arnold and Orban, Dominique and Schichl, Hermann}, TITLE = {Convexity and concavity detection in computational graphs: tree walks for convexity assessment}, JOURNAL = {INFORMS J. Comput.}, FJOURNAL = {INFORMS Journal on Computing}, VOLUME = {22}, YEAR = {2010}, NUMBER = {1}, PAGES = {26--43}, ISSN = {1091-9856}, MRCLASS = {90-04 (90C30)}, MRNUMBER = {2663505}, DOI = {10.1287/ijoc.1090.0321}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1287/ijoc.1090.0321}, } @article {MR2577262, AUTHOR = {Raymond, Vincent and Soumis, Fran\c{c}ois and Orban, Dominique}, TITLE = {A new version of the improved primal simplex for degenerate linear programs}, JOURNAL = {Comput. Oper. Res.}, FJOURNAL = {Computers \& Operations Research}, VOLUME = {37}, YEAR = {2010}, NUMBER = {1}, PAGES = {91--98}, ISSN = {0305-0548}, MRCLASS = {90C05}, MRNUMBER = {2577262}, MRREVIEWER = {James Andrew J. Hall}, DOI = {10.1016/j.cor.2009.03.020}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1016/j.cor.2009.03.020}, } @article {MR2424928, AUTHOR = {Armand, Paul and Benoist, Jo\"{e}l and Orban, Dominique}, TITLE = {Dynamic updates of the barrier parameter in primal-dual methods for nonlinear programming}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {41}, YEAR = {2008}, NUMBER = {1}, PAGES = {1--25}, ISSN = {0926-6003}, MRCLASS = {90C30 (65K05 90C51)}, MRNUMBER = {2424928}, MRREVIEWER = {Sven-\AA ke Gustafson}, DOI = {10.1007/s10589-007-9095-z}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10589-007-9095-z}, } @article {MR2257203, AUTHOR = {Audet, Charles and Orban, Dominique}, TITLE = {Finding optimal algorithmic parameters using derivative-free optimization}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {17}, YEAR = {2006}, NUMBER = {3}, PAGES = {642--664}, ISSN = {1052-6234}, MRCLASS = {90C56 (90C31)}, MRNUMBER = {2257203}, MRREVIEWER = {Warren L. Hare}, DOI = {10.1137/040620886}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/040620886}, } @article {MR2221821, AUTHOR = {Waltz, R.A. and Morales, J.L. and Nocedal, J. and Orban, D.}, TITLE = {An interior algorithm for nonlinear optimization that combines line search and trust region steps}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {107}, YEAR = {2006}, NUMBER = {3, Ser. A}, PAGES = {391--408}, ISSN = {0025-5610}, MRCLASS = {90C55 (90C30 90C51)}, MRNUMBER = {2221821}, MRREVIEWER = {Warren L. Hare}, DOI = {10.1007/s10107-004-0560-5}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10107-004-0560-5}, } @article {MR2177962, AUTHOR = {Gould, Nicholas I. M. and Orban, Dominique and Sartenaer, Annick and Toint, Phillipe L.}, TITLE = {Sensitivity of trust-region algorithms to their parameters}, JOURNAL = {4OR}, FJOURNAL = {4OR. A Quarterly Journal of Operations Research}, VOLUME = {3}, YEAR = {2005}, NUMBER = {3}, PAGES = {227--241}, ISSN = {1619-4500}, MRCLASS = {90C55 (90C30)}, MRNUMBER = {2177962}, MRREVIEWER = {Alberto Seeger}, DOI = {10.1007/s10288-005-0065-y}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10288-005-0065-y}, } @article {MR2168345, AUTHOR = {Gould, N. and Orban, D. and Toint, P.}, TITLE = {Numerical methods for large-scale nonlinear optimization}, JOURNAL = {Acta Numer.}, FJOURNAL = {Acta Numerica}, VOLUME = {14}, YEAR = {2005}, PAGES = {299--361}, ISSN = {0962-4929}, MRCLASS = {90C30 (65K10 90-02)}, MRNUMBER = {2168345}, MRREVIEWER = {Claudia A. Sagastiz\'{a}bal}, DOI = {10.1017/S0962492904000248}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1017/S0962492904000248}, } @article {MR2077337, AUTHOR = {Gould, Nicholas I. M. and Orban, Dominique and Toint, Philippe L.}, TITLE = {G{ALAHAD}, a library of thread-safe {F}ortran 90 packages for large-scale nonlinear optimization}, JOURNAL = {ACM Trans. Math. Software}, FJOURNAL = {Association for Computing Machinery. Transactions on Mathematical Software}, VOLUME = {29}, YEAR = {2003}, NUMBER = {4}, PAGES = {353--372}, ISSN = {0098-3500}, MRCLASS = {90-04 (90C06 90C20)}, MRNUMBER = {2077337}, DOI = {10.1145/962437.962438}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1145/962437.962438}, } @article {MR1926660, AUTHOR = {Wright, Stephen J. and Orban, Dominique}, TITLE = {Properties of the log-barrier function on degenerate nonlinear programs}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {27}, YEAR = {2002}, NUMBER = {3}, PAGES = {585--613}, ISSN = {0364-765X}, MRCLASS = {90C30 (90C31)}, MRNUMBER = {1926660}, MRREVIEWER = {Vladimir I. Venets}, DOI = {10.1287/moor.27.3.585.312}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1287/moor.27.3.585.312}, } @article {MR1905763, AUTHOR = {Gould, Nicholas I. M. and Orban, Dominique and Sartenaer, Annick and Toint, Philippe L.}, TITLE = {Componentwise fast convergence in the solution of full-rank systems of nonlinear equations}, NOTE = {ISMP 2000, Part 2 (Atlanta, GA)}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {92}, YEAR = {2002}, NUMBER = {3, Ser. B}, PAGES = {481--508}, ISSN = {0025-5610}, MRCLASS = {65H10 (65H20)}, MRNUMBER = {1905763}, DOI = {10.1007/s101070100287}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s101070100287}, } @article {MR1855217, AUTHOR = {Gould, Nicholas I. M. and Orban, Dominique and Sartenaer, Annick and Toint, Philippe L.}, TITLE = {Superlinear convergence of primal-dual interior point algorithms for nonlinear programming}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {11}, YEAR = {2001}, NUMBER = {4}, PAGES = {974--1002}, ISSN = {1052-6234}, MRCLASS = {90C51 (65K05 90C30)}, MRNUMBER = {1855217}, DOI = {10.1137/S1052623400370515}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/S1052623400370515}, } @article {MR1763849, AUTHOR = {Conn, Andrew R. and Gould, Nicholas I. M. and Orban, Dominique and Toint, Philippe L.}, TITLE = {A primal-dual trust-region algorithm for non-convex nonlinear programming}, NOTE = {Studies in algorithmic optimization}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {87}, YEAR = {2000}, NUMBER = {2, Ser. B}, PAGES = {215--249}, ISSN = {0025-5610}, MRCLASS = {90C51 (90C30)}, MRNUMBER = {1763849}, MRREVIEWER = {Joaqu\'{\i}m J. J\'{u}dice}, DOI = {10.1007/s101070050112}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s101070050112}, } @article {MR2299241, AUTHOR = {OKUN, O. and PRIISALU, H.}, TITLE = {Fast nonnegative matrix factorization and its application for protein fold recognition}, JOURNAL = {EURASIP J. Appl. Signal Process.}, FJOURNAL = {EURASIP Journal on Applied Signal Processing}, YEAR = {2006}, NUMBER = {Advanced signal processing techniques for bioinformatics}, PAGES = {Art. ID 71817, 8}, ISSN = {1110-8657}, MRCLASS = {15A48 (92C40 92D10)}, MRNUMBER = {MR2299241 (2008b:15082)}, } @article {MR2242729, AUTHOR = {FINESSO, L. and SPREIJ, P.}, TITLE = {Nonnegative matrix factorization and {$I$}-divergence alternating minimization}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {416}, YEAR = {2006}, NUMBER = {2-3}, PAGES = {270--287}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A22 (15A48 65F30)}, MRNUMBER = {MR2242729 (2007f:15011)}, MRREVIEWER = {Raf Vandebril}, } @article {MR2232918, AUTHOR = {PAUCA, V.P. and PIPER, J. and PLEMMONS, R.J.}, TITLE = {Nonnegative matrix factorization for spectral data analysis}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {416}, YEAR = {2006}, NUMBER = {1}, PAGES = {29--47}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A23 (65F30)}, MRNUMBER = {MR2232918 (2007g:15013)}, MRREVIEWER = {Johannes D. Botha}, } @article {plemmons08, AUTHOR = {ZHANG, Q. and WANG, R. and PLEMMONS, R.J. and PAUCA, V.P.}, TITLE = {Tensor Methods for Hyperspectral Data Analysis: A Space Object Material Identification Study}, JOURNAL = {J. Optical Soc. Amer. A}, VOLUME = {25}, YEAR = {2008}, NUMBER = {12}, PAGES = {3001--3012} } @article {MR2225355, AUTHOR = {Liu, W. and ZHENG, N. and YOU, Q.}, TITLE = {Nonnegative matrix factorization and its applications in pattern recognition}, JOURNAL = {Chinese Sci. Bull.}, FJOURNAL = {Chinese Science Bulletin}, VOLUME = {51}, YEAR = {2006}, NUMBER = {1}, PAGES = {7--18}, ISSN = {1001-6538}, MRCLASS = {68T10 (15A48 94A08)}, MRNUMBER = {MR2225355}, } @ARTICLE {Ole:80, author = "D.P. O'Leary", title = "The block conjugate gradient algorithm and related methods", journal = laa, year = "1980", volume = "29", pages = "293-322"} @article{olea:90, author = "D.P. O'Leary", year = "1990", title = "On Bounds For Scaled Projections and Pseudo-Inverses", journal = laa, volume = "132", pages = "115--117", kwds = "la, projection, ginv" } @article{O'Leary:2000:SLA:363882.363929, author = {O'Leary, D.P.}, title = {Symbiosis between linear algebra and optimization}, journal = {J. Comput. Appl. Math.}, volume = {123}, issue = {1-2}, month = {November}, year = {2000}, issn = {0377-0427}, pages = {447--465}, numpages = {19}, url = {http://dl.acm.org/citation.cfm?id=363882.363929}, doi = {10.1016/S0377-0427(00)00408-8}, acmid = {363929}, publisher = {Elsevier Science Publishers B. V.}, address = {Amsterdam, The Netherlands, The Netherlands}, } [download] @article{1083869, author = "D.P. O'Leary", title = {Solving Sparse Linear Systems: Taking the Direct Approach}, journal = {Computing in Science and Engg.}, volume = {7}, number = {5}, year = {2005}, issn = {1521-9615}, pages = {62--70}, doi = {http://dx.doi.org/10.1109/MCSE.2005.101}, publisher = {IEEE Educational Activities Department}, address = {Piscataway, NJ, USA}, } @article{ouel:81, AUTHOR = {Ouellette, D.V.}, TITLE = {Schur complements and statistics}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {36}, YEAR = {1981}, PAGES = {187--295}, ISSN = {0024-3795}, MRCLASS = {15A09 (62J05)}, MRNUMBER = {604341}, MRREVIEWER = {Winston T. Lin}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1016/0024-3795(81)90232-9}, } @ARTICLE {OlNe:75, author = "D.M. OLSSON and L.S. NELSON", title = "Nelder-{M}ead simplex procedure for function minimization", journal = "Technometrics", year = "1975", volume = "17", pages = "45"} @ARTICLE {Oren:73, author = "S.S. OREN", title = "Self-scaling variable metric algorithms without line search for unconstrained minimization", journal = "Math. Comp.", year = "1973", volume = "27", pages = "873-885"} @ARTICLE {Oren:74, author = "S.S. OREN", title = "On the selection of parameters in self-scaling variable metric algorithms", journal = "Math. Prog.", year = "1974", volume = "7", pages = "351-367"} @ARTICLE {OreLuen:74, author = "S.S. OREN and D.G. Luenberger", title = "Self-scaling variable metric {(SSVM)} algorithms, part {I}. {C}riteria and sufficient conditions for scaling a class of algorithms", journal = "Manage. Sci.", year = "1974", volume = "20", pages = "845-862"} @ARTICLE {OreSped:76, author = "S.S. OREN and E. SPEDICATO", title = "Optimal conditioning of self-scaling variable metric algorithms", journal = "Math. Prog.", year = "1976", volume = "10", pages = "70-90"} @article{Rheinboldt76, jstor_articletype = {primary_article}, title = {On Measures of Ill-Conditioning for Nonlinear Equations}, author = {Rheinboldt, W.C.}, journal = {Mathematics of Computation}, jstor_issuetitle = {}, volume = {30}, number = {133}, jstor_formatteddate = {Jan., 1976}, pages = {104--111}, url = {http://www.jstor.org/stable/2005433}, ISSN = {00255718}, abstract = {Let $x^\ast$ be a solution of the nonlinear equation $Fx = b$ on a normed linear space and $y^\ast$ that of a perturbed equation $Gx = c$. Estimates for the relativized error between $x^\ast$ and $y^\ast$ are derived which extend a known estimate for the corresponding matrix case. The condition number of $F$ depends now also on the domain, and special considerations are needed to determine the existence of the solution of the perturbed equation. For differentiable $F$, when the domain shrinks to a point, the condition number of $F$ is shown to reduce to that of the derivative at that point.}, language = {}, year = {1976}, publisher = {American Mathematical Society}, copyright = {Copyright ? 1976 American Mathematical Society}, } @BOOK {OrRhe:70, author = "J.M. ORTEGA and W.C. RHEINBOLDT", title = "Iterative Solution of Nonlinear Equations in Several Variables", publisher = "Academic Press", year = "1970", address = "New York, NY"} @ARTICLE {Osbor:76, author = "M.R. OSBORNE", title = "Nonlinear least squares - the {L}evenberg algorithm revisited", journal = "J. Austral. Math. Soc. Ser. B", year = "1976", volume = "19", pages = "343-357"} @TECHREPORT {OsbSun:89, author = "M.R. OSBORNE and L.P. SUN", title = "A new approach to the symmetric rank-one updating algorithm", institution = "Australian National University", year = "1989"} @ARTICLE {OsWat:69, author = "M.R. OSBORNE and G.A. WATSON", title = "An algorithm for minimax approximation in the nonlinear case", journal = "Comput. J.", year = "1969", volume = "12", pages = "64-69"} @INCOLLECTION {OsWat:78, author = "M.R. OSBORNE and G.A. WATSON", title = "Nonlinear approximation problems in vector norms", booktitle = "Lectures Notes in Mathematics \#630, Numerical Analysis, Dundee 1977", publisher = "Springer-Verlag", year = "1978", editor = "G.A. Watson", address = "Berlin"} @ARTICLE {Ov:88, author = "M.L. Overton", title = "On minimizing the maximum eigenvalue of a symmetric matrix", journal = simax, year = "1988", volume = "9", pages = "256-268"} @ARTICLE {Ov:92, author = "M.L. Overton", TITLE = {Large-scale optimization of eigenvalues}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {2}, YEAR = {1992}, NUMBER = {1}, PAGES = {88--120}, ISSN = {1052-6234}, CODEN = {SJOPE8}, MRCLASS = {49J52 (49R05 65F15 65K10)}, MRNUMBER = {MR1147885 (92k:49030)}, MRREVIEWER = {Henry Wolkowicz}, } @ARTICLE {Oz:92, author = "V.M. OZERNOY", title = "Choosing the ``best'' multiple criteria decision-making method", journal = "INFOR", year = "1992", volume = "30", pages = "159-171"} %PPPPPPPPPPPPP @article {MR1453318, AUTHOR = {PAN, V.Y.}, TITLE = {Solving a polynomial equation: some history and recent progress}, JOURNAL = {SIAM Rev.}, FJOURNAL = {SIAM Review. A Publication of the Society for Industrial and Applied Mathematics}, VOLUME = {39}, YEAR = {1997}, NUMBER = {2}, PAGES = {187--220}, ISSN = {0036-1445}, CODEN = {SIREAD}, MRCLASS = {65H05 (01A99 65-03)}, MRNUMBER = {MR1453318 (99b:65066)}, MRREVIEWER = {T. L. Freeman}, } @incollection {MR1646951, AUTHOR = {Lewis, A.S. and Pang, J-S.}, TITLE = {Error bounds for convex inequality systems}, BOOKTITLE = {Generalized convexity, generalized monotonicity: recent results (Luminy, 1996)}, SERIES = {Nonconvex Optim. Appl.}, VOLUME = {27}, PAGES = {75--110}, PUBLISHER = {Kluwer Acad. Publ.}, ADDRESS = {Dordrecht}, YEAR = {1998}, MRCLASS = {90C31 (90C25)}, MRNUMBER = {MR1646951 (2000d:90082)}, MRREVIEWER = {D. Klatte}, } @article {MR1464772, AUTHOR = {Pang, J.}, TITLE = {Error bounds in mathematical programming}, NOTE = {Lectures on mathematical programming (ismp97) (Lausanne, 1997)}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {79}, YEAR = {1997}, NUMBER = {1-3, Ser. B}, PAGES = {299--332}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C31 (49K40 49Mxx 65K10)}, MRNUMBER = {MR1464772 (98j:90075)}, MRREVIEWER = {D. Klatte}, } @article {MR83f:65048, AUTHOR = {Paige, C.C. and Saunders, M.A.}, TITLE = {L{S}{Q}{R}: an algorithm for sparse linear equations and sparse least squares}, JOURNAL = {ACM Trans. Math. Software}, FJOURNAL = {Association for Computing Machinery. Transactions on Mathematical Software}, VOLUME = {8}, YEAR = {1982}, NUMBER = {1}, PAGES = {43--71}, ISSN = {0098-3500}, CODEN = {ACMSCU}, MRCLASS = {65F10 (65F20)}, MRNUMBER = {83f:65048}, } @article {FongSaunders:10, AUTHOR = {D.C.-L. Fong and M.A. Saunders}, TITLE = {L{SMR}: an iterative algorithm for sparse least-squares problems}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {33}, YEAR = {2011}, NUMBER = {5}, PAGES = {2950--2971}, ISSN = {1064-8275}, CODEN = {SJOCE3}, MRCLASS = {65F10 (15A06 65F20 65F35)}, MRNUMBER = {2861656 (2012m:65094)}, MRREVIEWER = {A. Bultheel}, DOI = {10.1137/10079687X}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/10079687X}, } @PHDTHESIS {Pant:84, author = "J.F.A. PANTOJA", title = "Algorithms for constrained optimization problems", school = "London University", year = "1984"} @article {MR87i:90242, AUTHOR = {PAPPALARDO, M.}, TITLE = {On the duality gap in nonconvex optimization}, JOURNAL = mor, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {11}, YEAR = {1986}, NUMBER = {1}, PAGES = {30--35}, ISSN = {0364-765X}, } @techreport {PapaMarkov, AUTHOR = {D.A. Papa and I.L. Markov}, title = "Hypergraph partitioning and clustering", institution = "University of Michigan", address = "EECS Dept., Ann Arbor, MI", URL="www.cse.umich.edu/~imarkov/pubs/book/part_survey.pdf", year = ""} @article {MR1965800, AUTHOR = {PAPARRIZOS, K. and SAMARAS, N. and STEPHANIDES, G.}, TITLE = {An efficient simplex type algorithm for sparse and dense linear programs}, JOURNAL = {European J. Oper. Res.}, FJOURNAL = {European Journal of Operational Research}, VOLUME = {148}, YEAR = {2003}, NUMBER = {2}, PAGES = {323--334}, ISSN = {0377-2217}, CODEN = {EJORDT}, MRCLASS = {90C05 (90C08)}, MRNUMBER = {MR1965800 (2004b:90064)}, } @TECHREPORT {Pard:95, author = "P.M. Pardalos", title = "Continuous approaches to discrete optimization problems", institution = "University of Florida", year = "1995", keywords = "qap, sdp, qp", address = "Gainsville, Fa"} @TECHREPORT {PaRaReLi:94, author = "P.M. Pardalos and K.G. RAMAKRISHNAN and M.G.C. RESENDE and Y. LI", title = "Implementation of a variance reduction based lower bound in a branch and bound algorithm for the quadratic assignment problem", institution = "University of Florida", year = "1994", keywords = "qap", address = "Gainsville, Fa"} @ARTICLE {Pard:91, AUTHOR = {Pardalos, P.M. and Vavasis, S.A.}, TITLE = {Quadratic programming with one negative eigenvalue is {N}{P}-hard}, JOURNAL = {J. Global Optim.}, FJOURNAL = {Journal of Global Optimization. An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering}, VOLUME = {1}, YEAR = {1991}, NUMBER = {1}, PAGES = {15--22}, ISSN = {0925-5001}, CODEN = {JGOPEO}, MRCLASS = {90C20 (68Q25)}, MRNUMBER = {94k:90060}, } @ARTICLE {Pard:90, author = "P.M. Pardalos and G.P. RODGERS", title = "Computational aspects of a branch and bound algorithm for quadratic zero-one programming", journal = "Computing", year = "1990", volume = "45", pages = "131-144"} @book{PardRos87, author = "Pardalos, P.M. and ROSEN, J.B.", title = "Constrained global optimization: Algorithms and applications", series = "Lecture Notes in Computer Science", volume= "268", publisher = "Springer-Verlag", address = "Berlin", year = "1987" } @article{PardRos86, author = "Pardalos, P.M. and ROSEN, J.B.", title = "Methods for global concave minimization: A bibliographic survey", journal = "Siam Review", year = 1986, volume = "28", pages = "367--379" } @book {PardShallXue, TITLE = {Global minimization of nonconvex energy functions: molecular conformation and protein folding}, EDITOR = {Pardalos, P.M. and SHALLOWAY, D. and XUE, G.}, NOTE = {Papers from the DIMACS Workshop held as part of the DIMACS Special Year on Mathematical Support for Molecular Biology at Rutgers University, New Brunswick, New Jersey, March 20--21, 1995}, SERIES = {DIMACS Series in Discrete Mathematics and Theoretical Computer Science}, VOLUME = {23}, PUBLISHER = {American Mathematical Society}, ADDRESS = {Providence, RI}, YEAR = {1996}, PAGES = {xiv+271}, ISBN = {0-8218-0471-5}, } @article{PardVav91, author = "Pardalos, P.M. and Vavasis, S.", title = "Quadratic programming with one negative eigenvalue is {NP}-hard", journal = "J. Global Optimization", year = 1991, volume = "1", pages = "15--22" } @TECHREPORT {Park:85, author = "T.A. PARKS", title = "Reducible nonlinear programming problems", institution = "Department of Mathematical Sciences, Rice University", year = "1985", number = "TR 85-8", address = "Houston, TX"} @book {Pa, AUTHOR = {Parlett, B.N.}, TITLE = {The symmetric eigenvalue problem}, NOTE = {Corrected reprint of the 1980 original}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {1998}, PAGES = {xxiv+398}, ISBN = {0-89871-402-8}, MRCLASS = {65F15 (15A18)}, MRNUMBER = {99c:65072}, MRREVR = {F. Szidarovszky}, } @article {MR95b:01014, AUTHOR = {PARKS, P. C.}, TITLE = {A. {M}. {L}yapunov's stability theory---100 years on}, JOURNAL = {IMA J. Math. Control Inform.}, FJOURNAL = {IMA Journal of Mathematical Control and Information}, VOLUME = {9}, YEAR = {1992}, NUMBER = {4}, PAGES = {275--303}, ISSN = {0265-0754}, MRCLASS = {01A55 (01A70 34-03 34D20 93-03)}, MRNUMBER = {95b:01014}, } @ARTICLE {PaNa:88, author = "R. PATIL and P.E. NAGARAJ and P. BHATTACHARYYA and A. PAULRAJ", title = "Tactical Air Route Planning", journal = "J. Instn. Electronics \& Telecom. Engrs.", year = "1988", volume = "34", pages = "265-268"} @article {PengYuan:95, author = "J. Peng and Y. Yuan", TITLE = {Optimality conditions for the minimization of a quadratic with two quadratic constraints}, JOURNAL = siopt, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {7}, YEAR = {1997}, NUMBER = {3}, PAGES = {579--594}, ISSN = {1052-6234}, CODEN = {SJOPE8}, } @book {MR89f:90080, AUTHOR = {Peressini, A.L. and Sullivan, F.E. and Uhl, Jr., J.J.}, TITLE = {The Mathematics of Nonlinear Programming}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1988}, PAGES = {x+273}, ISBN = {0-387-96614-5}, MRCLASS = {90Cxx (46N05)}, MRNUMBER = {89f:90080}, MRREVIEWER = {Ferenc Forg{\'o}}, } @book {MR37:3315, AUTHOR = {PERESSINI, A.L.}, TITLE = {Ordered Topological Vector Spaces}, PUBLISHER = {Harper \& Row Publishers}, ADDRESS = {New York}, YEAR = {1967}, PAGES = {x+228}, } @article {MR0325154, AUTHOR = {Peterson, D.W.}, TITLE = {A review of constraint qualifications in finite-dimensional spaces}, JOURNAL = {SIAM Rev.}, FJOURNAL = {SIAM Review}, VOLUME = {15}, YEAR = {1973}, PAGES = {639--654}, ISSN = {0036-1445}, MRCLASS = {90C30}, MRNUMBER = {0325154}, MRREVIEWER = {Constantin Virsan}, DOI = {10.1137/1015075}, URL = {http://dx.doi.org/10.1137/1015075}, } @ARTICLE {PeWil:70, author = "G. PETERS and J. H. WILKINSON", title = "The least squares problem and pseudoinverses", journal = "Comput. J.", year = "1970", volume = "13", pages = "309-316"} @article {MR35:7141, AUTHOR = {PETRYSHYN, W.V.}, TITLE = {On a class of ${K}-{\rm p}.{\rm d}.$ and non-${K}-{\rm p}.{\rm d}.$\ operators and operator equations}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {10}, YEAR = {1965}, PAGES = {1--24}, MRCLASS = {47.10}, MRNUMBER = {35 #7141}, MRREVR = {D. G. de Figueiredo}, } @article {MR2003d:47087, AUTHOR = {BAI, C.-Z.}, TITLE = {Approximation of a solution for a {$K$}-positive definite operator equation in real separable {B}anach spaces}, JOURNAL = {Math. Appl.}, FJOURNAL = {Mathematica Applicata. Yingyong Shuxue}, VOLUME = {15}, YEAR = {2002}, NUMBER = {2}, PAGES = {117--120}, ISSN = {1001-9847}, MRCLASS = {47J25 (47H10)}, MRNUMBER = {2003d:47087}, MRREVIEWER = {Charles Ejike Chidume}, } @mastersthesis {spg, author = "PEREZ-GARCIA, S.", title=" Alternative Iterative Primal-Dual Interior-Point Algorithms for Linear Programming", school = "Simon Bolivar University, Center for Statistics and Mathematical Software (CESMa)", number="Report 2003-05", address="Venezuela", URL="http://www.cesma.usb.ve", year="2003", } @article {MR834098, AUTHOR = {PEROLD, A.F.}, TITLE = {Large-scale portfolio optimization}, JOURNAL = {Management Sci.}, FJOURNAL = {Management Science. Journal of the Institute of Management Science. Application and Theory Series}, VOLUME = {30}, YEAR = {1984}, NUMBER = {10}, PAGES = {1143--1160}, ISSN = {0025-1909}, CODEN = {MSCIAM}, MRCLASS = {90A09}, MRNUMBER = {MR834098 (87e:90012)}, } @ARTICLE {Ph:93, author = "H.X. PHU", title = "$\gamma$-subdifferential and $\gamma$-convexity of functions on the real line", journal = "Appl. Math. Optim.", year = "1993", volume = "27", pages = "145-160"} @ARTICLE {PhuScha:78a, author = "K.H. PHUA and D.F. SHANNO", title = "Matrix conditioning and nonlinear optimization", journal = "Math. Prog.", year = "1984", volume = "14", pages = "145-160"} @ARTICLE {PhuScha:78b, author = "K.H. PHUA and D.F. SHANNO", title = "Numerical comparison of several variable metric algorithms", journal = "J. Optim. Theory Appl.", year = "1978", volume = "25", pages = "507-518"} @ARTICLE {Piet:69, author = "T. PIETRZKOWSKI", title = "An exact potential method for constrained maxima", journal = "SIAM J. Numer. Anal.", year = "1969", volume = "6", pages = "299-304"} @techreport {Phan:14, AUTHOR = {H.M. Phan}, title = "Linear Convergence of the {D}ouglas-{R}achford Method for Two Closed Sets", institution = "University of British Columbia", address = "Vancouver, B.C.", year = "2014"} @techreport{Picciallietal:21, doi = {10.48550/ARXIV.2104.11542}, url = {https://arxiv.org/abs/2104.11542}, author = {Piccialli, V. and Sudoso, A.M. and Wiegele, A.}, keywords = {Optimization and Control (math.OC), FOS: Mathematics, FOS: Mathematics}, title = {{SOS-SDP}: an Exact Solver for Minimum Sum-of-Squares Clustering}, publisher = {arXiv}, year = {2021}, copyright = {arXiv.org perpetual, non-exclusive license} } @article{Piccialli_2022, doi = {10.1287/ijoc.2022.1166}, url = {https://doi.org/10.1287%2Fijoc.2022.1166}, year = 2022, month = {mar}, publisher = {Institute for Operations Research and the Management Sciences ({INFORMS})}, author = {V. Piccialli and A.M. Sudoso and A. Wiegele}, title = {{SOS}-{SDP}: An Exact Solver for Minimum Sum-of-Squares Clustering}, journal = {{INFORMS} Journal on Computing} } @ARTICLE{PolanciWainwright:15, AUTHOR = "Pilanci, M. and Wainwright, M.J.", TITLE = "Randomized sketches of convex programs with sharp guarantees", JOURNAL = "IEEE Trans. Infor. Theory", VOLUME = "61", number = "9", YEAR = "2015", PAGES = "5096-5115"} @techreport {PinarMezaetal:08, AUTHOR = {A. PINAR and J. MEZA and V. DONDE and B. LESIEUTRE}, title = "Optimization strategies for the vulnerability analysis of the electric power grid", institution = "High Performance Computing Research Department", address = "Lawrence Berkeley National Laboratory", year = "2008"} @ARTICLE {PiniGambolati:90, author = "G. Pini and G. Gamboniati", title = "Is a simple diagonal scaling the best preconditioner for conjugate gradients on supercomputers?", journal = "Advances in Water Resources", year = "1990", volume = "13", number = "3", pages = "147--153"} @article {MR2954482, AUTHOR = {Pinkus, A.}, TITLE = {On best rank {$n$} matrix approximations}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {437}, YEAR = {2012}, NUMBER = {9}, PAGES = {2179--2199}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A60}, MRNUMBER = {2954482}, DOI = {10.1016/j.laa.2012.05.016}, URL = {http://dx.doi.org/10.1016/j.laa.2012.05.016}, } @ARTICLE {PISINGERZIMMERMANN:07, author = "G. PISINGER and A. ZIMMERMANN", title = "Linear least squares problems with data over incomplete grids", journal = "BIT", year = "2007", volume = "47", number = "4", pages = "809-824"} @ARTICLE {Poly:71, author = "B.T. POLYAK", title = "The convergence rate of the penalty function method", journal = "Zh. vychisl. Mat. mat. fiz.", year = "1971", volume = "11", pages = "1-12"} @article{MR99i:90069, AUTHOR = {POLYAK, B.T.}, TITLE = {Convexity of quadratic transformations and its use in control and optimization}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {99}, YEAR = {1998}, NUMBER = {3}, PAGES = {553--583}, ISSN = {0022-3239}, CODEN = {JOTABN}, MRCLASS = {90C20 (90-02 93-02)}, MRNUMBER = {99i:90069}, MRREVIEWER = {T. Zolezzi}, } @TECHREPORT {pr1:91, author = "S. POLJAK and F. Rendl", title = "Computing the max--cut by eigenvalues", institution = "Institut fur Diskrete Mathematik, Universitat Bonn", year = "1991", number = "91735--OR"} @article {PoRe:94, author = "S. POLJAK and F. Rendl", title = "Node and edge relaxations for the max-cut problem", journal = comp, year = "1994", volume = "52", pages = "123-127"} @article {pr2:92, author = "S. POLJAK and F. Rendl", title = "Nonpolyhedral relaxations of graph-bisection problems", journal = siopt, volume = "5", number ="3", year = "1995", note = "467-487"} @TECHREPORT {PorResVeigJud:94, author = "L. PORTUGAL and M.G.C. RESENDE and G. VEIGA and J. JUDICE", title = "A truncated primal-infeasible dual-fesible network interior point method", institution = "Universidade de Coimbra", keywords = "interior point, primal-dual", year = "1994", address = "Coimbra, Portugal"} @TECHREPORT {PorResVeigJudtechrep:01, author = "J.J. JUDICE and J. PATRICIO and L.F. PORTUGAL and M.G.C. RESENDE and G. VEIGA", title = "A study of preconditioners for network interior point methods", institution = "Universidade de Coimbra", keywords = "interior point, primal-dual", year = "2001", address = "Coimbra, Portugal"} @article {PorResVeigJud:01, AUTHOR = {J{\'U}DICE, J.J. and PATRICIO, J. and PORTUGAL, L.F. and RESENDE, M.G.C. and VEIGA, G.}, TITLE = {A study of preconditioners for network interior point methods}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {24}, YEAR = {2003}, NUMBER = {1}, PAGES = {5--35}, ISSN = {0926-6003}, CODEN = {CPPPEF}, MRCLASS = {90C51 (65F10 90B10)}, MRNUMBER = {2004a:90118}, MRREVIEWER = {Volker Kaibel}, } @TECHREPORT {Pot:83, author = "T. POTEMPA", title = "Quasi-{N}ewton methods and {G}alerkin procedures for nonlinear elliptic boundary value problems", institution = "Department of Mathematical Sciences, Rice University", year = "1983", number = "TR83-29", address = "Houston, TX"} @article {MR0255025, AUTHOR = {Polak, E. and Ribi\`ere, G.}, TITLE = {Note sur la convergence de m\'ethodes de directions conjugu\'ees}, JOURNAL = {Rev. Fran\c{c}aise Informat. Recherche Op\'erationnelle}, VOLUME = {3}, YEAR = {1969}, NUMBER = {16}, PAGES = {35--43}, MRCLASS = {65.30}, MRNUMBER = {0255025}, MRREVIEWER = {P. J. Laurent}, } @article {MR1373072, AUTHOR = {Hasan, M.A. and Poore, A.B.}, TITLE = {Bifurcation analysis for singularities on a tangent space for quadratic penalty-barrier and multipliers methods for solving constrained optimization problems. {I}}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {197}, YEAR = {1996}, NUMBER = {3}, PAGES = {658--678}, ISSN = {0022-247X}, CODEN = {JMANAK}, MRCLASS = {90C30 (58E17)}, MRNUMBER = {1373072 (97a:90075)}, MRREVIEWER = {Alexander Shapiro}, DOI = {10.1006/jmaa.1996.0045}, URL = {http://dx.doi.org/10.1006/jmaa.1996.0045}, } @article {MR1054845, AUTHOR = {Tiahrt, C. A. and Poore, A. B.}, TITLE = {A bifurcation analysis of the nonlinear parametric programming problem}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {47}, YEAR = {1990}, NUMBER = {1, (Ser. A)}, PAGES = {117--141}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C31 (58E07)}, MRNUMBER = {1054845 (91h:90109)}, MRREVIEWER = {Andreas Griewank}, DOI = {10.1007/BF01580856}, URL = {http://dx.doi.org/10.1007/BF01580856}, } @incollection {MR1046861, AUTHOR = {Tiahrt, C. A. and Poore, A. B.}, TITLE = {Bifurcation and persistence of minima in nonlinear parametric programming}, BOOKTITLE = {Computation and control ({B}ozeman, {MT}, 1988)}, SERIES = {Progr. Systems Control Theory}, VOLUME = {1}, PAGES = {343--353}, PUBLISHER = {Birkh\"auser Boston}, ADDRESS = {Boston, MA}, YEAR = {1989}, MRCLASS = {90C30}, MRNUMBER = {1046861 (91e:90115)}, MRREVIEWER = {John J. Dinkel}, } @article {MR916004, AUTHOR = {Poore, A. B. and Tiahrt, C. A.}, TITLE = {Bifurcation problems in nonlinear parametric programming}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {39}, YEAR = {1987}, NUMBER = {2}, PAGES = {189--205}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C31 (58E05)}, MRNUMBER = {916004 (89a:90146)}, MRREVIEWER = {Hubertus Th. Jongen}, DOI = {10.1007/BF02592952}, URL = {http://dx.doi.org/10.1007/BF02592952}, } @incollection {MR605327, AUTHOR = {Heinemann, R. F. and Poore, A. B.}, TITLE = {Hopf bifurcation computations for distributed parameter systems}, BOOKTITLE = {Transactions of the {T}wenty-{S}ixth {C}onference of {A}rmy {M}athematicians ({H}anover, {N}.{H}., 1980)}, SERIES = {ARO Rep. 81}, VOLUME = {1}, PAGES = {313--325}, PUBLISHER = {U. S. Army Res. Office}, ADDRESS = {Research Triangle Park, N.C.}, YEAR = {1981}, MRCLASS = {35B32 (58E07 65H10 80A30 92A09)}, MRNUMBER = {605327 (82a:35012)}, } @article {MR0421509, AUTHOR = {Poore, A. B.}, TITLE = {On the dynamical behavior of the two-temperature feedback nuclear reactor model}, JOURNAL = {SIAM J. Appl. Math.}, FJOURNAL = {SIAM Journal on Applied Mathematics}, VOLUME = {30}, YEAR = {1976}, NUMBER = {4}, PAGES = {675--686}, ISSN = {0036-1399}, MRCLASS = {82.34 (34C99)}, MRNUMBER = {0421509 (54 \#9508)}, MRREVIEWER = {J. O. C. Ezeilo}, } @incollection {MR1441583, AUTHOR = {Pothen, Alex}, TITLE = {Graph partitioning algorithms with applications to scientific computing}, BOOKTITLE = {Parallel numerical algorithms ({H}ampton, {VA}, 1994)}, SERIES = {ICASE/LaRC Interdiscip. Ser. Sci. Eng.}, VOLUME = {4}, PAGES = {323--368}, PUBLISHER = {Kluwer Acad. Publ., Dordrecht}, YEAR = {1997}, MRCLASS = {65Y05 (05C85)}, MRNUMBER = {1441583}, DOI = {10.1007/978-94-011-5412-3_12}, URL = {http://dx.doi.org/10.1007/978-94-011-5412-3_12}, } @article {MR1054210, AUTHOR = {Pothen, A. and Simon, H.D. and Liou, K.-P.}, TITLE = {Partitioning sparse matrices with eigenvectors of graphs}, NOTE = {Sparse matrices (Gleneden Beach, OR, 1989)}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {11}, YEAR = {1990}, NUMBER = {3}, PAGES = {430--452}, ISSN = {0895-4798}, CODEN = {SJMAEL}, MRCLASS = {65F50 (05C50 05C85 68R10)}, MRNUMBER = {1054210 (91h:65064)}, DOI = {10.1137/0611030}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/0611030}, } @incollection {MR865176, AUTHOR = {Ruske, A.}, TITLE = {Numerical treatment of bifurcation problems in case of one-parametric nonlinear optimization problems}, BOOKTITLE = {Parametric optimization and ill-posed problems in mathematical optimization}, SERIES = {Seminarberichte}, VOLUME = {81}, PAGES = {109--129}, PUBLISHER = {Humboldt Univ. Berlin}, YEAR = {1986}, MRCLASS = {90C31 (65K05 90C30)}, MRNUMBER = {MR865176 (88a:90195)}, MRREVIEWER = {W. C. Rheinboldt}, } @book {MR865167, TITLE = {Parametric optimization and ill-posed problems in mathematical optimization}, SERIES = {Seminarberichte [Seminar Reports]}, VOLUME = {81}, EDITOR = {Er{\"e}min, I. I. and Guddat, J.}, PUBLISHER = {Humboldt Universit\"at Sektion Mathematik}, ADDRESS = {Berlin}, YEAR = {1986}, PAGES = {iv + 154}, MRCLASS = {90Cxx}, MRNUMBER = {MR865167 (87h:90125)}, } @ARTICLE {Pou:80, author = "B.H. Pourciau", title = "Modern multiplier methods", journal = "American Mathematical Monthly", year = "1980", volume = "87", number = "6", pages = "433-451"} @ARTICLE {Pow:64, author = "M.J.D. Powell", title = "An efficient method for finding the minimum of a function of several variables without calculating derivatives", journal = "Comp. J.", year = "1964", volume = "7", number = "2", pages = "155-162"} @INCOLLECTION {Pow:69, author = "M.J.D. Powell", title = "A method for nonlinear constraints in minimization problems", booktitle = "Optimization", publisher = "Academic Press", year = "1969", editor = "R. Fletcher", pages = "283-298", address = "New York, NY"} @INCOLLECTION {Pow:70a, author = "M.J.D. Powell", title = "A hybrid method for nonlinear equations", booktitle = "Numerical Methods for Nonlinear Algebraic Equations", publisher = "Gordon \& Breach", year = "1970", editor = "P. Rabinowitz", pages = "87-114", address = "London"} @INCOLLECTION {Pow:70b, author = "M.J.D. Powell", title = "A new algorithm for unconstrained optimization", booktitle = "Nonlinear Programming", publisher = "Academic Press", year = "1970", editor = "J.B. Rosen and O.L. Mangasarian and K. Ritter", pages = "31-65", address = "New York, NY"} @INCOLLECTION {Pow:70c, author = "M.J.D. Powell", title = "A {F}ortran subroutine for solving systems of nonlinear algebraic equations", booktitle = "Numerical Methods for Nonlinear Algebraic Equations", publisher = "Gordon \& Breach", year = "1970", editor = "P. Rabinowitz", pages = "115-149", address = "London"} @INCOLLECTION {Pow:75, author = "M.J.D. Powell", title = "Convergence properties of a class of minimization algorithms", booktitle = "Nonlinear Programming 2", publisher = "Academic Press", year = "1975", editor = "O.L. Mangasarian and R.R. Meyer and S.M. Robinson", pages = "1-27", address = "New York, NY"} @INCOLLECTION {Pow:76, author = "M.J.D. Powell", title = "Some global convergence properties of a variable metric algorithm without exact line searches", booktitle = "Nonlinear Programming", publisher = "AMS", year = "1976", editor = "R. Cottle and C. Lemke", pages = "53-72", address = "Providence, Rhode Island"} @INCOLLECTION {Pow:77a, author = "M.J.D. Powell", title = "A fast algorithm for nonlinearly constrained optimization calculations", booktitle = "Lecture notes in Mathematics, Numerical Analysis, Dundee 1977", publisher = "Springer-Verlag", year = "1978", editor = "G.A. Watson", pages = "144-157"} @TECHREPORT {Pow:77b, author = "M.J.D. Powell", title = "Constrained optimization by a variable metric method", institution = "University of Cambridge", year = "1977", type = "DAMTP Report", number = "1977/NA6", address = "Cambridge, England"} @INCOLLECTION {Pow:78, author = "M.J.D. Powell", title = "The convergence of variable metric methods for nonlinearly constrained optimization problems", booktitle = "Nonlinear Programming 3", publisher = "Academic Press", year = "1978", editor = "O.L. Mangasarian and R.R. Meyer and S.M. Robinson", pages = "27-63", address = "New York, NY"} @INCOLLECTION {Pow:81a, author = "M.J.D. Powell", title = "An upper triangular matrix method for quadratic programming", booktitle = "Nonlinear Programming 4", publisher = "Academic Press", year = "1981", pages = "1-24", address = "New York, NY"} @ARTICLE {Pow:81b, author = "M.J.D. Powell", title = "A note on quasi-{N}ewton formulae for sparse second derivative matrices", journal = "Math. Prog.", year = "1981", volume = "20", pages = "144-151"} @TECHREPORT {Pow:83, author = "M.J.D. Powell", title = "General algorithms for discrete nonlinear approximation calculations", institution = "Department of Applied Mathematics and Theoretical Physics, University of Cambridge", year = "1983", type = "DAMTP Report", number = "1983/NA2", address = "Cambridge, England"} @ARTICLE {Pow:84a, author = "M.J.D. Powell", title = "On the global convergence of trust region algorithms for unconstrained minimization", journal = "Math. Prog.", year = "1984", volume = "29", pages = "297-303"} @TECHREPORT {Pow:84b, author = "M.J.D. Powell", title = "The performance of two subroutines for constrained optimization on some difficult test problems", institution = "Department of Applied Mathematics and Theoretical Physics, University of Cambridge", year = "1984", type = "DAMTP Report", number = "1984/NA6", address = "Cambridge, England"} @ARTICLE {Pow:86, author = "M.J.D. Powell", title = "How bad are the {BFGS} and {DFP} methods when the objective function is quadratic", journal = "Math. Prog.", year = "1986", volume = "34", pages = "34-47"} @TECHREPORT {Pow:92, author = "M.J.D. Powell", title = "Overview of constrained optimization", institution = "Siam Conference on Optimization", year = "1992", type = "Introductory Address", address = "Chicago, Ill."} @incollection {Pow:97, AUTHOR = {Powell, M. J. D.}, TITLE = {The use of band matrices for second derivative approximations in trust region algorithms}, BOOKTITLE = {Advances in nonlinear programming (Beijing, 1996)}, PAGES = {3--28}, PUBLISHER = {Kluwer Acad. Publ.}, ADDRESS = {Dordrecht}, YEAR = {1998}, MRCLASS = {90C30 (65F30)}, MRNUMBER = {99g:90133}, MRREVR = {Yin Zhang}, } @techreport{powell2, AUTHOR = "M.J.D. Powell", TITLE = "Trust region calculations revisited", NOTE = "Presented at the 17th Biennial Conference on Numerical Analysis (Dundee)", TYPE = "Report", NUMBER = "DAMTP 1997/NA18", INSTITUTION = "Cambridge University", YEAR = "1997", } @ARTICLE {PowToi:79, author = "M.J.D. Powell and Ph.L. Toint ", title = "On the estimation of sparse {H}essian matrices", journal = "SIAM J. Numer. Anal.", year = "1979", volume = "16", pages = "1060-1074"} @TECHREPORT {PowYua:83, author = "M.J.D. Powell and Y. YUAN", title = "Conditions for superlinear convergence in $l_{1}$ and $l_{\infty}$ solutions of overdetermined nonlinear equations", institution = "Department of Applied Mathematics and Theoretical Physics, University of Cambridge", year = "1983", type = "DAMTP Report", number = "1983/NA8", address = "Cambridge, England"} \@ARTICLE {Po:88, author = "D.L. POWERS", title = "Graph partitioning by eigenvectors", journal = laa, year = "1988 ", volume = "101", pages = "121-133"} @TECHREPORT {Prat:77, author = "J.W. PRATT", title = "When to stop a quasi-{N}ewton search for a maximum likelihood estimate", institution = "Harvard School of Business", year = "1977", number = "WP 77-16"} @book {MR0276845, AUTHOR = {Pshenichnyi, B.N.}, TITLE = {Necessary conditions for an extremum}, SERIES = {Translated from the Russian by Karol Makowski. Translation edited by Lucien W. Neustadt. Pure and Applied Mathematics}, VOLUME = {4}, PUBLISHER = {Marcel Dekker Inc.}, ADDRESS = {New York}, YEAR = {1971}, PAGES = {xviii+230}, MRCLASS = {47.90 (90.00)}, MRNUMBER = {MR0276845 (43 \#2585)}, } @book {Puk:93, author = "F. PUKELSHEIM", TITLE = {Optimal Design of Experiments}, SERIES = {Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics}, NOTE = {A Wiley-Interscience Publication}, PUBLISHER = {John Wiley \& Sons Inc.}, ADDRESS = {New York}, YEAR = {1993}, PAGES = {xxvi+454}, ISBN = {0-471-61971-X}, } @article {MR97c:90134, AUTHOR = {PULLAN, M. C.}, TITLE = {A duality theory for separated continuous linear programs}, JOURNAL = {SIAM J. Control Optim.}, FJOURNAL = {SIAM Journal on Control and Optimization}, VOLUME = {34}, YEAR = {1996}, NUMBER = {3}, PAGES = {931--965}, ISSN = {0363-0129}, CODEN = {SJCODE}, } @article {MR2000b:14078, AUTHOR = {Putinar, M. and VASILESCU, F.-H.}, TITLE = {Positive polynomials on semi-algebraic sets}, JOURNAL = {C. R. Acad. Sci. Paris S\'er. I Math.}, FJOURNAL = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I. Math\'ematique}, VOLUME = {328}, YEAR = {1999}, NUMBER = {7}, PAGES = {585--589}, ISSN = {0764-4442}, CODEN = {CASMEI}, MRCLASS = {14P10}, MRNUMBER = {2000b:14078}, MRREVR = {Digen Zhang}, } @article {MR95h:47014, AUTHOR = {Putinar, M.}, TITLE = {Positive polynomials on compact semi-algebraic sets}, JOURNAL = {Indiana Univ. Math. J.}, FJOURNAL = {Indiana University Mathematics Journal}, VOLUME = {42}, YEAR = {1993}, NUMBER = {3}, PAGES = {969--984}, ISSN = {0022-2518}, CODEN = {IUMJAB}, MRCLASS = {47A57 (14P10 44A60 47B20)}, MRNUMBER = {95h:47014}, MRREVR = {Ameer Athavale}, } %QQQQQQQQQQQQQQQ @article{QiYang:04, AUTHOR = {QI, H. and YANG, X.}, TITLE = {Regularity and well-posedness of a dual program for convex best {$C\sp 1$}-spline interpolation}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {37}, YEAR = {2007}, NUMBER = {3}, PAGES = {409--425}, ISSN = {0926-6003}, MRCLASS = {49K40 (41A05 41A15)}, MRNUMBER = {MR2335102}, MRREVIEWER = {Anders Linn{\'e}r}, } @article{doi:10.1137/21M1441080, author = {Yuan, Y. and Chang, T.-H. and Sun, D. and Toh, K.-C.}, title = {A Dimension Reduction Technique for Large-Scale Structured Sparse Optimization Problems with Application to Convex Clustering}, journal = {SIAM Journal on Optimization}, volume = {32}, number = {3}, pages = {2294-2318}, year = {2022}, doi = {10.1137/21M1441080}, URL = {https://doi.org/10.1137/21M1441080}, eprint = {https://doi.org/10.1137/21M1441080} } @article {Sun06, AUTHOR = {Sun, D.}, TITLE = {The strong second-order sufficient condition and constraint nondegeneracy in nonlinear semidefinite programming and their implications}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {31}, YEAR = {2006}, NUMBER = {4}, PAGES = {761--776}, ISSN = {0364-765X}, MRCLASS = {90C22 (90C31)}, MRNUMBER = {2281228 (2007m:90060)}, MRREVIEWER = {Ji-Ming Peng}, DOI = {10.1287/moor.1060.0195}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1287/moor.1060.0195}, } @article{QiSun:93nonsmooth, title={A nonsmooth version of {N}ewton's method}, author={Qi, L. and Sun, J.}, journal={Mathematical programming}, volume={58}, number={1-3}, pages={353--367}, year={1993}, publisher={Springer} } @ARTICLE{QiSun:06, AUTHOR = "H. Qi and D. Sun", TITLE = {A Quadratically Convergent {N}ewton Method for Computing the Nearest Correlation Matrix}, JOURNAL = simax, YEAR = 2006, VOLUME = 28, NUMBER = 2, PAGES = {360--385} } @article{Qi:2011, Author = {Qi, H. and Sun, D.}, Journal = {IMA Journal of Numerical Analysis}, Number = {2}, Pages = {491-511}, Title = {An augmented {L}agrangian dual approach for the {$H$}-weighted nearest correlation matrix problem}, Volume = {31}, Year = {2011}} @article {MR85e:15016, AUTHOR = {QI, L.Q.}, TITLE = {Some simple estimates for singular values of a matrix}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {56}, YEAR = {1984}, PAGES = {105--119}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A18 (15A42 65F15)}, MRNUMBER = {85e:15016}, MRREVIEWER = {Ludwig Elsner}, } @article {MR2021493, AUTHOR = {QI, H. and QI, L.}, TITLE = {Finite termination of a dual {N}ewton method for convex best {$C\sp 1$} interpolation and smoothing}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {96}, YEAR = {2003}, NUMBER = {2}, PAGES = {317--337}, ISSN = {0029-599X}, CODEN = {NUMMA7}, MRCLASS = {41A29 (65Kxx 90C25)}, MRNUMBER = {2 021 493}, } @article {radius, AUTHOR = {Dontchev, A.L. and Lewis, A.S. and Rockafellar, R.T.}, TITLE = {The radius of metric regularity}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {355}, YEAR = {2003}, NUMBER = {2}, PAGES = {493--517 (electronic)}, ISSN = {0002-9947}, CODEN = {TAMTAM}, MRCLASS = {49J53 (49J52 49K40 90C31)}, MRNUMBER = {1932710 (2003i:49026)}, MRREVIEWER = {Alexander D. Ioffe}, DOI = {10.1090/S0002-9947-02-03088-X}, URL = {http://dx.doi.org/10.1090/S0002-9947-02-03088-X}, } @article {MR2004a:41024, AUTHOR = {Dontchev, A.L. and Qi, H-D and Qi, L. and Yin, H.}, TITLE = {A {N}ewton method for shape-preserving spline interpolation}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {13}, YEAR = {2002}, NUMBER = {2}, PAGES = {588--602 (electronic)}, ISSN = {1095-7189}, MRCLASS = {41A29 (49J45 65D07 90C25)}, MRNUMBER = {2004a:41024}, MRREVIEWER = {Stephen C. Billups}, } @article {MR2003j:65049, AUTHOR = {TONG, X. and LI, D.-H. and QI, L.}, TITLE = {An iterative method for solving semismooth equations}, NOTE = {Sino-Japan Optimization Meeting (Hong Kong, 2000)}, JOURNAL = {J. Comput. Appl. Math.}, FJOURNAL = {Journal of Computational and Applied Mathematics}, VOLUME = {146}, YEAR = {2002}, NUMBER = {1}, PAGES = {1--10}, ISSN = {0377-0427}, CODEN = {JCAMDI}, MRCLASS = {65H10 (90C33)}, MRNUMBER = {2003j:65049}, MRREVIEWER = {C. Ilioi}, } @article {MR2003g:90079, AUTHOR = {Qi, L. and Sun, D.}, TITLE = {Smoothing functions and smoothing {N}ewton method for complementarity and variational inequality problems}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {113}, YEAR = {2002}, NUMBER = {1}, PAGES = {121--147}, ISSN = {0022-3239}, CODEN = {JOTABN}, MRCLASS = {90C30 (65K10 90C33 90C53)}, MRNUMBER = {2003g:90079}, MRREVIEWER = {Nobuo Yamashita}, } @article {MR99f:65079, AUTHOR = {Potra, F.A. and Qi, L. and Sun, D.}, TITLE = {Secant methods for semismooth equations}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {80}, YEAR = {1998}, NUMBER = {2}, PAGES = {305--324}, ISSN = {0029-599X}, CODEN = {NUMMA7}, MRCLASS = {65H10}, MRNUMBER = {99f:65079}, } @article {Potra:04, AUTHOR = {POTRA, F.A.}, TITLE = {A superlinearly convergent predictor-corrector method for degenerate LCP in a wide neighborhood of the central path with $O(\sqrt{n}L)$-iteration complexity}, JOURNAL = {Numer. Math.}, FJOURNAL = {Mathematical Programming: Series A}, VOLUME = {100}, YEAR = {2004}, NUMBER = {2}, PAGES = {317--337}, } @article {MR98e:90169, AUTHOR = {QI, L. and JIANG, H.}, TITLE = {Semismooth {K}arush-{K}uhn-{T}ucker equations and convergence analysis of {N}ewton and quasi-{N}ewton methods for solving these equations}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {22}, YEAR = {1997}, NUMBER = {2}, PAGES = {301--325}, ISSN = {0364-765X}, MRCLASS = {90C30 (65K05)}, MRNUMBER = {98e:90169}, MRREVIEWER = {G. M. Ostrovsky}, } @INCOLLECTION {Qian96, author = "T. QIAN and Y. YE and P.M. Pardalos", title = " A pseudo $\epsilon$-approximation algorithm for {FVS}", booktitle = " State of the Art in Global Optimization", editor ="C Floudas and P. Pardalos", publisher = "Kluwer Academic Press", year = "1996", pages = "341-351"} %RRRRRRRRRRRRRR @article{Rademacher, title={Uber partielle und totale Differenzierbarkeit I.}, author={Rademacher, H.}, journal={Math. Ann.}, volume ={89}, pages={340--359}, year={1919} } @mastersthesis {Rasmussen:01, author = "J.M. RASMUSSEN", title = "Compact Linear Operators and Krylov Subspace Methods 2001-9", year = "2001-9", school = {Technical University of Denmark}, address = {Anker Engelundsvej, Denmark} } @book {MR2849884, AUTHOR = {Escalante, R. and Raydan, M.}, TITLE = {Alternating projection methods}, SERIES = {Fundamentals of Algorithms}, VOLUME = {8}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA}, YEAR = {2011}, PAGES = {x+127}, ISBN = {978-1-611971-93-4}, MRCLASS = {46C05 (47J25 65J05)}, MRNUMBER = {2849884 (2012h:46042)}, MRREVIEWER = {Heinz H. Bauschke}, DOI = {10.1137/1.9781611971941}, URL = {http://dx.doi.org/10.1137/1.9781611971941}, } @ARTICLE {Ray:93, author = "M. Raydan", title = "On the {B}arzilai and {B}orwein choice of steplength for the gradient method", journal = imajna, year = "1993", volume = "13", pages = "321-326"} @article {MR98b:90131, AUTHOR = {Raydan, M.}, TITLE = {The {B}arzilai and {B}orwein gradient method for the large scale unconstrained minimization problem}, JOURNAL = siopt, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {7}, YEAR = {1997}, NUMBER = {1}, PAGES = {26--33}, ISSN = {1052-6234}, CODEN = {SJOPE8}, } @phdthesis {Rayphd:93, author = "M. Raydan", title = "Convergence Properties of the {B}arzilai and {B}orwein gradient method", year = "1998", school = {Rice University}, address = {Houston, TX} } @ARTICLE {ReSch:84, author = "U. REHDER and W. SCHULTZE", title = "Organization and morphogenesis of the human seminiferous epithelium", journal = "Cellular Tissue Review", year = "1984", volume = "237", pages = "395"} @INPROCEEDINGS {Reid:73, author = "J.K. REID", title = "Least squares solution of sparse systems of non-linear equations by a modified {M}arquardt algorithm", booktitle = "Proceedings of the NATO Conf. at Cambridge, July 1972", pages = "437-445", note = "North-Holland, Amsterdam, 1973"} @ARTICLE {Reil:80, author = "T.W. REILAND", title = "Optimality conditions and duality in continuous programming. II. The linear problem revisited", journal = "J. Math. Anal. Appl.", year = "1980", volume = "77", pages = "329-343"} @ARTICLE {Rein:67, author = "C. Reinsch", title = "Smoothing by spline functions", journal = "Numer. Math.", year = "1967", volume = "10", pages = "177-183"} @ARTICLE {Rein:71, author = "C. Reinsch", title = "Smoothing by spline functions {II}", journal = "Numer. Math.", year = "1971", volume = "16", pages = "451-454"} @book {MR39:2014, AUTHOR = {RELLICH, F.}, TITLE = {Perturbation theory of eigenvalue problems}, SERIES = {Assisted by J. Berkowitz. With a preface by Jacob T. Schwartz}, PUBLISHER = {Gordon and Breach Science Publishers}, ADDRESS = {New York}, YEAR = {1969}, PAGES = {x+127}, MRCLASS = {47.48}, MRNUMBER = {39 \#2014}, } @incollection {MR16:263e, AUTHOR = {RELLICH, F.}, TITLE = {New results in the perturbation theory of eigenvalue problems}, BOOKTITLE = {Simultaneous linear equations and the determination of eigenvalues}, SERIES = {National Bureau of Standards Applied Mathematics Series, No. 29}, PAGES = {95--99}, PUBLISHER = {U. S. Government Printing Office}, ADDRESS = {Washington, D. C.}, YEAR = {1953}, MRCLASS = {46.3X}, MRNUMBER = {16,263e}, MRREVIEWER = {Franti{\v{s}}ek Wolf}, } @TECHREPORT {Re:92, author = "F. Rendl", title = "An inverse parametric eigenvalue approach to Trust Region Problems", institution = "Technische Universitat Graz", year = "1992", address = "Graz, Austria"} @TECHREPORT {Ren:93old, author = "J. Renegar", title = "Linear programming, complexity theory and elementary functional analysis", institution = "Cornell University", year = "1993", address = "Ithaca, NY"} @article {MR1896819, AUTHOR = {Reusken, Arnold}, TITLE = {Approximation of the determinant of large sparse symmetric positive definite matrices}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {23}, YEAR = {2001/02}, NUMBER = {3}, PAGES = {799--818 (electronic)}, ISSN = {0895-4798}, MRCLASS = {65F40 (15A15 15A48 65F50)}, MRNUMBER = {1896819 (2003e:65067)}, DOI = {10.1137/S089547980036869X}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/S089547980036869X}, } @article {MR1707203, AUTHOR = {POWERS, V. and REZNICK, B.}, TITLE = {Polynomials that are positive on an interval}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, ISSN = {0002-9947}, CODEN = {TAMTAM}, MRCLASS = {12Dxx (14Pxx)}, MRNUMBER = {1 707 203}, } @article {MR96e:11056, AUTHOR = {REZNICK, B.}, TITLE = {Uniform denominators in {H}ilbert's seventeenth problem}, JOURNAL = {Math. Z.}, FJOURNAL = {Mathematische Zeitschrift}, VOLUME = {220}, YEAR = {1995}, NUMBER = {1}, PAGES = {75--97}, ISSN = {0025-5874}, CODEN = {MAZEAX}, MRCLASS = {11E76 (11E25)}, MRNUMBER = {96e:11056}, MRREVR = {Victoria Powers}, } @inproceedings{Rheinboldt:04, author = "W.C. Rheinboldt", title = {Nonlinear Systems and Bifurcations}, booktitle = "Encyclopedia of Computational Mecahnics", editors="E. Stein and R. de Borst and T.J.R. Hughes", Publisher="J. Wiley and Sons", year = "2004", address = "MA, USA" } @techreport{Ricceri:04, AUTHOR = "B. RICCERI", TITLE = "Sublevel sets and global minima of coercive functionals and local minima of their perturbations", TYPE = "Report", INSTITUTION = "University of Catania", ADDRESS = "Catania, Italy", URL={http://arxiv.org/abs/math/0402444}, YEAR = "2004", } @techreport{Ricceri:04b, AUTHOR = "B. RICCERI", TITLE = "Integral functionals on Sobolev spaces having multiple local minima", TYPE = "Report", INSTITUTION = "University of Catania", ADDRESS = "Catania, Italy", URL={http://arxiv.org/abs/math/0402445}, YEAR = "2004", } @ARTICLE{RoBi:69, AUTHOR = "P.D. Robers and A. Ben-Israel", TITLE = "Interval programming", JOURNAL = "I\&EC Process Design and Development", VOLUME = 8, YEAR = 1969, PAGES = "496-501" } @article {RoBe:70, AUTHOR = {Ben-Israel, A. and Robers, P.D.}, TITLE = {A decomposition method for interval linear programming}, JOURNAL = {Management Sci.}, VOLUME = {16}, YEAR = {1969/70}, PAGES = {374--387}, MRCLASS = {90C05}, MRNUMBER = {46 #4928}, MRREVR = {A. G. Azpeitia}, } @article {RoBe:70b, AUTHOR = {Robers, P.D. and BEN-ISRAEL, A.}, TITLE = {A suboptimization method for interval linear programming: {A} new method for linear programming}, JOURNAL = {Linear Algebra and Appl.}, VOLUME = {3}, YEAR = {1970}, PAGES = {383--405}, MRCLASS = {90.50}, MRNUMBER = {43 #5913}, MRREVR = {M. Yamasaki}, } t @BOOK {RoVa:73, author = "A.W. Robers and D.E. VARBERG", title = "Convex Functions", publisher = "Academic Press", year = "1973", address = "New York"} @article{rob76, AUTHOR = {Robinson, S. M.}, title={Regularity and stability for convex multivalued functions}, journal=mor, year={1976}, volume={1}, pages={130-143},} @article{rob76a, AUTHOR = {Robinson, S.M.}, title={Stability theorems for systems of inequalities, Part II: differentiable nonlinear systems}, journal={SIAM J. Numerical Analysis}, year={1976}, volume={13}, pages={497-513},} @article{rob75a, AUTHOR = {Robinson, S.M.}, title={Stability theorems for systems of inequalities, Part I: linear systems}, journal={SIAM J. Numerical Analysis}, year={1975}, volume={12}, pages={754-769},} @article{rob76b, AUTHOR = {Robinson, S. M.}, title={First order conditions for general nonlinear optimization}, journal={ SIAM Journal on Applied Mathematics}, year={1976}, volume={ 30}, pages={597-607},} @article {Robinson76, AUTHOR = {Robinson, S.M.}, TITLE = {First order conditions for general nonlinear optimization}, JOURNAL = {SIAM J. Appl. Math.}, FJOURNAL = {SIAM Journal on Applied Mathematics}, VOLUME = {30}, YEAR = {1976}, NUMBER = {4}, PAGES = {597--607}, ISSN = {0036-1399}, MRCLASS = {90C30}, MRNUMBER = {0406529 (53 \#10316)}, MRREVIEWER = {Norman P. Coleman, Jr.}, } @article {MR84d:90084, AUTHOR = {Robinson, S. M.}, TITLE = {Generalized equations and their solutions. {I}{I}. {A}pplications to nonlinear programming}, NOTE = {Optimality and stability in mathematical programming}, JOURNAL = {Math. Programming Stud.}, FJOURNAL = {Mathematical Programming Study}, volume = {19}, YEAR = {1982}, PAGES = {200--221}, ISSN = {0303-3929}, CODEN = {MPSTDF}, } @article {MR56:4815, AUTHOR = {Robinson, S. M.}, TITLE = {A characterization of stability in linear programming}, JOURNAL = {Operations Res.}, VOLUME = {25}, YEAR = {1977}, NUMBER = {3}, PAGES = {435--447}, } @article {MR47:6307, AUTHOR = {Robinson, S. M.}, TITLE = {Bounds for error in the solution set of a perturbed linear program}, JOURNAL = {Linear Algebra and Appl.}, VOLUME = {6}, YEAR = {1973}, PAGES = {69--81}, } @article {MR95c:65093, AUTHOR = {Robinson, S. M.}, TITLE = {{N}ewton's method for a class of nonsmooth functions}, NOTE = {Set convergence in nonlinear analysis and optimization}, JOURNAL = {Set-Valued Anal.}, FJOURNAL = {Set-Valued Analysis. An International Journal Devoted to the Theory of Multifunctions and its Applications}, VOLUME = {2}, YEAR = {1994}, NUMBER = {1-2}, PAGES = {291--305}, ISSN = {0927-6947}, CODEN = {SVANEG}, } @article {MR52:6531, AUTHOR = {Robinson, S. M.}, TITLE = {An application of error bounds for convex programming in a linear space}, JOURNAL = {SIAM J. Control}, VOLUME = {13}, YEAR = {1975}, PAGES = {271--273}, } @inproceedings {MR50:1729, AUTHOR = {Robinson, S. M.}, TITLE = {Computable error bounds for nonlinear programming}, BOOKTITLE = {Transactions of the Nineteenth Conference of Army Mathematicians (U.S. Army Training Device Agency, Naval Training Equipment Center, Orlando, Fla., 1973)}, PAGES = {1105--1117. U.S. Army Research Office (Durham), Report No. 73-3}, PUBLISHER = {U.S. Army Research Office (Durham), Durham, N.C.}, YEAR = {1973}, } @article {MR49:4574, AUTHOR = {Robinson, S. M.}, TITLE = {Computable error bounds for nonlinear programming}, JOURNAL = {Math. Programming}, VOLUME = {5}, YEAR = {1973}, PAGES = {235--242}, } @ARTICLE {Rocka:66, author = "R.T. Rockafellar", title = "Characterization of the subdifferentials of convex functions", journal = "Pacific J. Math.", year = "1966", volume = "17", pages = "497-510"} @ARTICLE {Rocka:68, author = "R.T. Rockafellar", title = "Integrals which are convex functionals", journal = "Pacific J. Math.", year = "1968", volume = "24", pages = "525-539"} @ARTICLE {Rocka:67, author = "R.T. Rockafellar", title = "Duality and stability in extremum problems involving convex functions", journal = "Pacific J. Math.", year = "1967", volume = "21", pages = "167-187"} @incollection {MR43:7217, AUTHOR = {Rockafellar, R. Tyrrell}, TITLE = {Some convex programs whose duals are linearly constrained}, YEAR = {1970}, BOOKTITLE = {Nonlinear Programming (Proc. Sympos., Univ. of Wisconsin, Madison, Wis., 1970)}, PAGES = {293--322}, PUBLISHER = {Academic Press}, ADDRESS = {New York}, } @ARTICLE {Rocka:71, author = "R.T. Rockafellar", title = "Integrals which are convex functionals, II", journal = "Pacific J. Math.", year = "1971", volume = "39", pages = "439-469"} @ARTICLE {Rocka2:71, author = "R.T. Rockafellar", title = "Ordinary convex programs without a duality gap", journal = "JOTA", year = "1971", volume = "7", pages = "143-148"} @BOOK {Rocka:74, author = "R.T. Rockafellar", title = "Conjugate Duality and Optimization", publisher = "SIAM", year = "1974", note = "Regional Conference Series in Applied Mathematics", address = "Philadelphia, PA"} @INPROCEEDINGS {Rocka:76, author = "R.T. Rockafellar", title = "Lagrange multipliers in optimization", booktitle = "SIAM-AMS Proceedings \#9", year = "1976", editor = "R.W. Cottle and C.E. Lemke", pages = "145-168"} @article {MR549128, AUTHOR = {Spingarn, J.E. and Rockafellar, R.T.}, TITLE = {The generic nature of optimality conditions in nonlinear programming}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {4}, YEAR = {1979}, NUMBER = {4}, PAGES = {425--430}, ISSN = {0364-765X}, MRCLASS = {90C30}, MRNUMBER = {MR549128 (80j:90099)}, MRREVIEWER = {J. Parida}, } @article {MR2065984, AUTHOR = {Ioffe, A.D. and Lucchetti, R.E. and Revalski, J. P.}, TITLE = {Almost every convex or quadratic programming problem is well posed}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {29}, YEAR = {2004}, NUMBER = {2}, PAGES = {369--382}, ISSN = {0364-765X}, MRCLASS = {49K40 (90C20 90C31)}, MRNUMBER = {MR2065984 (2005d:49046)}, MRREVIEWER = {Jane Juan-Juan Ye}, } @article {MR1885571, AUTHOR = {Ioffe, A.D. and Lucchetti, R.E. and Revalski, J. P.}, TITLE = {A variational principle for problems with functional constraints}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {12}, YEAR = {2001/02}, NUMBER = {2}, PAGES = {461--478 (electronic)}, ISSN = {1052-6234}, MRCLASS = {49K40 (49J53 90C31)}, MRNUMBER = {MR1885571 (2002m:49042)}, MRREVIEWER = {T. Zolezzi}, } @article {MR1845940, AUTHOR = {Penot, Jean-Paul}, TITLE = {Genericity of well-posedness, perturbations and smooth variational principles}, NOTE = {Wellposedness in optimization and related topics (Gargnano, 1999)}, JOURNAL = {Set-Valued Anal.}, FJOURNAL = {Set-Valued Analysis. An International Journal Devoted to the Theory of Multifunctions and its Applications}, VOLUME = {9}, YEAR = {2001}, NUMBER = {1-2}, PAGES = {131--157}, ISSN = {0927-6947}, CODEN = {SVANEG}, MRCLASS = {49K40 (47N10 90C31)}, MRNUMBER = {MR1845940 (2002f:49053)}, MRREVIEWER = {T. Zolezzi}, } @INCOLLECTION {Rocka:79, author = "R.T. Rockafellar", title = "La th\'{e}orie des sous-gradients et ses applications \`{a} l'optimization: fonctions convexes et non convexes", booktitle = "Collection Chaire Aisenstad", publisher = "Presses de l'Universite de Montr\'{e}al", year = "1979", pages = "130"} @ARTICLE {Rocka2:65, author = "R.T. Rockafellar", title = "{H}elly's theorem and minima of convex functions", journal = "Duke Math", year = "1965", volume = "32", pages = "381-397"} @ARTICLE {Rocka:80, author = "R.T. Rockafellar", title = "Generalized directional derivatives and subgradients of nonconvex functions", journal = "Canadian J. Math.", year = "1980", volume = "32", pages = "157-180"} @BOOK {Rocka:81, author = "R.T. Rockafellar", title = "The Theory of Subgradients and Its Applications to Problems of Optimization: Convex and Nonconvex Functions", publisher = "Holderman Verlag", year = "1981", address = "Berlin"} @ARTICLE {Rocka:93, AUTHOR = {Rockafellar, R.T.}, TITLE = {Lagrange multipliers and optimality}, JOURNAL = {SIAM Rev.}, FJOURNAL = {SIAM Review. A Publication of the Society for Industrial and Applied Mathematics}, VOLUME = {35}, YEAR = {1993}, NUMBER = {2}, PAGES = {183--238}, ISSN = {0036-1445}, CODEN = {SIREAD}, MRCLASS = {49-02 (49N15 90C30)}, MRNUMBER = {1220880 (94h:49004)}, MRREVIEWER = {Hubertus Th. Jongen}, DOI = {10.1137/1035044}, URL = {http://dx.doi.org/10.1137/1035044}, } @book {MR1491362, AUTHOR = {Rockafellar, R.T. and Wets, R.J.-B.}, TITLE = {Variational analysis}, SERIES = {Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]}, VOLUME = {317}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1998}, PAGES = {xiv+733}, ISBN = {3-540-62772-3}, MRCLASS = {49-02 (46N10 47N10 49J52 49K40 90C30)}, MRNUMBER = {MR1491362 (98m:49001)}, MRREVIEWER = {Francis H. Clarke}, DOI = {10.1007/978-3-642-02431-3}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/978-3-642-02431-3}, } @BOOK {int:Roos, author = "K. ROOS and T. Terlaky and J.-Ph. VIAL", title="Theory and Algorithms for Linear Optimization: An interior Point Approach", publisher = "John Wiley \& Sons, New York", year = "1997"} @article {MR22:3601, AUTHOR = {ROSEN, J. B.}, TITLE = {The gradient projection method for nonlinear programming. {I}. {L}inear constraints}, JOURNAL = {J. Soc. Indust. Appl. Math.}, VOLUME = {8}, YEAR = {1960}, PAGES = {181--217}, } @article {MR24:B2030, AUTHOR = {ROSEN, J. B.}, TITLE = {The gradient projection method for nonlinear programming. {I}{I}. {N}onlinear constraints}, JOURNAL = {J. Soc. Indust. Appl. Math.}, VOLUME = {9}, YEAR = {1961}, PAGES = {514--532}, MRCLASS = {90.58}, MRNUMBER = {24 \#B2030}, MRREVIEWER = {A.S. Householder}, } @article {MR1160980, AUTHOR = {ROSEN, J. B.}, TITLE = {The gradient projection method and its motivation}, JOURNAL = {Qufu Shifan Daxue Xuebao Ziran Kexue Ban}, FJOURNAL = {Qufu Shifan Daxue Xuebao. Ziran Kexue Ban. Journal of Qufu Normal University. Natural Science Edition}, VOLUME = {18}, YEAR = {1992}, NUMBER = {1}, PAGES = {50--52}, ISSN = {1001-5337}, CODEN = {QSDXEI}, MRCLASS = {90C30}, MRNUMBER = {1 160 980}, } @article {MR0270957, AUTHOR = {Rose, D.J.}, TITLE = {Triangulated graphs and the elimination process}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {32}, YEAR = {1970}, PAGES = {597--609}, ISSN = {0022-247x}, MRCLASS = {05.40 (65.00)}, MRNUMBER = {0270957}, MRREVIEWER = {S. V. Parter}, DOI = {10.1016/0022-247X(70)90282-9}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/0022-247X(70)90282-9}, } @ARTICLE {Rosen:60, author = "H.H. ROSENBROCK", title = "An automatic method for finding the greatest or least value of a function", journal = "Comp. J.", year = "1960", volume = "3", number = "3", pages = "175-184"} @INCOLLECTION {RosSchna:88, author = "M. ROSING and R.B. Schnabel", title = "An overview of {D}ino{--A} new language for numerical computation on distributed memory multiprocessors", booktitle = "Parallel Processing for Scientific Computation", publisher = "SIAM", year = "1988", editor = "G. Rodrique", pages = "312-316", address = "Philadelphia"} @INCOLLECTION {RosSchnaWea:88, author = "M. ROSING and R.B. Schnabel and R. WEAVER", title = "Dino: Summary and Examples", booktitle = "The Third Conference on Hypercube Concurrent Computers and Applications", publisher = "ACM", year = "1988", editor = "G. Fox", address = "New York, NY"} @TECHREPORT {RosSchnaWea:89, author = "M. ROSING and R.B. Schnabel and R. WEAVER", title = "Expressing complex parallel algorithms in {D}ino", institution = "Department of Computer Science, University of Colorado", year = "1989", number = "CU-CS-430-89", address = "Boulder, CO", note = "To appear in Proceedings of the Fourth Conference on Hypercubes, Concurrent Computers and Applications, Monterey, CA, Mar. 1989"} \@INCOLLECTION{RoHa:89, AUTHOR = "C. Roucairol and P. Hansen", TITLE = "Cut cost minimization in graph partitioning", BOOKTITLE = "Numerical and Applied Mathematics", PUBLISHER = "J.C. Baltzer AG", YEAR = 1989, EDITOR = "C. Brezinski", PAGES ="585-587" } @article {MR0137189, AUTHOR = {Ruben, Harold}, TITLE = {Probability content of regions under spherical normal distributions. {IV}. {T}he distribution of homogeneous and non-homogeneous quadratic functions of normal variables}, JOURNAL = {Ann. Math. Statist.}, FJOURNAL = {Annals of Mathematical Statistics}, VOLUME = {33}, YEAR = {1962}, PAGES = {542--570}, ISSN = {0003-4851}, MRCLASS = {62.40}, MRNUMBER = {0137189 (25 \#645)}, MRREVIEWER = {S. S. Wilks}, } @ARTICLE {RubWag:90, author = "D.S. RUBIN and H.M. WAGNER", title = "Shadow Prices: tips and traps for managers and instructors", journal = "Interfaces", year = "1990", volume = "20", pages = "150-157", kwds = "sensitivity analysis" } @BOOK {Rudin:66, author = "W. RUDIN", title = "Real and Complex Analysis", publisher = "McGraw-Hill", year = "1966", address = "New York, NY"} @ARTICLE {Rut:70, author = "H. RUTISHAUSER", title = "Simultaneous iteration method for symmetric matrices", journal = "Numerische Mathematik", year = "1970", volume = "16", pages = "205-223", kwds = "nla, eig, subspace iteration, symmetric matrix, sparse, software" } @ARTICLE {Ryk:80a, author = "A.S. RYKOV", title = "Simplex methods of direct search", journal = "Engrg. Cybernetics", year = "1980", volume = "18", pages = "12"} @ARTICLE {Ryk:80b, author = "A.S. RYKOV", title = "Simplex direct search algorithms", journal = "Automat. Remote Control", year = "1980", volume = "41", pages = "784"} %SSSSSSSSSSSSSSSSSSS @ARTICLE{SalahiFallahi2015, AUTHOR = {Salahi, M. and Fallahi, S.}, TITLE = {Trust region subproblem with an additional linear inequality constraint}, JOURNAL = {Optim. Lett.}, FJOURNAL = {Optimization Letters}, VOLUME = {10}, YEAR = {2016}, NUMBER = {4}, PAGES = {821--832}, ISSN = {1862-4472}, MRCLASS = {Preliminary Data}, MRNUMBER = {3477379}, DOI = {{10.1007/s11590-015-0957-5}}, URL = {{http://dx.doi.org/10.1007/s11590-015-0957-5}}, } @article {MR1501980, AUTHOR = {Schoenberg, I.J.}, TITLE = {Metric spaces and positive definite functions}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {44}, YEAR = {1938}, NUMBER = {3}, PAGES = {522--536}, ISSN = {0002-9947}, CODEN = {TAMTAM}, MRCLASS = {42A82 (43A35 46B99 54E35)}, MRNUMBER = {1501980}, DOI = {10.2307/1989894}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.2307/1989894}, } @article{SalahiTaati2015, author = {{Salahi}, M. and {Taati}, A.}, title = {A fast eigenvalue approach for solving the trust region subproblem with an additional linear inequality}, journal = "Computat. Appl. Math.", year = "2016", volume = {}, pages = {}, DOI = {{10.1007/s40314-016-0347-3}}, } @book {MR0270044, AUTHOR = {Singer, I.}, TITLE = {Best approximation in normed linear spaces by elements of linear subspaces}, SERIES = {Die Grundlehren der mathematischen Wissenschaften, Band 171}, NOTE = {Translated from the Romanian by Radu Georgescu}, PUBLISHER = {Publishing House of the Academy of the Socialist Republic of Romania, Bucharest; Springer-Verlag, New York-Berlin}, YEAR = {1970}, PAGES = {415}, MRCLASS = {41.60}, MRNUMBER = {0270044}, } @TECHREPORT {Sor:95, author = "S.A. Santos and D.C. Sorensen", title = "A new matrix-free algorithm for the large-scale trust-region subproblem", institution = "Rice University", year = "1995", type = "Technical Report", number = "TR95-20", address = "Houston, TX"} @article{LRSV:11, author = "J. Lampe and M. Rojas and D.C. Sorensen and H. Voss", title = "{Accelerating the LSTRS Algorithm}", journal = "SIAM J. Sci. Comput.", volume = 33, number = 1, pages = "175-194", year = 2011 } @article {Sor:99, author = "M. Rojas and S.A. Santos and D.C. Sorensen", TITLE = {A new matrix-free algorithm for the large-scale trust-region subproblem}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {11}, YEAR = {2000/01}, NUMBER = {3}, PAGES = {611--646 (electronic)}, ISSN = {1095-7189}, MRCLASS = {90C25 (65F15)}, MRNUMBER = {MR1814035 (2002j:90055)}, MRREVIEWER = {Khalil Mouallif}, } @article {MR2401375, AUTHOR = {Rojas, M. and Santos, S.A. and Sorensen, D.C.}, TITLE = {Algorithm 873: {LSTRS}: {MATLAB} software for large-scale trust-region subproblems and regularization}, JOURNAL = {ACM Trans. Math. Software}, FJOURNAL = {Association for Computing Machinery. Transactions on Mathematical Software}, VOLUME = {34}, YEAR = {2008}, NUMBER = {2}, PAGES = {Art. 11, 28}, ISSN = {0098-3500}, CODEN = {ACMSCU}, MRCLASS = {65K10}, MRNUMBER = {2401375}, DOI = {10.1145/1326548.1326553}, URL = {http://dx.doi.org/10.1145/1326548.1326553}, } @article {MR1923715, AUTHOR = {Rojas, M. and Sorensen, D.C.}, TITLE = {A trust-region approach to the regularization of large-scale discrete forms of ill-posed problems}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {23}, YEAR = {2002}, NUMBER = {6}, PAGES = {1842--1860 (electronic)}, ISSN = {1095-7197}, MRCLASS = {65J20 (65F22 86A22)}, MRNUMBER = {1 923 715}, } @article {MR1943393, AUTHOR = {Rojas, M. and Steihaug, T.}, TITLE = {An interior-point trust-region-based method for large-scale non-negative regularization}, JOURNAL = {Inverse Problems}, FJOURNAL = {Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data}, VOLUME = {18}, YEAR = {2002}, NUMBER = {5}, PAGES = {1291--1307}, ISSN = {0266-5611}, CODEN = {INPEEY}, MRCLASS = {90C51 (65F20 65F22)}, MRNUMBER = {MR1943393 (2003k:90097)}, MRREVIEWER = {Vladimir K. Gorbunov}, } @BOOK{ Saad92, AUTHOR = {Y. Saad}, TITLE = {Numerical Methods for Large Eigenvalue Problems}, PUBLISHER = {Halsted Press}, YEAR = 1992, ADDRESS = {New York}, ENTERED = {19980811} } @TECHREPORT {SaaSch:83, author = "Y. SAAD and M.H. SCHULTZ", title = "A {G}eneralized {M}inimal {R}esidual algorithm for solving nonsymmetric linear systems", institution = "Department of Computer Science, Yale University", year = "1983", type = "Research Report", number = "RR-254", address = "New Haven, CT"} @ARTICLE {SaaSch:85, author = "Y. SAAD and M.H. SCHULTZ", title = "Conjugate gradient-like algorithms for solving nonsymmetric linear systems", journal = "Math Comp.", year = "1985", volume = "44", pages = "417-424"} @BOOK {Saat:80, author = "T.L. SAATY", title = "The Analytic Hierarchy Process", publisher = "McGraw-Hill", year = "1980", address = "New York, NY"} @BOOK {SaVar:82, author = "T.L. SAATY and L.G. VARGAS", title = "The Logic of Priorities", publisher = "Kluwer-Nijhoff Publishing", year = "1982", address = "Boston, MA"} @ARTICLE {SaLe:90, author = "G. SACHS and K. LESCH", title = "Fuel savings by optimal aircraft cruise with singular and chattering control", journal = "Proceeding on Optimal Control", year = "1990", pages = "590-599"} @ARTICLE {Sard:42, author = "A. SARD", title = "The measure of the critical values of differential maps", journal = "Bull. Amer. Math. Soc.", year = "1942", pages = "883-890"} @techreport{sz, AUTHOR = "R.W.H.\ SARGENT and X.\ ZHANG", TITLE = "An interior-point algorithm for general nonlinear complementarity problems and nonlinear programs", TYPE = "Report", INSTITUTION = "Centre for Process Systems Engineering, Imperial College", ADDRESS = "London", YEAR = "1998", } @book {MR874114, AUTHOR = {Schrijver, A.}, TITLE = {Theory of linear and integer programming}, SERIES = {Wiley-Interscience Series in Discrete Mathematics}, NOTE = {A Wiley-Interscience Publication}, PUBLISHER = {John Wiley \& Sons, Ltd., Chichester}, YEAR = {1986}, PAGES = {xii+471}, ISBN = {0-471-90854-1}, MRCLASS = {90C05 (90C10)}, MRNUMBER = {874114 (88m:90090)}, MRREVIEWER = {J{\"u}rgen K{\"o}hler}, } @article{ssb, AUTHOR = " SHULTZ, G.A. and Schnabel, R.B. and Byrd, R.H. ", TITLE = "A family of trust-region based algorithms for unconstrained optimization with strong global convergence properties", JOURNAL = sinum, VOLUME = "22", NUMBER ="1", YEAR = "1985", PAGES = "47--67", } @ARTICLE {Seymour93, author = "P. SEYMOUR", title = " Packing directed circuits fractionally", journal = "Combinatorica", year = "1993", volume = "15", pages = "182-188"} @phdthesis{jason, author = "J.B. SCHATTMAN", title = "Portfolio selection under nonconvex transaction costs and capital gains taxes", school = "Rutgers Center for Operations Research", address = "Rutgers University, USA", year = "2000" } @Article{Schon66, author={P. H. Schonemann}, title={A generalized solution of the orthogonal procrustes problem}, journal={Psychometrika}, year=1966, volume={31}, number={1}, pages={1-10}, month={March}, keywords={}, abstract={}, url={http://ideas.repec.org/a/spr/psycho/v31y1966i1p1-10.html} } @article {MR2167178, AUTHOR = {NI, Q. and ZILLOBER, C. and SCHITTKOWSKI, K.}, TITLE = {Sequential convex programming methods for solving large topology optimization problems: implementation and computational results}, JOURNAL = {J. Comput. Math.}, FJOURNAL = {Journal of Computational Mathematics. An International Journal on Numerical Methods, Analysis and Applications}, VOLUME = {23}, YEAR = {2005}, NUMBER = {5}, PAGES = {491--502}, ISSN = {0254-9409}, CODEN = {JCMMEB}, MRCLASS = {90C55 (65K05 74P15 90C90)}, MRNUMBER = {MR2167178 (2006d:90237)}, } @incollection {MR2155303, AUTHOR = {SCHITTKOWSKI, K. and ZILLOBER, C.}, TITLE = {Nonlinear programming: algorithms, software, and applications. {F}rom small to very large scale optimization}, BOOKTITLE = {System modeling and optimization}, SERIES = {IFIP Int. Fed. Inf. Process.}, VOLUME = {166}, PAGES = {73--107}, PUBLISHER = {Kluwer Acad. Publ.}, ADDRESS = {Boston, MA}, YEAR = {2005}, MRCLASS = {90C55 (90-04 90C30)}, MRNUMBER = {MR2155303 (2006b:90123)}, } @incollection {MR2144382, AUTHOR = {SCHITTKOWSKI, K. and ZILLOBER, C.}, TITLE = {S{QP} versus {SCP} methods for nonlinear programming}, BOOKTITLE = {Optimization and control with applications}, SERIES = {Appl. Optim.}, VOLUME = {96}, PAGES = {305--330}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {2005}, MRCLASS = {90C55 (90-04 90C30)}, MRNUMBER = {MR2144382 (2006a:90170)}, MRREVIEWER = {Jos{\'e} Mario Mart{\'{\i}}nez}, } @article {MR2062238, AUTHOR = {ZILLOBER, C. and SCHITTKOWSKI, K. and MORITZEN, K.}, TITLE = {Very large scale optimization by sequential convex programming}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods \& Software}, VOLUME = {19}, YEAR = {2004}, NUMBER = {1}, PAGES = {103--120}, ISSN = {1055-6788}, MRCLASS = {90C06 (90C25)}, MRNUMBER = {MR2062238 (2005a:90098)}, } @techreport {SchittkowskiNLPQLP, AUTHOR = {SCHITTKOWSKI, K.}, TITLE = {NLPQLP: A New Fortran Implementation of a Sequential Quadratic Programming Algorithm}, institution = "Department of Mathematics", number = " ", address = " University of Bayreuth, Bayreuth, Germany", YEAR = {2002}, note = "URL http://www.optimization-online.org/DB\_HTML/2002/01/425.html", } @ARTICLE {Schi:81, author = "K. SCHITTKOWSKIK", title = "The nonlinear programming method of {W}ilson, {H}an and {P}owell with an augmented {L}agrangian type line search function, {P}art 2: An efficient implementation with linear least squares subproblems", journal = "Numer. Math.", year = "1981", volume = "38", pages = "115-127"} @TECHREPORT {Schi:82, author = "K. SCHITTKOWSKIK", title = "On the convergence of a sequential quadratic programming method with an augmented {L}agrangian line search function", institution = "Department of Operations Research, Stanford University", year = "1982", number = "SOL 82-4", address = "Stanford, CA"} @PHDTHESIS {Schna:77, author = "R.B. Schnabel", title = "Analysing and improving quasi-{N}ewton methods for unconstrained optimization", school = "Department of Computer Science, Cornell University", year = "1977", address = "Ithaca, NY", note = "Also available as TR-77-320"} @ARTICLE {Schna:78a, author = "R.B. Schnabel", title = "Minimum norm symmetric quasi-{N}ewton updates restricted to subspaces", journal = "Math. Comp.", year = "1978", pages = "829-837"} @ARTICLE {Schna:78b, author = "R.B. Schnabel", title = "Optimal conditioning in the convex class of rank-two updates", journal = "Math. Prog.", year = "1978", pages = "247-260"} @TECHREPORT {Schna:78c, author = "R.B. Schnabel", title = "Q-superlinear convergence of {Biggs'} method and related methods for unconstrained optimization", institution = "Department of Computer Science, University of Colorado", year = "1978", number = "CU-CS-133-78", address = "Boulder, CO"} @TECHREPORT {Schna:78d, author = "R.B. Schnabel", title = "On the {Q}-superlinear convergence of self-scaling quasi-{N}ewton methods", institution = "Department of Computer Science, University of Colorado", year = "1978", number = "CU-CS-144-78", address = "Boulder, CO"} @INCOLLECTION {Schna:79, author = "R.B. Schnabel", title = "Developing modular software for unconstrained optimization", booktitle = "Performance Evaluation of Numerical Software", publisher = "North-Holland", year = "1979", editor = "L.D. Fosdick", pages = "245-251", address = "Amsterdam"} @ARTICLE {Schna:82a, author = "R.B. Schnabel", title = "Determining feasibility of a set of nonlinear inequality constraints", journal = "Math. Programming Studies", year = "1982", volume = "16", pages = "137-148"} @INCOLLECTION {Schna:82b, author = "R.B. Schnabel", title = "Comments on evaluating algorithms and codes for mathematical programming", booktitle = "Evaluating Mathematical Programming Techniques", publisher = "Springer-Verlag", year = "1982", editor = "J.M. Mulvey", pages = "166-169", address = "Berlin"} @INCOLLECTION {Schna:82c, author = "R.B. Schnabel", title = "Unconstrained Optimization in 1981", booktitle = "Nonlinear Optimization 1981", publisher = "Academic Press", year = "1982", editor = "M.J.D. Powell", pages = "3-16", address = "London"} @TECHREPORT {Schna:82d, author = "R.B. Schnabel", title = "Finite difference derivatives - theory and practice", institution = "National Bureau of Standards", year = "1982"} @ARTICLE {Schna:83a, author = "R.B. Schnabel", title = "Forcing sparsity by projecting with respect to a non-diagonally weighted {F}robenius norm", journal = "Math. Prog.", year = "1983", volume = "25", pages = "125-129"} @INCOLLECTION {Schna:83b, author = "R.B. Schnabel", title = "Conic methods for unconstrained minimization and tensor methods for nonlinear equations", booktitle = "Mathematical Programming, The State of the Art", publisher = "Springer-Verlag", year = "1983", editor = "A. Bachem and M. Grotschel and B. Korte", pages = "417-438", address = "Berlin"} @TECHREPORT {Schna:83c, author = "R.B. Schnabel", title = "Quasi-{N}ewton methods using multiple secant equations", institution = "Department of Computer Science, University of Colorado", year = "1983", number = "CU-CS-247-83", address = "Boulder, CO"} @INCOLLECTION {Schna:85, author = "R.B. Schnabel", title = "Parallel computing in optimization", booktitle = "Computational Mathematical Programming", publisher = "Springer-Verlag", year = "1985", editor = "K. Schittkowski", pages = "357-381", address = "Berlin"} @ARTICLE {Schna:87, author = "R.B. Schnabel", title = "Concurrent function evaluations in local and global optimization", journal = "Computer Methods in Applied Mechanics and Engineering", year = "1987", volume = "64", pages = "537-552"} @TECHREPORT {Schna:88a, author = "R.B. Schnabel", title = "Sequential and parallel methods for unconstrained optimization", institution = "Department of Computer Science, University of Colorado", year = "1988", number = "CU-CS-414-88", address = "Boulder, CO", note = "To appear in book of plenary and survey talks from 13th International Conference on Mathematical Programming, Tokyo, Japan, Aug. 1988"} @INPROCEEDINGS {Schna:88b, author = "R.B. Schnabel", title = "Why are all us parallel numerical analysts doing parallel software tools?", booktitle = "Proceedings of IBM/NSF Workshop on Opportunities and Constraints of Parallel Computing", year = "1988"} @article {MR1257614, AUTHOR = {Rothblum, Uriel G. and Schneider, Hans and Schneider, Michael H.}, TITLE = {Scaling matrices to prescribed row and column maxima}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {15}, YEAR = {1994}, NUMBER = {1}, PAGES = {1--14}, ISSN = {0895-4798}, CODEN = {SJMAEL}, MRCLASS = {90B10 (15A23)}, MRNUMBER = {1257614 (95b:90026)}, MRREVIEWER = {Henry Wolkowicz}, DOI = {10.1137/S0895479891222088}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/S0895479891222088}, } @article {MR1106798, AUTHOR = {Schneider, Hans and Schneider, Michael H.}, TITLE = {Max-balancing weighted directed graphs and matrix scaling}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {16}, YEAR = {1991}, NUMBER = {1}, PAGES = {208--222}, ISSN = {0364-765X}, MRCLASS = {90C35 (15A12)}, MRNUMBER = {1106798 (92k:90114)}, MRREVIEWER = {Uwe Zimmermann}, DOI = {10.1287/moor.16.1.208}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1287/moor.16.1.208}, } @article {MR1049771, AUTHOR = {Schneider, Michael H.}, TITLE = {Matrix scaling, entropy minimization, and conjugate duality. {II}. {T}he dual problem}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {48}, YEAR = {1990}, NUMBER = {1, (Ser. B)}, PAGES = {103--124}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C25 (65F35 65K05)}, MRNUMBER = {1049771 (91c:90086)}, MRREVIEWER = {D. S. Tracy}, DOI = {10.1007/BF01582253}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/BF01582253}, } @article {MR986907, AUTHOR = {Schneider, Michael H.}, TITLE = {Matrix scaling, entropy minimization, and conjugate duality. {I}. {E}xistence conditions}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {114/115}, YEAR = {1989}, PAGES = {785--813}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {90C25 (15A99 94C15)}, MRNUMBER = {986907 (90f:90110)}, MRREVIEWER = {D. S. Tracy}, DOI = {10.1016/0024-3795(89)90493-X}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/0024-3795(89)90493-X}, } @article {MR14:1055a, AUTHOR = {Schneider, H.}, TITLE = {An inequality for latent roots applied to determinants with dominant principal diagonal}, JOURNAL = {J. London Math. Soc.}, VOLUME = {28}, YEAR = {1953}, PAGES = {8--20}, MRCLASS = {09.0X}, MRNUMBER = {14,1055a}, MRREVIEWER = {G. E. Forsythe}, } \@INCOLLECTION{Zo:88, AUTHOR = "H. SCHRAMM and J. ZOWE", TITLE = "A Combination of the Bundle approach and the Trust Region Concept", BOOKTITLE = "Advances in Mathematical Optimization", PUBLISHER = "Akademie Verlag Berlin", YEAR = 1988, EDITOR = "J. Guddat et al." } @ARTICLE{SZ:92, AUTHOR = "H. SCHRAMM and J. ZOWE", TITLE = "A version of the Bundle idea for Minimizing a Nonsmooth Function: Conceptual Idea, Convergence Analysis, Numerical Results", JOURNAL = siopt, VOLUME = 2, YEAR = 1992, PAGES = "121-152" } @ARTICLE{Z0:92, AUTHOR = "H. SCHRAMM and J. ZOWE", TITLE = "A version of the Bundle idea for Minimizing a Nonsmooth Function: Conceptual Idea, Convergence Analysis, Numerical Results", JOURNAL = siopt, VOLUME = 2, YEAR = 1992, PAGES = "121-152"} @ARTICLE{Sch:79, AUTHOR = "A. SCHRIJVER", TITLE = "A comparison of the {D}elsarte and {L}ov{\'{a}}sz bounds", JOURNAL = "IEEE Trans. Infor. Theory", VOLUME = "IT-25", YEAR = "1979", PAGES = "425-429"} @ARTICLE {Schu:70, author = "L.K. SCHUBERT", title = "Modification of a quasi-{N}ewton method for nonlinear equations with a sparse {J}acobian", journal = "Math. Comp.", year = "1970", volume = "24", pages = "27-30"} @TECHREPORT {Scolnik, author = "H.D. SCOLNIK", title = "Test functions for unconstrained optimization", institution = "Departamento de Computacion, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires", year = "1989", number = "1-89"} @TECHREPORT {Sc:79, author = "D.S. SCOTT", title = "Block Lanczos software for symmetric eigenvalue problems", institution = "Oak Ridge National laboratory", number = "84-08", year = "1979"} @book {MR986070, AUTHOR = {SEBER, G.A.F. and WILD, C.J.}, TITLE = {Nonlinear regression}, SERIES = {Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics}, PUBLISHER = {John Wiley \& Sons Inc.}, ADDRESS = {New York}, YEAR = {1989}, PAGES = {xxii+768}, ISBN = {0-471-61760-1}, MRCLASS = {62-02 (62J02)}, MRNUMBER = {MR986070 (90j:62004)}, MRREVIEWER = {Roy T. Saint Laurent}, } @BOOK {Shae:71, author = "H. SHAEFER", title = "Topological Vector Spaces", publisher = "Springer-Verlag", address = "New York", year = "1971"} @article {MR2869369, AUTHOR = {Shanker, R. and Arora, S.R. and Saxena, R.R.}, TITLE = {Relation between set partitioning and set covering problems with quadratic fractional objective functions}, JOURNAL = {Opsearch}, FJOURNAL = {Opsearch. Quarterly Journal of the Operational Research Society of India}, VOLUME = {48}, YEAR = {2011}, NUMBER = {3}, PAGES = {247--256}, ISSN = {0030-3887}, MRCLASS = {90C32 (05A18 90C10)}, MRNUMBER = {2869369 (2012j:90183)}, DOI = {10.1007/s12597-011-0052-3}, URL = {http://dx.doi.org/10.1007/s12597-011-0052-3}, } @ARTICLE {Shan:70, author = "D.F. SHANNO", title = "Conditioning of quasi-{N}ewton methods for function minimization", journal = "Math. Comp.", year = "1970", volume = "24", pages = "647-657"} @ARTICLE {Shan:78a, author = "D.F. SHANNO", title = "Conjugate gradient methods with inexact searches", journal = "Math. Oper. Res.", year = "1978", volume = "3", number = "3", pages = "244-256"} @ARTICLE {Shan:78b, author = "D.F. SHANNO", title = "On the convergence of a new conjugate gradient algorithm", journal = "SIAM J. Numer. Anal.", year = "1978", volume = "15", number = "6", pages = "1247-1257"} @ARTICLE {Shan:80, author = "D.F. SHANNO", title = "On variable metric methods for sparse {H}essians", journal = "Math. Comp.", year = "1980", volume = "34", pages = "499-514"} @TECHREPORT {Shan:84, author = "D.F. SHANNO", title = "Globally convergent conjugate gradient algorithms", institution = "Graduate School of Administration, University of California at Davis", year = "1984", type = "Working Paper", number = "84-08"} @book {MR0437981, AUTHOR = {Shapiro, Harold S.}, TITLE = {Topics in approximation theory}, NOTE = {With appendices by Jan Boman and Torbj\"orn Hedberg, Lecture Notes in Math., Vol. 187}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1971}, PAGES = {viii+275}, MRCLASS = {41-02}, MRNUMBER = {MR0437981 (55 \#10902)}, MRREVIEWER = {David A. Sprecher}, } @book {MR0412669, AUTHOR = {Shapiro, Harold S.}, TITLE = {Smoothing and approximation of functions}, NOTE = {Revised and expanded edition of mimiographed notes (Matscience Report No. 55), Van Nostrand Reinhold Mathematical Studies}, PUBLISHER = {Van Nostrand Reinhold Co.}, ADDRESS = {New York}, YEAR = {1969}, PAGES = {viii+136}, MRCLASS = {41-02}, MRNUMBER = {MR0412669 (54 \#791)}, MRREVIEWER = {R. C. Buck}, } \@ARTICLE {Sh:85, author = "A. SHAPIRO", title = "Optimal block diagonal $l_2$-scaling of matrices", journal = sinum, year = "1985", volume = "22", pages = "81-94" } @ARTICLE {Shap:91, author = "A. SHAPIRO", title = "Upper bounds for nearly diagonal scaling of matrices", journal = lama, year = "1991", volume = "29", pages = "145-148"} @article {MR45:4692, AUTHOR = {SHAW, Jr., C.B.}, TITLE = {Improvement of the resolution of an instrument by numerical solution of an integral equation}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {37}, YEAR = {1972}, PAGES = {83--112}, MRCLASS = {65R05}, MRNUMBER = {45 \#4692}, MRREVIEWER = {G. F. Miller}, } @article {sharpe:94, AUTHOR = {Sharpe, W.F}, TITLE = {The {S}harpe ratio}, JOURNAL = {Journal of Portfolio Management}, VOLUME = {Fall}, YEAR = {1994}, PAGES = {49--58}, } @BOOK {Shew:94, author = "J.R. Shewchuk", title = "An Introduction to the Conjugate Gradient Method Without the Agonizing Pain", publisher = "Carnegie Mellon University", year = "1994", keywords = "iter", address = "Pittsburgh, PA 15213"} @book {MR86f:90138, AUTHOR = {Shor, N.Z.}, TITLE = {Minimization methods for nondifferentiable functions}, NOTE = {Translated from the Russian by K. C. Kiwiel and A. Ruszczy\'nski}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1985}, PAGES = {viii+162}, ISBN = {3-540-12763-1}, MRCLASS = {90C30 (49D07 65K10)}, MRNUMBER = {86f:90138}, MRREVR = {K. G. Murty}, } @ARTICLE {Sie:91, author = "D. SIEGEL", title = "Modifying the {BFGS} update by a new column scaling technique", journal = mprog, year = "1994", volume = "66", pages = "45-78", number = "1"} @TECHREPORT {Sil:78, author = "G.L. SILVER", title = "Non-{E}uclidean simplex optimization", institution = "USDOE", year = "1978", number = "MlM-2427"} @ARTICLE {Sil:81, author = "G.L. SILVER", title = "Space modification: An alternative approach to chemistry problems involving geometry", journal = "Journal Comput. Chem.", year = "1981", volume = "2", pages = "478"} @TECHREPORT {Si:93, author = "H. SIMON", title = "Personal communication", institution = "NASA Ames Research Center", year = "1993", address = "Moffett Field, CA"} @ARTICLE{simon91, AUTHOR = "SIMON, H. D.", TITLE = "Partitioning of Unstructured Problems for Parallel Processsing", JOURNAL = "Computing Systems in Engineering", VOLUME = "2", NUMBER = "2/3", PAGES = "135 - 148", YEAR = "1991"} @TECHREPORT{barnardsim92, AUTHOR = "BARNARD, S. T. and SIMON, H. D.", TITLE = "A Fast Multilevel Implementation of Recursive Spectral Bisection for Partitioning Unstructured Problems", INSTITUTION = "NASA Ames Research Center", ADDRESS = "Moffett Field, CA 94035", NUMBER = "RNR-092-033", MONTH = "November", NOTE = "(To appear in Concurrency: Practice and Experience)", YEAR = "1992"} @article {Sipics:08, author = "M. SIPICS", title = "Novel algorithm speeds discovery of electric power grid vulnerabilities", journal = "SIAM News", year = "2008", volume = "41", number = "4" } @ARTICLE {Sko:90, author = "J. SKORIN-KAPOV", title = "Tabu search applied to the quadratic assignment problem", journal = " ORSA Journal on Computing", year = "1990", volume = "2(1)", pages = "33-45"} @article {MR0256546, AUTHOR = {VAN der SLUIS, A.}, TITLE = {Stability of solutions of linear algebraic systems}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {14}, YEAR = {1969/1970}, PAGES = {246--251}, ISSN = {0029-599X}, MRCLASS = {65.35}, MRNUMBER = {MR0256546 (41 \#1202)}, MRREVIEWER = {J. D. P. Donnelly}, } @article {MR40:6760, AUTHOR = {VAN der SLUIS, A.}, TITLE = {Condition numbers and equilibration of matrices}, JOURNAL = {Numer. Math.}, VOLUME = {14}, YEAR = {1969/1970}, PAGES = {14--23}, MRCLASS = {65.35}, MRNUMBER = {40 \#6760}, MRREVIEWER = {R. P. Tewarson}, } @article{Laugesen199864, title = "Extremals for Eigenvalues of Laplacians under Conformal Mapping", journal = "Journal of Functional Analysis", volume = "155", number = "1", pages = "64 - 108", year = "1998", note = "", issn = "0022-1236", doi = "DOI: 10.1006/jfan.1997.3222", url = "http://www.sciencedirect.com/science/article/B6WJJ-45M2TH8-3/2/a463354e3a8e123692ae16d795577f4b", author = "R.S. LAUGESEN and C. MORPURGO", keywords = "conformal mapping radius; isoperimetric inequality; trace of heat kernel; zeta function of Laplacian; curvature bound; conformal class" } @article {MR1250002, AUTHOR = {Smith, Murray D.}, TITLE = {Expectations of ratios of quadratic forms in normal variables: evaluating some top-order invariant polynomials}, JOURNAL = {Austral. J. Statist.}, FJOURNAL = {The Australian Journal of Statistics}, VOLUME = {35}, YEAR = {1993}, NUMBER = {3}, PAGES = {271--282}, ISSN = {0004-9581}, CODEN = {AUJSA3}, MRCLASS = {62H10 (33C55 65D20)}, MRNUMBER = {1250002 (94j:62121)}, MRREVIEWER = {Yasuko Chikuse}, } @article {MR95a:49094, AUTHOR = {SOLOVIOV, V.}, TITLE = {Duality for nonconvex optimization and its applications}, JOURNAL = {Anal. Math.}, FJOURNAL = {Analysis Mathematica}, VOLUME = {19}, YEAR = {1993}, NUMBER = {4}, PAGES = {297--315}, ISSN = {0133-3852}, CODEN = {ANMADK}, } @article{int:Sonnevend7, author = "G. SONNEVEND", title = "Applications of the notion of analytic center in approximation (estimation) problem", journal = "Journal of Computational and Applied Mathematics", volume = "28", year = "1989", pages = "349--358" } @PHDTHESIS {Sor:77a, author = "D.C. Sorensen", title = "Updating the symmetric indefinite factorization with applications in a modified {N}ewton's method", school = "University of California at San Diego", year = "1977"} @TECHREPORT {Sor:77b, author = "D.C. Sorensen", title = "Updating the symmetric indefinite factorization with applications in a modified {N}ewton's method", institution = "Argonne National Labs", year = "1977", number = "ANL-77-49", address = "Argonne, IL"} @ARTICLE {Sor:80, author = "D.C. Sorensen", title = "The {Q}-superlinear convergence of a collinear scaling algorithm for unconstrained optimization", journal = "SIAM J. Numer. Anal.", year = "1980", volume = "17", number = "1", pages = "84-114"} @ARTICLE {Sor:81, author = "D.C. Sorensen", title = "An example concerning quasi-{N}ewton estimation of a sparse {H}essian", journal = "SIGNUM Newsletter", year = "1981", volume = "16", pages = "8-10"} @ARTICLE {Sor:82a, author = "D.C. Sorensen", title = "{N}ewton's method with a model trust region modification", journal = "SIAM J. Numer. Anal.", year = "1982", volume = "19", pages = "409-426"} @INCOLLECTION {Sor:82b, author = "D.C. Sorensen", title = "Trust region methods for unconstrained minimization", booktitle = "Nonlinear Optimization 1981", publisher = "Academic Press", year = "1982", editor = "M.J.D. Powell", address = "London"} @article {Sor:94, author = "D.C. Sorensen", title = {Minimization of a large-scale quadratic function subject to a spherical constraint}, journal = {SIAM Journal on Optimization}, year = {1997}, volume = {7}, number = {1}, pages = {141-161}, } @techreport{So09, author = "A.M.-C. So", title = "Moment Inequalities for Sums of Random Matrices and Their Applications in Optimization", institution = "The Chinese University of Hong Kong", year = 2009, number = "Math. Progr.", address = "to appear", } @ARTICLE{ Sorensen92, AUTHOR = {D.C. Sorensen}, TITLE = {Implicit Application of Polynomial filters in a k-step {A}rnoldi Method}, JOURNAL = simax, YEAR = 1992, VOLUME = 13, NUMBER = 1, PAGES = {357--385} } @article {MR2166552, AUTHOR = {de Souza, C. and Balas, E.}, TITLE = {The vertex separator problem: algorithms and computations}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {103}, YEAR = {2005}, NUMBER = {3, Ser. A}, PAGES = {609--631}, ISSN = {0025-5610}, MRCLASS = {90C57 (05C69 05C85 90C11 90C27 90C35)}, MRNUMBER = {2166552 (2006j:90145)}, MRREVIEWER = {Garth T. Isaak}, DOI = {10.1007/s10107-005-0573-8}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s10107-005-0573-8}, } @book {MR2830310, AUTHOR = {Sottile, F.}, TITLE = {Real solutions to equations from geometry}, SERIES = {University Lecture Series}, VOLUME = {57}, PUBLISHER = {American Mathematical Society, Providence, RI}, YEAR = {2011}, PAGES = {x+200}, ISBN = {978-0-8218-5331-3}, MRCLASS = {14P05 (12D10 14M15 14N10 14P25)}, MRNUMBER = {2830310 (2012h:14144)}, MRREVIEWER = {Didier Henrion}, } @article {MR2145860, AUTHOR = {Spielman, D.A. and Teng, S-H.}, TITLE = {Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time}, JOURNAL = {J. ACM}, FJOURNAL = {Journal of the ACM}, VOLUME = {51}, YEAR = {2004}, NUMBER = {3}, PAGES = {385--463 (electronic)}, ISSN = {0004-5411}, MRCLASS = {90C05 (68W40 90C60)}, MRNUMBER = {2145860 (2006f:90029)}, MRREVIEWER = {Panos M. Pardalos}, DOI = {10.1145/990308.990310}, URL = {http://dx.doi.org/10.1145/990308.990310}, } @article {MR2004403, AUTHOR = {Spielman, D.A. and Teng, S-H.}, TITLE = {Smoothed analysis of termination of linear programming algorithms}, NOTE = {ISMP, 2003 (Copenhagen)}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {97}, YEAR = {2003}, NUMBER = {1-2, Ser. B}, PAGES = {375--404}, ISSN = {0025-5610}, MRCLASS = {90C05 (68Q25 90C51)}, MRNUMBER = {2004403 (2005b:90069)}, MRREVIEWER = {Reha H. T{\"u}t{\"u}nc{\"u}}, } @article {MR0391951, AUTHOR = {SPOSITO, V.A. and DAVID, H.T.}, TITLE = {A note on {F}arkas lemmas over cone domains}, JOURNAL = {SIAM J. Appl. Math.}, FJOURNAL = {SIAM Journal on Applied Mathematics}, VOLUME = {22}, YEAR = {1972}, PAGES = {356--358}, ISSN = {1095-712X}, MRCLASS = {90C05}, MRNUMBER = {MR0391951 (52 \#12769)}, MRREVIEWER = {S. Zlobec}, } @article {MR0297383, AUTHOR = {SPOSITO, V.A. and DAVID, H.T.}, TITLE = {Saddle-point optimality criteria of nonlinear programming problems over cones without differentiability}, JOURNAL = {SIAM J. Appl. Math.}, FJOURNAL = {SIAM Journal on Applied Mathematics}, VOLUME = {20}, YEAR = {1971}, PAGES = {698--702}, ISSN = {1095-712X}, MRCLASS = {90C30}, MRNUMBER = {MR0297383 (45 \#6440)}, MRREVIEWER = {A. Ben-Israel}, } @ARTICLE {Sor:94a, author = "D. Calvetti and L. Reichel and D.C. Sorensen", title = "An implicitly restarted {L}anczos method for large symmetric eigenvalue problems", journal = "ETNA", year = "1994", volume = "2", note = "URL http://etna.mcs.kent.edu/vol.2.1994/index.html", pages = "1-21"} @ARTICLE {Sped:83, author = "E. SPEDICATO", title = "A class of rank-one positive quasi-{N}ewton updates for unconstrained minimization", journal = "Mathematische Operations und Statistic, Ser. Optimization", year = "1983", volume = "14", pages = "61-70"} @ARTICLE {SpKi:86, author = "T.P. SPEED and H.T. KIIVERI", title = "Gaussian {M}arkov distributions over finite graphs", journal = "The Annals of Statistics", year = "1986", volume = "14", pages = "138-150"} @inproceedings{sra2004triangle, title={Triangle fixing algorithms for the metric nearness problem}, author={Sra, S. and Tropp, J. and Dhillon, I.S}, booktitle={Advances in Neural Information Processing Systems}, pages={361--368}, year={2004} } @techreport{MekaJainDhillon:09, author = "R. Meka and P. Jain and I.S. Dhillon", title = "Guaranteed Rank Minimization via Singular Value Projection", institution = "Department of Computer Science, University of Texas at Austin", year = "2009", number = "Advanced Studies in Pure Mathematics", address = "Austin" } @article {MR2399586, AUTHOR = {Brickell, J. and Dhillon, I.S. and Sra, S. and Tropp, J.A.}, TITLE = {The metric nearness problem}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {30}, YEAR = {2008}, NUMBER = {1}, PAGES = {375--396}, ISSN = {0895-4798}, MRCLASS = {51K05 (51F99 65Y20 90C06 90C08)}, MRNUMBER = {2399586 (2009j:51006)}, MRREVIEWER = {Wen Yu Sun}, DOI = {10.1137/060653391}, URL = {http://dx.doi.org/10.1137/060653391}, } @ARTICLE {Sprin:81, author = "J.E. SPRINGARN", title = "Submonotone subdifferentials of {L}ipschitz functions", journal = "Trans. Amer. Math. Soc.", year = "1981", volume = "264", pages = "77-89"} @TECHREPORT {Stei:80, author = "T. Steihaug", title = "Quasi-{N}ewton methods for large scale nonlinear problems", institution = "Yale University", year = "1980", type = "SOM Technical Report", number = "49", address = "New Haven, CT"} @TECHREPORT {Stei:81, author = "T. Steihaug", title = "The conjugate gradient method and trust region in large scale optimization", institution = "Department of Mathematical Sciences, Rice University", year = "1981", number = "TR81-1", address = "Houston, TX"} @ARTICLE {Stei:83, author = "T. Steihaug", title = "The conjugate gradient method and trust regions in large scale optimization", journal = "SIAM J. Num. Anal.", year = "1983", volume = "20", pages = "626-637"} @article{StYe:92, author = "R.J. STERN and J.J. YE", TITLE = {Variational analysis of an extended eigenvalue problem}, BOOKTITLE = {Proceedings of the Workshop ``Nonnegative Matrices, Applications and Generalizations'' and the Eighth Haifa Matrix Theory Conference (Haifa, 1993)}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {220}, YEAR = {1995}, PAGES = {391--417}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {49J52 (15A18)}, MRNUMBER = {96c:49031}, MRREVIEWER = {Henry Wolkowicz}, } } @BOOK {Ste:86, author = "R.E. STEUER", title = "Multiple Criteria Optimization : Theory, Computation, and Application", publisher = "Wiley", year = "1986", address = "New York, Toronto"} @incollection {MR1250182, AUTHOR = {Stewart, G.W.}, TITLE = {Determining rank in the presence of error}, BOOKTITLE = {Linear algebra for large scale and real-time applications (Leuven, 1992)}, SERIES = {NATO Adv. Sci. Inst. Ser. E Appl. Sci.}, VOLUME = {232}, PAGES = {275--291}, PUBLISHER = {Kluwer Acad. Publ.}, ADDRESS = {Dordrecht}, YEAR = {1993}, MRCLASS = {65F10}, MRNUMBER = {MR1250182}, } @article {MR1211802, AUTHOR = {Stewart, G.W.}, TITLE = {Updating a rank-revealing {$ULV$} decomposition}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {14}, YEAR = {1993}, NUMBER = {2}, PAGES = {494--499}, ISSN = {0895-4798}, CODEN = {SJMAEL}, MRCLASS = {65F05}, MRNUMBER = {MR1211802 (93m:65039)}, } @article {MR740857, AUTHOR = {Stewart, G.W.}, TITLE = {Rank degeneracy}, JOURNAL = {SIAM J. Sci. Statist. Comput.}, FJOURNAL = {Society for Industrial and Applied Mathematics. Journal on Scientific and Statistical Computing}, VOLUME = {5}, YEAR = {1984}, NUMBER = {2}, PAGES = {403--413}, ISSN = {0196-5204}, CODEN = {SIJCD4}, MRCLASS = {65F25 (65F15)}, MRNUMBER = {MR740857 (85h:65086)}, MRREVIEWER = {G. C. Barozzi}, } @ARTICLE {Stew:67, author = "G.W. {Stewart}", title = "A modification of {D}avidon's method to accept difference approximations of derivatives", journal = "J. Assoc. Comput. Mach.", year = "1967", volume = "14", pages = "72-83"} @ARTICLE {Stew:69, author = "G.W. {Stewart}", title = "On the continuity of the generalized inverse", journal = "SIAM J. Appl. Math.", year = "1969", volume = "17", pages = "33-45"} @BOOK {Stew:73, author = "G.W. {Stewart}", title = "Introduction to Matrix Computations", publisher = "Academic Press", year = "1973", address = "New York, NY"} @article{stew:89, author = "G.W. Stewart", year = "1989", title = "On Scaled Projections and Pseudo-Inverses", journal = laa, volume = "112", pages = "189--194", kwds = "la, projection, ginv" } @TECHREPORT {StewSch:92, author = "E. SCHR{\"O}DER", title = "On infinitely many algorithms for solving equations", institution = "University of Maryland", address = "College Park, MD", year = "1992", number = "TR-92-121", note = "translation of 1870 paper by G.W. Stewart" } @ARTICLE {splinebib:97, author = "Larry Schumaker and Carl de Boor", title = "Spline Bibliography", journal = "URL: http://www.cs.wisc.edu/~deboor/bib/bib.html", year = "1997", volume = "email: deboor@cs.wisc.edu", pages = " "} @incollection {MR2203286, AUTHOR = {Srebro, N. and Shraibman, A.}, TITLE = {Rank, trace-norm and max-norm}, BOOKTITLE = {Learning theory}, SERIES = {Lecture Notes in Comput. Sci.}, VOLUME = {3559}, PAGES = {545--560}, PUBLISHER = {Springer, Berlin}, YEAR = {2005}, MRCLASS = {15A03 (15A60 62H25 68Q32 68T05)}, MRNUMBER = {2203286}, DOI = {10.1007/11503415_37}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/11503415_37}, } @book {MR2717223, AUTHOR = {Srebro, N.}, TITLE = {Learning with matrix factorizations}, NOTE = {Thesis (Ph.D.)--Massachusetts Institute of Technology}, PUBLISHER = {ProQuest LLC, Ann Arbor, MI}, YEAR = {2004}, PAGES = {(no paging)}, MRCLASS = {Thesis}, MRNUMBER = {2717223}, URL = {http://gateway.proquest.com.proxy.lib.uwaterloo.ca/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:0807530}, } @article {MR2258634, AUTHOR = {STANCU-MINASIAN, I. M.}, TITLE = {A sixth bibliography of fractional programming}, JOURNAL = {Optimization}, FJOURNAL = {Optimization. A Journal of Mathematical Programming and Operations Research}, VOLUME = {55}, YEAR = {2006}, NUMBER = {4}, PAGES = {405--428}, ISSN = {0233-1934}, MRCLASS = {90-00 (00A15 90C32)}, MRNUMBER = {MR2258634 (2007d:90001)}, } @ARTICLE {Stief:35, author = "E. STIEFEL", title = "Richtungsfelder und fernparallelismus in $n$-dimensionalem mannig faltigkeiten", journal = "Commentarii Math. Helvetici", year = "1935-36", volume = "8", pages = "305-353"} @ARTICLE {Stin:74, author = "R.W. STINEMAN", title = "Calculation of a constrained minimal symmetric matrix", journal = "SIAM J. Appl. Math.", year = "1974", volume = "27", pages = "500-502"} @ARTICLE {Stoe:75, author = "J. STOER", title = "On the convergence rate of imperfect minimization algorithms in {B}royden's $\beta$ class", journal = "Math. Prog.", year = "1975", volume = "9", pages = "313-335"} @INCOLLECTION {St:85, author = "J. STOER", title = "Principles of sequential quadratic programming methods for solving nonlinear programs", booktitle = "Computational Mathematical Programming", publisher = "Springer-Verlag", year = "1985", editor = "K. Schittkowski", pages = "165-207", address = "Berlin"} @BOOK {StoBul:80, author = "J. Stoer and R. Bulirsch", title = "Introduction to Numerical Analysis", publisher = "Springer-Verlag", year = "1980", address = "New York, NY"} @BOOK {StoWit:70, author = "J. Stoer and C. Witzgall", title = "Convexity and Optimization in Finite Dimensions", publisher = "Springer", year = "1970", address = "Berlin-Heidelberg-New York"} @article{stoll:582, author = {M. Stoll and A. Wathen}, collaboration = {}, title = {Combination Preconditioning and the Bramble--Pasciak$^{+}$ Preconditioner}, publisher = {SIAM}, year = {2008}, journal = {SIAM Journal on Matrix Analysis and Applications}, volume = {30}, number = {2}, pages = {582-608}, keywords = {linear systems; Krylov subspaces; nonstandard inner products}, url = {http://link.aip.org/link/?SML/30/582/1}, doi = {10.1137/070688961} } @ARTICLE{2016arXiv161205664S, author = {{Stott}, N.}, title = "{Maximal lower bounds in the L$\backslash$``owner order}", journal = {ArXiv e-prints}, archivePrefix = "arXiv", eprint = {1612.05664}, primaryClass = "math.RA", keywords = {Mathematics - Rings and Algebras, Mathematics - Functional Analysis, Mathematics - Operator Algebras}, year = 2016, month = dec, adsurl = {http://adsabs.harvard.edu/abs/2016arXiv161205664S}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } @BOOK {Stra:76, author = "G. Strang", title = laa, publisher = "Academic Press", year = "1976", address = "New York, NY"} @BOOK {Stra:93, author = "G. Strang", title = "Introduction to Linear Algebra", publisher = "Wellesley-Cambridge Press", year = "1993", address = "Wellesley, MA"} @TECHREPORT {LoSturmfelsVi:11, author = "J.A. De Loera and B. Sturmfels and C. Vinzant", title = "The central curve in linear programming", institution = "Department of Mathematics, University of California", year = "2011", number = "arXiv:1012.3978v2", address = "Berkeley and Davis, CA"} @inproceedings {MR3451047, AUTHOR = {Di Summa, M. and Eisenbrand, F. and Faenza, Y. and Moldenhauer, C.}, TITLE = {On largest volume simplices and sub-determinants}, BOOKTITLE = {Proceedings of the {T}wenty-{S}ixth {A}nnual {ACM}-{SIAM} {S}ymposium on {D}iscrete {A}lgorithms}, PAGES = {315--323}, PUBLISHER = {SIAM, Philadelphia, PA}, YEAR = {2015}, MRCLASS = {68U05 (52A38 68W25)}, MRNUMBER = {3451047}, DOI = {10.1137/1.9781611973730.23}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/1.9781611973730.23}, } @TECHREPORT {Sunsqr:95, author = "C. SUN", title = "Dealing with dense rows in the solution of sparse linear least squares problems", institution = "Department of Computer Science, Cornell University", year = "1995", number = "TR95-227", address = "Ithaca, NY"} @INCOLLECTION {Swa:72, author = "W.H. SWANN", title = "Direct search methods", booktitle = "Numerical Methods for Unconstrained Optimization", publisher = "Academic Press", year = "1972", editor = "W. Murray", pages = "13-18", address = "London and New York"} @article{Swartz:1982, Author = {SWARTZ, C.}, Journal = {Applicable Analysis: An International Journal}, Number = {2}, Pages = {155--159}, Title = {Images of cones under linear mappings}, Volume = {14}, Year = {1982}} %TTTTTTTTTTTTTTTTTTTT @article{TAM20101734, title = {On the reduced signless {L}aplacian spectrum of a degree maximal graph}, journal = {Linear Algebra and its Applications}, volume = {432}, number = {7}, pages = {1734-1756}, year = {2010}, issn = {0024-3795}, doi = {https://doi.org/10.1016/j.laa.2009.11.031}, url = {https://www.sciencedirect.com/science/article/pii/S0024379509006119}, author = {B.S. Tam and S.H. Wu}, keywords = {Degree maximal graph, Reduced signless Laplacian, Signless Laplacian spectrum, Characteristic polynomial, Neighborhood equivalence class}, abstract = {For a (simple) graph G, the signless Laplacian of G is the matrix A(G)+D(G), where A(G) is the adjacency matrix and D(G) is the diagonal matrix of vertex degrees of G; the reduced signless Laplacian of G is the matrix Δ(G)+B(G), where B(G) is the reduced adjacency matrix of G and Δ(G) is the diagonal matrix whose diagonal entries are the common degrees for vertices belonging to the same neighborhood equivalence class of G. A graph is said to be (degree) maximal if it is connected and its degree sequence is not majorized by the degree sequence of any other connected graph. For a maximal graph, we obtain a formula for the characteristic polynomial of its reduced signless Laplacian and use the formula to derive a localization result for its reduced signless Laplacian eigenvalues, and to compare the signless Laplacian spectral radii of two well-known maximal graphs. We also obtain a necessary condition for a maximal graph to have maximal signless Laplacian spectral radius among all connected graphs with given numbers of vertices and edges.} } @article {MR86k:65045, AUTHOR = {TANABE, K.}, TITLE = {Global analysis of continuous analogues of the {L}evenberg-{M}arquardt and {N}ewton-{R}aphson methods for solving nonlinear equations}, JOURNAL = {Ann. Inst. Statist. Math.}, FJOURNAL = {Annals of the Institute of Statistical Mathematics}, VOLUME = {37}, YEAR = {1985}, NUMBER = {1}, PAGES = {189--203}, ISSN = {0020-3157}, CODEN = {AISXAD}, MRCLASS = {65H10 (58C30)}, MRNUMBER = {86k:65045}, MRREVIEWER = {G. D. Maystrovsky}, } @article {MR2119311, AUTHOR = {An, L..H. and Tao, P.D.}, TITLE = {The {DC} (difference of convex functions) programming and {DCA} revisited with {DC} models of real world nonconvex optimization problems}, JOURNAL = {Ann. Oper. Res.}, FJOURNAL = {Annals of Operations Research}, VOLUME = {133}, YEAR = {2005}, PAGES = {23--46}, ISSN = {0254-5330}, MRCLASS = {90C90 (90C26)}, MRNUMBER = {2119311}, DOI = {10.1007/s10479-004-5022-1}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s10479-004-5022-1}, } @article {TaoAn:95, AUTHOR = {Tao, P.D. and An, L.T.H.}, TITLE = {Difference of convex functions optimization algorithms ({DCA}) for globally minimizing nonconvex quadratic forms on {E}uclidean balls and spheres}, JOURNAL = {Oper. Res. Lett.}, FJOURNAL = {Operations Research Letters}, VOLUME = {19}, YEAR = {1996}, NUMBER = {5}, PAGES = {207--216}, ISSN = {0167-6377}, CODEN = {ORLED5}, MRCLASS = {90C26 (65K05)}, MRNUMBER = {1421026 (97i:90055)}, DOI = {10.1016/S0167-6377(96)00036-3}, URL = {http://dx.doi.org/10.1016/S0167-6377(96)00036-3}, } @ARTICLE {Tapia:74a, author = "R.A. Tapia", title = "{N}ewton's method for problems with equality constraints", journal = "SIAM J. Numer. Anal.", year = "1974", volume = "11", pages = "174-196"} @ARTICLE {Tapia:74b, author = "R.A. Tapia", title = "{N}ewton's method for optimization problems with equality constraints", journal = "SIAM J. Numer. Anal.", year = "1974", volume = "11", pages = "874-886"} @ARTICLE {Tapia:77, author = "R.A. Tapia", title = "Diagonalized multiplier methods and quasi-{N}ewton methods for constrained optimization", journal = "J. Optim. Theory Appl.", year = "1977", volume = "22", number = "2", pages = "135-194"} @INCOLLECTION {Tapia:78, author = "R.A. Tapia", title = "Quasi-{N}ewton methods for equality constrained optimization: equivalence of existing methods and a new implementation", booktitle = "Nonlinear Programming 3", publisher = "Academic Press", year = "1978", editor = "O.L. Mangasarian and R.R. Meyer and S.M. Robinson", pages = "125-164", address = "New York, NY"} @INCOLLECTION {Tapia:80, author = "R.A. Tapia", title = "On the role of slack variables in quasi-{Ne}wton methods for constrained optimization", booktitle = "Numerical Optimization of Dynamical Systems", publisher = "North-Holland", year = "1980", editor = "L.C.W. Dixon and T.P. Szego", pages = "235-246", address = "Amsterdam"} @TECHREPORT {Tapia:84a, author = "R.A. Tapia", title = "On the characterization of {Q}-superlinear convergence of quasi-{N}ewton methods for constrained optimization", institution = "Department of Mathematical Sciences, Rice University", year = "1984", number = "TR84-2", address = "Houston, TX"} @TECHREPORT {Tapia:84b, author = "R.A. Tapia", title = "On secant updates for use in general constrained optimization", institution = "Department of Mathematical Sciences, Rice University", year = "1984", number = "TR84-3", address = "Houston, TX", note = "Revised in January, 1987"} @article {MR2890931, AUTHOR = {Kurata, H. and Tarazaga, P.}, TITLE = {Majorization for the eigenvalues of {E}uclidean distance matrices}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {436}, YEAR = {2012}, NUMBER = {5}, PAGES = {1473--1481}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15B48 (15A42)}, MRNUMBER = {2890931}, MRREVIEWER = {Tin-Yau Tam}, DOI = {10.1016/j.laa.2011.08.022}, URL = {http://dx.doi.org/10.1016/j.laa.2011.08.022}, } @article {MR2653818, AUTHOR = {Kurata, H. and Tarazaga, P.}, TITLE = {Multispherical {E}uclidean distance matrices}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {433}, YEAR = {2010}, NUMBER = {3}, PAGES = {534--546}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15B57}, MRNUMBER = {2653818 (2011c:15106)}, MRREVIEWER = {Julio Ben{\'{\i}}tez}, DOI = {10.1016/j.laa.2010.03.018}, URL = {http://dx.doi.org/10.1016/j.laa.2010.03.018}, } @article {MR2357790, AUTHOR = {Tarazaga, P. and Sterba-Boatwright, B. and Wijewardena, K.}, TITLE = {Euclidean distance matrices: special subsets, systems of coordinates and multibalanced matrices}, JOURNAL = {Comput. Appl. Math.}, FJOURNAL = {Computational \& Applied Mathematics}, VOLUME = {26}, YEAR = {2007}, NUMBER = {3}, PAGES = {415--438}, ISSN = {0101-8205}, MRCLASS = {15A57}, MRNUMBER = {2357790 (2008m:15061)}, MRREVIEWER = {Oskar Maria Baksalary}, DOI = {10.1590/S0101-82052007000300006}, URL = {http://dx.doi.org/10.1590/S0101-82052007000300006}, } @inproceedings {MR1159330, AUTHOR = {Tardos, E.}, TITLE = {Strongly polynomial and combinatorial algorithms in optimization}, BOOKTITLE = {Proceedings of the {I}nternational {C}ongress of {M}athematicians, {V}ol.\ {I}, {II} ({K}yoto, 1990)}, PAGES = {1467--1478}, PUBLISHER = {Math. Soc. Japan}, ADDRESS = {Tokyo}, YEAR = {1991}, MRCLASS = {90C27 (90C35 90C60)}, MRNUMBER = {1159330 (94b:90062)}, MRREVIEWER = {Michael A. Trick}, } @article {MR861043, AUTHOR = {Tardos, E.}, TITLE = {A strongly polynomial algorithm to solve combinatorial linear programs}, JOURNAL = {Oper. Res.}, FJOURNAL = {Operations Research}, VOLUME = {34}, YEAR = {1986}, NUMBER = {2}, PAGES = {250--256}, ISSN = {0030-364X}, CODEN = {OPREAI}, MRCLASS = {90C05}, MRNUMBER = {861043 (87i:90151)}, DOI = {10.1287/opre.34.2.250}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1287/opre.34.2.250}, } @article {MR1412749, AUTHOR = {Hayden, T. L. and Lee, Jon and Wells, J. and Tarazaga, P.}, TITLE = {Block matrices and multispherical structure of distance matrices}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {247}, YEAR = {1996}, PAGES = {203--216}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A57 (65F10)}, MRNUMBER = {1412749 (97h:15032)}, MRREVIEWER = {Gang Song Leng}, DOI = {10.1016/0024-3795(95)00100-X}, URL = {http://dx.doi.org/10.1016/0024-3795(95)00100-X}, } @article {MR1340702, AUTHOR = {Johnson, C.R. and Tarazaga, P.}, TITLE = {Connections between the real positive semidefinite and distance matrix completion problems}, NOTE = {Special issue honoring Miroslav Fiedler and Vlastimil Pt{\'a}k}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {223/224}, YEAR = {1995}, PAGES = {375--391}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A99 (05C50)}, MRNUMBER = {1340702 (96g:15031)}, MRREVIEWER = {Linda J. Patton}, DOI = {10.1016/0024-3795(95)00096-A}, URL = {http://dx.doi.org/10.1016/0024-3795(95)00096-A}, } @article {MR1081882, AUTHOR = {Hayden, T. L. and Wells, J. and Liu, Wei Min and Tarazaga, P.}, TITLE = {The cone of distance matrices}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {144}, YEAR = {1991}, PAGES = {153--169}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {51K05 (15A48)}, MRNUMBER = {1081882 (91i:51023)}, DOI = {10.1016/0024-3795(91)90068-8}, URL = {http://dx.doi.org/10.1016/0024-3795(91)90068-8}, } @ARTICLE {Ta:91, author = "P. Tarazaga", title = "Eigenvalue bounds", journal = laa, year = "1991", volume = "149", pages = "97-110"} @INCOLLECTION {Taus:67, author = "O. TAUSSKY", title = "Positive definite matrices", booktitle = "Inequalities", publisher = "Academic Press Inc.", address = "New York and London", year = "1967", editor = "O. Shisha"} @article {MR40:2697, AUTHOR = {Duke, John W.}, TITLE = {A note on the similarity of matrix and its conjugate transpose}, JOURNAL = {Pacific J. Math.}, VOLUME = {31}, YEAR = {1969}, PAGES = {321--323}, MRCLASS = {15.30}, MRNUMBER = {40 #2697}, MRREVR = {G. E. Wall}, } @article {MR21:7216, AUTHOR = {Taussky, Olga and Zassenhaus, Hans}, TITLE = {On the similarity transformation between a matirx and its transpose. }, JOURNAL = {Pacific J. Math.}, VOLUME = {9}, YEAR = {1959}, PAGES = {893--896}, MRCLASS = {15.00}, MRNUMBER = {21 #7216}, MRREVR = {H. K. Farahat}, } @article {MR1733549, AUTHOR = {Solomon, Louis}, TITLE = {Similarity of the companion matrix and its transpose}, NOTE = {Special issue dedicated to Hans Schneider (Madison, WI, 1998)}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {302/303}, YEAR = {1999}, PAGES = {555--561}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A21}, MRNUMBER = {1 733 549}, } @ARTICLE {TeThZi:66a, author = "J. TELGEN and G.L. THOMPSON and S. ZIONTS", title = "Techniques for removing nonbinding constraints and extraneaous variables from linear programming problems", journal = "Management Sci.", year = "1966", volume = "12", pages = "588"} @ARTICLE {TeThZi:66b, author = "J. TELGEN and G.L. THOMPSON and S. ZIONTS", title = "Redundancy and linear programs", journal = "Math. Centre Tracts", year = "1966", volume = "137"} @ARTICLE {Telg:79, author = "J. TELGEN", title = "On {R.W. L}lewellyn's rules to identify redundant constraints: a detailed critique and some generalizations", journal = "Z. Oper. Res.", year = "1979", volume = "23", pages = "197"} @ARTICLE {Telg:81, author = "J. TELGEN", title = "Redundancy and linear programs", journal = "Math. Centre Tracts", year = "1981", volume = "137"} @article {MR2338358, AUTHOR = {Hadigheh, A.G. and Terlaky, T. and Romanko, O.}, TITLE = {Sensitivity analysis in convex quadratic optimization: simultaneous perturbation of the objective and right-hand-side vectors}, JOURNAL = {Algorithmic Oper. Res.}, FJOURNAL = {Algorithmic Operations Research}, VOLUME = {2}, YEAR = {2007}, NUMBER = {2}, PAGES = {94--111}, ISSN = {1718-3235}, MRCLASS = {90C31 (90C05 90C20 90C25)}, MRNUMBER = {MR2338358 (2008h:90103)}, MRREVIEWER = {Alexander Engau}, } @article {MR2174011, AUTHOR = {Hadigheh, A.G. and Terlaky, T.}, TITLE = {Sensitivity analysis in linear optimization: invariant support set intervals}, JOURNAL = {European J. Oper. Res.}, FJOURNAL = {European Journal of Operational Research}, VOLUME = {169}, YEAR = {2006}, NUMBER = {3}, PAGES = {1158--1175}, ISSN = {0377-2217}, CODEN = {EJORDT}, MRCLASS = {90C31 (90C05)}, MRNUMBER = {MR2174011 (2006e:90128)}, MRREVIEWER = {S. Zlobec}, DOI = {10.1016/j.ejor.2004.09.058}, URL = {http://dx.doi.org/10.1016/j.ejor.2004.09.058}, } incollection {MR2503774, AUTHOR = {Deza, A. and Xie, F.}, TITLE = {Hyperplane arrangements with large average diameter}, BOOKTITLE = {Polyhedral computation}, SERIES = {CRM Proc. Lecture Notes}, VOLUME = {48}, PAGES = {103--114}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {2009}, MRCLASS = {52C35 (90C05)}, MRNUMBER = {2503774 (2010h:52041)}, } @techreport{DezaMorMiyXie:10, author = "A. Deza and S. Moriyama and F. Xie", title = "Hyperplane arrangements with large average diaemter: a computational approach", institution = "Department of Computer Science", year = 2010, number = "Advanced Studies in Pure Mathematics", address = "to appear" } @incollection {MR3971979, AUTHOR = {Moursi, W.M. and Zinchenko, Y.}, TITLE = {A note on the equivalence of operator splitting methods}, BOOKTITLE = {Splitting algorithms, modern operator theory, and applications}, PAGES = {331--349}, PUBLISHER = {Springer, Cham}, YEAR = {[2019] \copyright 2019}, MRCLASS = {47H05 (49M27 49M29 49N15 90C25 90C48)}, MRNUMBER = {3971979}, } @article {MR2471877, AUTHOR = {Deza, A. and Terlaky, T. and Zinchenko, Yuriy}, TITLE = {A continuous {$d$}-step conjecture for polytopes}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {41}, YEAR = {2009}, NUMBER = {2}, PAGES = {318--327}, ISSN = {0179-5376}, CODEN = {DCGEER}, MRCLASS = {52B12 (52A40)}, MRNUMBER = {2471877 (2010e:52022)}, DOI = {10.1007/s00454-008-9096-4}, URL = {http://dx.doi.org/10.1007/s00454-008-9096-4}, } @article {MR2396599, AUTHOR = {Deza, A. and Terlaky, T. and Zinchenko, Yuriy}, TITLE = {Polytopes and arrangements: diameter and curvature}, JOURNAL = {Oper. Res. Lett.}, FJOURNAL = {Operations Research Letters}, VOLUME = {36}, YEAR = {2008}, NUMBER = {2}, PAGES = {215--222}, ISSN = {0167-6377}, CODEN = {ORLED5}, MRCLASS = {52C35 (90C57)}, MRNUMBER = {2396599 (2009b:52059)}, DOI = {10.1016/j.orl.2007.06.007}, URL = {http://dx.doi.org/10.1016/j.orl.2007.06.007}, } %%%%%%%%%%%%%colourful papers - colourful simplex e.g. by Deza et al @article {MR1467385, AUTHOR = {B{\'a}r{\'a}ny, I. and Onn, S.}, TITLE = {Colourful linear programming and its relatives}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {22}, YEAR = {1997}, NUMBER = {3}, PAGES = {550--567}, ISSN = {0364-765X}, MRCLASS = {90C08 (68Q25)}, MRNUMBER = {1467385 (99g:90069)}, DOI = {10.1287/moor.22.3.550}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1287/moor.22.3.550}, } @incollection {MR1441787, AUTHOR = {B{\'a}r{\'a}ny, I. and Onn, S.}, TITLE = {Colourful linear programming}, BOOKTITLE = {Integer programming and combinatorial optimization ({V}ancouver, {BC}, 1996)}, SERIES = {Lecture Notes in Comput. Sci.}, VOLUME = {1084}, PAGES = {1--15}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1996}, MRCLASS = {90C08}, MRNUMBER = {1441787 (98b:90087)}, DOI = {10.1007/3-540-61310-2_1}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/3-540-61310-2_1}, } @article {MR3041975, AUTHOR = {Deza, A. and Stephen, T. and Xie, F.}, TITLE = {A note on lower bounds for colourful simplicial depth}, JOURNAL = {Symmetry}, FJOURNAL = {Symmetry}, VOLUME = {5}, YEAR = {2013}, NUMBER = {1}, PAGES = {47--53}, ISSN = {2073-8994}, MRCLASS = {52C10 (05D05 52A35 52B05)}, MRNUMBER = {3041975}, DOI = {10.3390/sym5010047}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.3390/sym5010047}, } @article {MR3035020, AUTHOR = {Simonyi, G. and Tardif, C. and Zsb{\'a}n, A.}, TITLE = {Colourful theorems and indices of homomorphism complexes}, JOURNAL = {Electron. J. Combin.}, FJOURNAL = {Electronic Journal of Combinatorics}, VOLUME = {20}, YEAR = {2013}, NUMBER = {1}, PAGES = {Paper 10, 15}, ISSN = {1077-8926}, MRCLASS = {05C15 (05C60)}, MRNUMBER = {3035020}, MRREVIEWER = {Erika {\v{S}}krabul'{\'a}kov{\'a}}, } @article {MR2765529, AUTHOR = {Deza, A. and Stephen, T. and Xie, F.}, TITLE = {More colourful simplices}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {45}, YEAR = {2011}, NUMBER = {2}, PAGES = {272--278}, ISSN = {0179-5376}, CODEN = {DCGEER}, MRCLASS = {52A35}, MRNUMBER = {2765529 (2012b:52009)}, MRREVIEWER = {Marilyn Breen}, DOI = {10.1007/s00454-010-9291-y}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s00454-010-9291-y}, } @article {MR2447951, AUTHOR = {Stephen, T. and Thomas, H.}, TITLE = {A quadratic lower bound for colourful simplicial depth}, JOURNAL = {J. Comb. Optim.}, FJOURNAL = {Journal of Combinatorial Optimization}, VOLUME = {16}, YEAR = {2008}, NUMBER = {4}, PAGES = {324--327}, ISSN = {1382-6905}, MRCLASS = {52B55 (90C57)}, MRNUMBER = {2447951 (2009m:52031)}, DOI = {10.1007/s10878-008-9149-x}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s10878-008-9149-x}, } @article {MR2437008, AUTHOR = {Deza, A. and Huang, S. and Stephen, T. and Terlaky, T.}, TITLE = {The colourful feasibility problem}, JOURNAL = {Discrete Appl. Math.}, FJOURNAL = {Discrete Applied Mathematics. The Journal of Combinatorial Algorithms, Informatics and Computational Sciences}, VOLUME = {156}, YEAR = {2008}, NUMBER = {11}, PAGES = {2166--2177}, ISSN = {0166-218X}, CODEN = {DAMADU}, MRCLASS = {68W40 (68Q25 90C60)}, MRNUMBER = {2437008 (2009k:68286)}, DOI = {10.1016/j.dam.2008.01.016}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/j.dam.2008.01.016}, } @article {MR2225675, AUTHOR = {Deza, A. and Huang, S. and Stephen, T. and Terlaky, T.}, TITLE = {Colourful simplicial depth}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {35}, YEAR = {2006}, NUMBER = {4}, PAGES = {597--615}, ISSN = {0179-5376}, CODEN = {DCGEER}, MRCLASS = {52B05 (05D05)}, MRNUMBER = {2225675 (2007d:52012)}, MRREVIEWER = {Jen{\H{o}} Lehel}, DOI = {10.1007/s00454-006-1233-3}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s00454-006-1233-3}, } @incollection {MR1470753, AUTHOR = {B{\'a}r{\'a}ny, I. and Onn, S.}, TITLE = {Carath\'eodory's theorem, colourful and applicable}, BOOKTITLE = {Intuitive geometry ({B}udapest, 1995)}, SERIES = {Bolyai Soc. Math. Stud.}, VOLUME = {6}, PAGES = {11--21}, PUBLISHER = {J\'anos Bolyai Math. Soc.}, ADDRESS = {Budapest}, YEAR = {1997}, MRCLASS = {52A35 (52B55)}, MRNUMBER = {1470753 (98f:52005)}, MRREVIEWER = {Rade {\v{Z}}ivaljevi{\'c}}, } %%%%%%%%%%%%%%%%%%%%%%%%%%%%end colourful simplices @article {MR2437263, AUTHOR = {Nematollahi, E. and Terlaky, T.}, TITLE = {A redundant {K}lee-{M}inty construction with all the redundant constraints touching the feasible region}, JOURNAL = {Oper. Res. Lett.}, FJOURNAL = {Operations Research Letters}, VOLUME = {36}, YEAR = {2008}, NUMBER = {4}, PAGES = {414--418}, ISSN = {0167-6377}, CODEN = {ORLED5}, MRCLASS = {90C05 (90C49)}, MRNUMBER = {2437263 (2009j:90068)}, MRREVIEWER = {James Andrew J. Hall}, DOI = {10.1016/j.orl.2008.02.004}, URL = {http://dx.doi.org/10.1016/j.orl.2008.02.004}, } @article {MR2399470, AUTHOR = {Nematollahi, E. and Terlaky, T.}, TITLE = {A simpler and tighter redundant {K}lee-{M}inty construction}, JOURNAL = {Optim. Lett.}, FJOURNAL = {Optimization Letters}, VOLUME = {2}, YEAR = {2008}, NUMBER = {3}, PAGES = {403--414}, ISSN = {1862-4472}, MRCLASS = {90C05}, MRNUMBER = {2399470 (2009b:90063)}, MRREVIEWER = {James Andrew J. Hall}, DOI = {10.1007/s11590-007-0068-z}, URL = {http://dx.doi.org/10.1007/s11590-007-0068-z}, } @article {MR2367063, AUTHOR = {Deza, A. and Nematollahi, E. and Terlaky, T.}, TITLE = {How good are interior point methods? {K}lee-{M}inty cubes tighten iteration-complexity bounds}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {113}, YEAR = {2008}, NUMBER = {1, Ser. A}, PAGES = {1--14}, ISSN = {0025-5610}, MRCLASS = {90C05 (90C51 90C60)}, MRNUMBER = {2367063 (2008i:90038)}, DOI = {10.1007/s10107-006-0044-x}, URL = {http://dx.doi.org/10.1007/s10107-006-0044-x}, } @article {MR2238662, AUTHOR = {Deza, A. and Nematollahi, E. and Peyghami, R. and Terlaky, T.}, TITLE = {The central path visits all the vertices of the {K}lee-{M}inty cube}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods \& Software}, VOLUME = {21}, YEAR = {2006}, NUMBER = {5}, PAGES = {851--865}, ISSN = {1055-6788}, MRCLASS = {90C05 (90C51 90C60)}, MRNUMBER = {2238662 (2007d:90051)}, DOI = {10.1080/10556780500407725}, URL = {http://dx.doi.org/10.1080/10556780500407725}, } @book {Terl:96, TITLE = {Interior point methods of mathematical programming}, EDITOR = {Terlaky, T.}, PUBLISHER = {Kluwer Academic Publishers}, ADDRESS = {Dordrecht}, YEAR = {1996}, PAGES = {xxii+528}, ISBN = {0-7923-4201-1}, MRCLASS = {90-06 (65K05 90C05 90C30)}, MRNUMBER = {99a:90005}, MRREVR = {Yin Zhang}, } @ARTICLE {Terl:85, author = "T. Terlaky", title = "On $l_p$ programming", journal = ejor, year = "1985", volume = "22", pages = "70--100"} @ARTICLE {Thib:82, author = "L. THIBAULT", title = "Sudifferentials of nonconvex vector-valued functions", journal = "J. Math. Anal. Appl.", year = "1982", volume = "86", pages = "319-344"} @TECHREPORT {Thom:75, author = "S.W. THOMAS", title = "Sequential estimation techniques for quasi-{N}ewton algorithms", institution = "Department of Computer Science, Cornell University", year = "1975", number = "TR75-227", address = "Ithaca, NY"} @article {MR54:12805, AUTHOR = {THOMPSON, R.C.}, TITLE = {Singular values, diagonal elements, and convexity}, JOURNAL = {SIAM J. Appl. Math.}, VOLUME = {32}, YEAR = {1977}, NUMBER = {1}, PAGES = {39--63}, MRCLASS = {15A18 (65F15)}, MRNUMBER = {54 \#12805}, MRREVIEWER = {L. Mirsky}, } @BOOK {Tiel:76, author = "J. VAN TIEL", title = "Convex Analysis: An Introductory Text", publisher = "John Wiley and Sons", year = "1976", address = "New York, NY"} @BOOK {TiAr:77, author = "A.N. Tikhonov and V.Y. Arsenin", title = "Solutions of Ill-Posed Problems", publisher = " V.H. Winston \& Sons, John Wiley \& Sons", year = "1977", note = "Translation editor Fritz John", address = "Washington D.C."} @article {Tit:75, AUTHOR = {TITTERINGTON, D.M.}, TITLE = {Optimal design: some geometrical aspects of ${D}$-optimality}, JOURNAL = {Biometrika}, VOLUME = {62}, YEAR = {1975}, NUMBER = {2}, PAGES = {313--320}, } @ARTICLE{PaTi:93, AUTHOR = "E.R. PANIER and A.L. TITS", TITLE = "On combining feasibility, descent and superlinear convergence in inequality constrained optimization", JOURNAL = mprog, VOLUME = 59, YEAR = 1993, PAGES = "261-276" } @ARTICLE {To:92, author = "M.J. Todd", title = "A low complexity interior-point algorithm for linear programming", journal = siopt, year = "1992", volume = "2", pages = "198-209"} @ARTICLE {Todd:93b, author = "M.J. Todd", title = "Scaling, Shifting and Weighting in Interior-Point Methods", journal = "Computational Optimization and Applications", year = "1994", volume = "3", pages = "305-315"} @ARTICLE {Todd:93, author = "M.J. Todd and Y. YE", TITLE = {Approximate {F}arkas lemmas and stopping rules for iterative infeasible-point algorithms for linear programming}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {81}, YEAR = {1998}, NUMBER = {1, Ser. A}, PAGES = {1--21}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C05 (46N10)}, MRNUMBER = {MR1617705 (99h:90064)}, MRREVIEWER = {Levent Tun{\c{c}}el}, } @ARTICLE {Toin:77, author = "Ph.L. Toint", title = "On sparse and symmetric matrix updating subject to a linear equation", journal = "Math. Comp.", year = "1977", volume = "31", pages = "954-961"} @ARTICLE {Toin:78, author = "Ph.L. Toint", title = "Some numerical results using a sparse matrix updating formula in unconstrained optimization", journal = "Math. Comp.", year = "1978", volume = "32", pages = "839-851"} @ARTICLE {Toin:81, author = "Ph.L. Toint", title = "A sparse quasi-{N}ewton update derived variationally with a non-diagonally weighted {F}robenius norm", journal = "Math. Comp.", year = "1978", volume = "37", pages = "425-434"} @TECHREPORT {Toin:84, author = "Ph.L. Toint", title = "Numerical solution of large sets of algebraic nonlinear equations", institution = "Depart\'{e}ment de Math\'{e}matique, Facult\'{e}s Universitaires de Namur", year = "1984", number = "84/9", address = "Belgium"} @TECHREPORT {Toin:94, author = "Ph.L. Toint", title = "An assessment of non-monotone linesearch techniques for unconstrained optimization: the complete numerical results", institution = "Depart\'{e}ment de Math\'{e}matique, Facult\'{e}s Universitaires de Namur", year = "1994", keywords = "nlop", number = "TR94-15", address = "Belgium"} @incollection {Tomlin:89, AUTHOR = {TOMLIN, J. A.}, TITLE = {The influences of algorithmic and hardware developments on computational mathematical programming}, BOOKTITLE = {Mathematical programming (Tokyo, 1988)}, PAGES = {159--175}, SERIES = {Math. Appl. (Japanese Ser.)}, VOLUME = {6}, PUBLISHER = {KTK Scientific}, ADDRESS = {Tokyo}, YEAR = {1989}, } @ARTICLE {ToVe:67, author = "D.M. TOPKIS and A.F. VEINOTT", title = "On the convergenceof some feasible direction algorithms for nonlinear programming", journal = "SIAM J. Control", year = "1967", volume = "5", pages = "268-279"} @ARTICLE {TsUh:91, author = "N. TSING and F. UHLIG", title = "Inertia, numerical range, and zeros of quadratic forms for matrix pencils", journal = simax, year = "1991", volume = "12", pages = "146-159"} @TECHREPORT {Tu:92a, author = "L. TUN{\c{C}}EL", title = "A note on the primal-dual affine scaling algorithms", institution = "Cornell University", year = "1992", number = "TR 1004", address = "Ithaca, NY"} @TECHREPORT {Tu:92c, author = "L. TUN{\c{C}}EL", title = "On the Convergence of Primal-Dual Interior-Point Methods with Wide Neighborhoods", institution = "Cornell University", year = "1992", number = "TR 1003", address = "Ithaca, NY"} @book {MR54:14769, TITLE = {Pivoting and extensions}, EDITOR = {Balinski, M. L.}, NOTE = {In honor of A. W. Tucker, Math. Programming Stud. No. 1. (1974)}, PUBLISHER = {North-Holland Publishing Co.}, ADDRESS = {Amsterdam}, YEAR = {1974}, PAGES = {vii+205 pp. (1 plate)}, MRCLASS = {90CXX}, MRNUMBER = {54 \#14769}, } @TECHREPORT {Tu:92b, author = "L. TUN{\c{C}}EL", title = "On the Convergence of Primal-Dual Interior Point Methods with Wide Neighborhoods", institution = "Cornell University", year = "1992", number = "TR 1003", address = "Ithaca, NY"} @book {MR2003e:62004, AUTHOR = {TURKINGTON, D.A.}, TITLE = {Matrix calculus and zero-one matrices}, NOTE = {Statistical and econometric applications}, PUBLISHER = {Cambridge University Press}, ADDRESS = {New York}, YEAR = {2002}, PAGES = {xii+206}, ISBN = {0-521-80788-3}, MRCLASS = {62-02 (15-02 62J05 62M10 62P20 91B82)}, MRNUMBER = {2003e:62004}, MRREVIEWER = {A. L. Nagar}, } @article {MR2103763, AUTHOR = {T\"{u}t\"{u}nc\"{u}, R.H. and Koenig, M.}, TITLE = {Robust asset allocation}, JOURNAL = {Ann. Oper. Res.}, FJOURNAL = {Annals of Operations Research}, VOLUME = {132}, YEAR = {2004}, PAGES = {157--187}, ISSN = {0254-5330}, MRCLASS = {91B28 (90C15 91B32)}, MRNUMBER = {MR2103763 (2005g:91113)}, MRREVIEWER = {Kurt Marti}, } @incollection{Tuy:95, author = "H. TUY", title = "{D.C.} optimization: Theory, Methods and Algorithms", booktitle = "Handbook of Global Optimization", editor = "R. Horst and P.M. Pardalos", Publisher="Kluwer Academic Publishers", ADDRESS = {Boston, MA}, pages = {149-216}, year = "1995" } %UUUUUUUUUUUUUU @article {MR0352147, author = "F. UHLIG", TITLE = {Definite and semidefinite matrices in a real symmetric matrix pencil}, JOURNAL = {Pacific J. Math.}, FJOURNAL = {Pacific Journal of Mathematics}, VOLUME = {49}, YEAR = {1973}, PAGES = {561--568}, ISSN = {0030-8730}, MRCLASS = {15A48}, MRNUMBER = {MR0352147 (50 \#4634)}, MRREVIEWER = {Marvin Marcus}, } @ARTICLE {Uh:79, author = "F. UHLIG", title = "A recurring theorem about pairs of quadratic forms and extensions: A survey", journal = laa, year = "1970", volume = "25", pages = "219-237"} @TECHREPORT {UrbTitsLaw:98, author = "T. URBAN, A. TITS and C.T. LAWRENCE", title = "A Primal-Dual Interior-Point Method for Nonconvex Optimization with Multiple Logarithmic Barrier Parameters and with Strong Convergence Properties", institution = "University of Maryland", year = "1998"} %VVVVVVVVV @article {MR1778427, author = "R.J. Vanderbei", TITLE = {L{O}{Q}{O} user's manual---version 3.10}, NOTE = {Interior point methods}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods and Software}, VOLUME = {11/12}, YEAR = {1999}, NUMBER = {1-4}, PAGES = {485--514}, ISSN = {1055-6788}, CODEN = {OMSOE2}, MRCLASS = {90C51 (90-04)}, MRNUMBER = {1 778 427}, } @article {Vanderbei:94, author = "R.J. Vanderbei", TITLE = {L{O}{Q}{O}: an interior point code for quadratic programming}, NOTE = {Interior point methods}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods and Software}, VOLUME = {11/12}, YEAR = {1999}, NUMBER = {1-4}, PAGES = {451--484}, ISSN = {1055-6788}, CODEN = {OMSOE2}, MRCLASS = {90C20 (90-04 90C51)}, MRNUMBER = {1 778 426}, } @BOOK {Vanderbei:98, author = "R.J. Vanderbei", title = "Linear Programming: Foundations and Extensions", PUBLISHER = {Kluwer Acad. Publ.}, ADDRESS = {Dordrecht}, year = "1998"} @BOOK {Vanderbei:2004, author = "R.J. Vanderbei", title = "The Amateur Astrophotographer", PUBLISHER = {forthcoming}, ADDRESS = { }, year = " . "} @article{int:Vanderbei7, author = "R.J. Vanderbei and M.S. MEKETON and B.A. FREEDMAN", title = "A modification of {K}armarkar's linear programming algorithm", journal = "Algorithmica", volume = "1", number = "4", year = "1986", pages = "395--407" } @TECHREPORT {VandShanno:97, author = "R.J. Vanderbei and D. SHANNO", title = "An Interior Point Algorithm for Nonconvex Nonlinear Programming", institution = "Program in Statistics \& Operations Research, Princeton University", year = "1997", keywords = "nlop,ipg,qp", number = "SOR-97-21", address = "Princeton,NJ"} @ARTICLE {Va:68, author = "J. VANDERGRAFT", title = "Spectral properties of matrices which have invariant cones", journal = "SIAM J. Applied Math.", year = "1968", volume = "16", pages = "1208-1222"} @article {MR1832223, AUTHOR = {Vardi, Y. and Zhang, C.-H.}, TITLE = {A modified {W}eiszfeld algorithm for the {F}ermat-{W}eber location problem}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {90}, YEAR = {2001}, NUMBER = {3, Ser. A}, PAGES = {559--566}, ISSN = {0025-5610}, MRCLASS = {90B85 (65K05 90C90)}, MRNUMBER = {1832223 (2002d:90045)}, MRREVIEWER = {Stefan Nickel}, DOI = {10.1007/PL00011435}, URL = {http://dx.doi.org/10.1007/PL00011435}, } @PHDTHESIS {Var:80, author = "A. VARDI", title = "Trust region strategies for unconstrained and constrained minimization", school = "School of Operations Research and Industrial Engineering, Cornell University", year = "1980", address = "Ithaca, NY"} @article {MR1983210, AUTHOR = {Varah, J.M.}, TITLE = {Positive definite {H}ankel matrices of minimal condition}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {368}, YEAR = {2003}, PAGES = {303--314}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A57}, MRNUMBER = {MR1983210 (2004d:15040)}, MRREVIEWER = {Wen Yu Sun}, } @book{con:70, Address = {Princeton, N.J.}, Author = {Rockafellar, R.T.}, Date-Added = {2013-09-12 18:12:30 -0400}, Date-Modified = {2013-10-23 18:30:20 -0400}, Mrclass = {26.52 (46.00)}, Mrnumber = {0274683 (43 \#445)}, Mrreviewer = {Ky Fan}, Pages = {xviii+451}, Publisher = {Princeton University Press}, Series = {Princeton Mathematical Series, No. 28}, Title = {Convex analysis}, Year = {1970}, Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=0274683}} @ARTICLE {Va:85, author = "A. VARDI", title = "A trust region algorithm for equality constrained minimization: convergence properties and implementation", journal = "SIAM J. Numer. Anal.", year = "1985", volume = "22", pages = "575-591"} @article {Ger:31, author = "S.A. GER\v SGORIN", TITLE = {\v {U}ber die {A}bgrenzung der {E}igenwerte einer {M}atrix}, JOURNAL = {Izv. Akad. Nauk SSSR Ser. Fiz.-Mat.}, VOLUME = {6}, YEAR = {1931}, PAGES = {749--754}, } @article {MR0151473, AUTHOR = {Feingold, D.G. and Varga, R.S.}, TITLE = {Block diagonally dominant matrices and generalizations of the {G}erschgorin circle theorem}, JOURNAL = {Pacific J. Math.}, FJOURNAL = {Pacific Journal of Mathematics}, VOLUME = {12}, YEAR = {1962}, PAGES = {1241--1250}, ISSN = {0030-8730}, MRCLASS = {15.25}, MRNUMBER = {0151473 (27 \#1458)}, MRREVIEWER = {O. Taussky-Todd}, } @book {MR2093409, AUTHOR = {VARGA, R.S.}, TITLE = {Ger\v sgorin and his circles}, SERIES = {Springer Series in Computational Mathematics}, VOLUME = {36}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {2004}, PAGES = {x+226}, ISBN = {3-540-21100-4}, MRCLASS = {15-02 (15-03 15A18 15A42 65-02 65-03 65F15)}, MRNUMBER = {MR2093409 (2005h:15002)}, MRREVIEWER = {David Scott Watkins}, } @INPROCEEDINGS{vaughn, AUTHOR = "C. Vaughan", TITLE = "Structural Analysis on Massively Parallel Computers", BOOKTITLE = "Proceedings of the Conference on Parallel Methods on Large Scale Structural Analysis and Physics Applications", YEAR = "1991", PUBLISHER = "Pergammon Press", EDITOR = "O. Storaasli and E. Carmona", PAGES = "261 - 267"} @BOOK {Vav:91, author = "S.A. Vavasis", title = "Nonlinear Optimization: Complexity Issues", publisher = "Oxford Science", year = "1991", address = "New York"} @incollection {MR98b:90084, AUTHOR = {Vavasis, S.A. and Ye, Y.}, TITLE = {On the relationship between layered least squares and affine scaling steps}, BOOKTITLE = {The mathematics of numerical analysis (Park City, UT, 1995)}, PAGES = {857--865}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {1996}, MRCLASS = {90C05 (65K05)}, MRNUMBER = {98b:90084}, MRREVIEWER = {John J. Dinkel}, } @article {MR97k:90063, AUTHOR = {Vavasis, S.A. and Ye, Y.}, TITLE = {A primal-dual interior point method whose running time depends only on the constraint matrix}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {74}, YEAR = {1996}, NUMBER = {1, Ser. A}, PAGES = {79--120}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C05 (90C60)}, MRNUMBER = {97k:90063}, MRREVIEWER = {F. Pickel}, } @article {MR96m:90036, AUTHOR = {Vavasis, S.A. and Ye, Y.}, TITLE = {Identifying an optimal basis in linear programming}, NOTE = {Interior point methods in mathematical programming}, JOURNAL = {Ann. Oper. Res.}, FJOURNAL = {Annals of Operations Research}, VOLUME = {62}, YEAR = {1996}, PAGES = {565--572}, ISSN = {0254-5330}, MRCLASS = {90C05}, MRNUMBER = {96m:90036}, } @article {MR96f:90071, AUTHOR = {Vavasis, S.A. and Ye, Y.}, TITLE = {Condition numbers for polyhedra with real number data}, JOURNAL = {Oper. Res. Lett.}, FJOURNAL = {Operations Research Letters}, VOLUME = {17}, YEAR = {1995}, NUMBER = {5}, PAGES = {209--214}, ISSN = {0167-6377}, CODEN = {ORLED5}, MRCLASS = {90C05 (90C08 90C60)}, MRNUMBER = {96f:90071}, } @incollection {MR1748772, AUTHOR = {Vavasis, S.A. and Ye, Y.}, TITLE = {A simplification to ``a primal-dual interior point method whose running time depends only on the constraint matrix''}, BOOKTITLE = {High performance optimization}, PAGES = {233--243}, PUBLISHER = {Kluwer Acad. Publ.}, ADDRESS = {Dordrecht}, YEAR = {2000}, MRCLASS = {90C51}, MRNUMBER = {1 748 772}, } @TECHREPORT {VavZip:90, author = "S.A. Vavasis and R. ZIPPEL", title = "Proving polynomial-time for sphere-constrained quadratic programming", institution = "Department of Computer Science, Cornell University", year = "1990", address = "Ithaca, NY"} @ARTICLE{venkat91, AUTHOR = "VENKATAKRISHNAN, V. and SIMON, H. and BARTH, T.", TITLE = "A MIMD Implementation of A Parallel Euler Solver for Unstructured Grids", JOURNAL = "The Journal of Supercomputing", VOLUME = "6", NUMBER = "2", PAGES = "117 - 127", YEAR = "1992"} @preamble{ "\def\cprime{$'$} " } @article {MR2140670, AUTHOR = {VERBITSKY, O.V.}, TITLE = {A note on the approximability of the dense subgraph problem}, JOURNAL = {Mat. Stud.}, FJOURNAL = {Matematichn\=\i\ Stud\=\i \"\i. Prats\=\i\ L\cprime v\=\i vs\cprime kogo Matematichnogo Tovaristva}, VOLUME = {22}, YEAR = {2004}, NUMBER = {2}, PAGES = {198--201}, ISSN = {1027-4634}, MRCLASS = {05C85 (68Q17 68R10)}, MRNUMBER = {MR2140670 (2005k:05229)}, } @Article{Villarroel2013, author="Villarroel, J.A. and Taylor, J.E. and Tucci, C.L.", title="Innovation and learning performance implications of free revealing and knowledge brokering in competing communities: insights from the Netflix Prize challenge", journal="Computational and Mathematical Organization Theory", year="2013", month="Mar", day="01", volume="19", number="1", pages="42--77", abstract="Firms increasingly use open competitions to extend their innovation process and access new diverse knowledge. The Netflix Prize case we study in this paper is a multi-stage repeat-submission open competition involving the creation of new knowledge from across knowledge domains, a process which benefits from knowledge sharing across competing communities. The extant literature says little about the effects of different types and levels of knowledge sharing behavior on the learning and innovation outcomes of such a competitive system, or what the performance boundaries may be for the system as a result of such differences. Our research explores those boundaries unveiling important tradeoffs involving free revealing behavior---defined as voluntarily giving away codified knowledge and making it into a `public good'---and knowledge brokering behavior---defined as using knowledge from one domain to innovate in another---on the learning performance of competing communities. The results, analyzing the system-level average and volatility of learning outcomes, lead to three conclusions: (i) greater knowledge sharing, as portrayed by greater free revealing and knowledge brokering, helps achieve better average learning for the system as a whole, however, (ii) achieving the best overall outcome possible from the system actually requires controlling the amount of knowledge brokering activity in the system. The results further suggest that (iii) it should not be possible to simultaneously achieve both the best overall outcome from the system and the best average learning for the system. The tradeoffs that ensue from these findings have important implications for innovation policy and management. This research contributes to practice by showing how it is possible to achieve different learning performance outcomes by managing the types and levels of knowledge sharing in open competitive systems.", issn="1572-9346", doi="10.1007/s10588-012-9137-7", url="https://doi.org/10.1007/s10588-012-9137-7" } @article {MR2012813, AUTHOR = {XU, D. and HAN, J. and HUANG, Z. and ZHANG, L.}, TITLE = {Improved approximation algorithms for {MAX} {$\frac{n}{2}$}-{DIRECTED}-{BISECTION} and {MAX} {$\frac{n}{2}$}-{DENSE}-{SUBGRAPH}}, JOURNAL = {J. Global Optim.}, FJOURNAL = {Journal of Global Optimization. An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering}, VOLUME = {27}, YEAR = {2003}, NUMBER = {4}, PAGES = {399--410}, ISSN = {0925-5001}, CODEN = {JGOPEO}, MRCLASS = {90C35 (05C85)}, MRNUMBER = {MR2012813 (2004h:90084)}, } @incollection {MR1677349, AUTHOR = {SRIVASTAV, A. and WOLF, K.}, TITLE = {Finding dense subgraphs with semidefinite programming}, BOOKTITLE = {Approximation algorithms for combinatorial optimization (Aalborg, 1998)}, SERIES = {Lecture Notes in Comput. Sci.}, VOLUME = {1444}, PAGES = {181--191}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1998}, MRCLASS = {90C35 (05C85)}, MRNUMBER = {MR1677349 (99k:90191)}, MRREVIEWER = {H. T. Lau}, } @incollection {MR1465947, AUTHOR = {ASAHIRO, Y. and IWAMA, K. and TAMAKI, H. and TOKUYAMA, T.}, TITLE = {Greedily finding a dense subgraph}, BOOKTITLE = {Algorithm theory---SWAT '96 (Reykjav\'\i k, 1996)}, SERIES = {Lecture Notes in Comput. Sci.}, VOLUME = {1097}, PAGES = {136--148}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1996}, MRCLASS = {68R10 (05C85 68Q25)}, MRNUMBER = {MR1465947 (98g:68120)}, } @INPROCEEDINGS {Vin:76, author = "P.K.W. VINSOME", title = "Orthomin, an iterative method for solving sparse sets of simultaneous linear equations", booktitle = "Proceedings of the 4th Symposium on Reservoir Simulation, in the Society of Petroleum Engineers of AIME", year = "1976", editor = "R.W. Cottle and C.E. Lemke", pages = "145-168"} @article {Zang, AUTHOR = {ZANG, I.}, TITLE = {A smoothing-out technique for min-max optimization}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {19}, YEAR = {1980}, NUMBER = {1}, PAGES = {61--77}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C30 (65K05)}, MRNUMBER = {MR579403 (82c:90085)}, MRREVIEWER = {K. Schittkowski}, } @ARTICLE {Zang:67a, author = "W.I. ZANGWILL", title = "Nonlinear programming via penalty functions", journal = "Management Sci.", year = "1967", volume = "13", pages = "344-358"} @ARTICLE {Zang:67b, author = "W.I. ZANGWILL", title = "Minimizing a function without calculating derivatives", journal = "Comp. J.", year = "1967", volume = "10", number = "3", pages = "293-296"} @BOOK {Zang:69, author = "W.I. ZANGWILL", title = "Nonlinear Programming. A Unified Approach", publisher = "Prentice-Hall", year = "1969", address = "Englewood Cliffs, NJ"} @ARTICLE {Ziri:82, author = "F. ZIRILLI", title = "The solution of nonlinear systems of equations by second order systems of o.d.e. and linearly implicit {A}-stable techniques", journal = "SIAM J. Numer. Anal.", year = "1982", volume = "19", pages = "800-816"} @TECHREPORT{Zo88, AUTHOR = "J. ZOWE", TITLE = "The BT-algorithm for minimizing a nonsmooth functional subject to linear constraints", NUMBER = "1088", INSTITUTION = "University of Bergen", YEAR = 1988 } @ARTICLE{ab63, AUTHOR = "G. C. ARMOUR and E. S. BUFFA", TITLE = "A Heuristic Algorithm and Simulative Approach to Relative Location of Facilities ", JOURNAL = "Management Science ", VOLUME = 9, YEAR = 1963, PAGES = "294-309" } @ARTICLE{ass85, AUTHOR = "A. A. Assad and W. Xu", TITLE = "On Lower Bounds For A Class Of Quadratic 0,1 Programs", JOURNAL = "Operations Research Letters", VOLUME = 4, NUMBER = 4, YEAR = 1985, PAGES = "175-180" } @TECHREPORT{balmaz80, AUTHOR = "E. BALAS and J. B. MAZZOLA", TITLE = "Linearizing nonlinear 0-1 programs", NUMBER = "467", INSTITUTION = "Carnegie-Mellon University, Pittsburgh", YEAR = 1980 } @ARTICLE{bazel79, AUTHOR = "M. S. BAZARAA and A. N. ELSHAFEI", TITLE = "An Exact Branch-and-Bound Procedure for the Quadratic-Assignment Problem", JOURNAL = "Naval Research Logistics Quarterly ", VOLUME = 26, YEAR = 1979, PAGES = "109-121" } @BOOK{bs79, AUTHOR = "M. S. BAZARAA and C. M. SHETTY", TITLE = "Nonlinear Programming : Theory and Algorithms", PUBLISHER = "Wiley and Sons", YEAR = 1979 } @ARTICLE{baz83, AUTHOR = "M. S. Bazaraa and O. Kirca", TITLE = "A Branch-and-Bound Heuristic for Solving the Quadratic Assignment Problem", JOURNAL = "Naval Research Logistics Quarterly ", VOLUME = 30, YEAR = 1983, PAGES = "287-304" } @ARTICLE{bazsh80, AUTHOR = "M. S. Bazaraa and H. D. Sherali ", TITLE = "Benders' partitioning scheme applied to a new formulation of the quadratic assignment problem", JOURNAL = "Naval Research Logistics Quarterly ", VOLUME = 27, YEAR = 1980, PAGES = "29-41" } @ARTICLE{bazsh82, AUTHOR = "M. S. Bazaraa and H. D. Sherali ", TITLE = "On The Use of Exact and Heuristic Cutting Plane Methods for the Quadratic Assignment Problem", JOURNAL = "Journal of the Operational Research Society ", VOLUME = 33, NUMBER = 11, YEAR = 1982, PAGES = "991-1003" } @ARTICLE{bi:69, AUTHOR = "A. Ben-Israel", TITLE = {Linear equations and inequalities on finite dimensional, real or complex, vector spaces: {A} unified theory}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {27}, YEAR = {1969}, PAGES = {367--389}, ISSN = {0022-247x}, MRCLASS = {15.50 (52.00)}, MRNUMBER = {MR0242865 (39 \#4192)}, MRREVIEWER = {M. F. Smiley}, } @ARTICLE{bi:66, AUTHOR = "A. Ben-Israel", TITLE = "On error bounds for generalized inverses", JOURNAL = sinum, VOLUME = 3, YEAR = 1966, PAGES = "585-592" } @incollection{benisrael:95, AUTHOR = {Ben-Israel, ADI}, TITLE = {{N}ewton's method with modified functions}, BOOKTITLE = {Recent developments in optimization theory and nonlinear analysis (Jerusalem, 1995)}, PAGES = {39--50}, SERIES = {Contemp. Math.}, VOLUME = {204}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {1997}, } @ARTICLE{biCh:68, AUTHOR = "A. Ben-Israel and A. Charnes", TITLE = "An explicit solution of a special class of linear programming problems", JOURNAL = "Journal of the Operational Research Society ", VOLUME = 16, NUMBER = 6, YEAR = 1968, PAGES = "1166-1175" } @ARTICLE{biChKo:69, AUTHOR = "A. Ben-Israel and A. Charnes and K. Kortanek", TITLE = "Duality and asymptotic solvability over cones", JOURNAL = "Bulletin of American Mathematical Society", VOLUME = 75, NUMBER = 2, YEAR = 1969, PAGES = "318-324" } @article {MR667079, AUTHOR = {Kortanek, K.O. and Yamasaki, M.}, TITLE = {Semi-infinite transportation problems}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {88}, YEAR = {1982}, NUMBER = {2}, PAGES = {555--565}, ISSN = {0022-247X}, MRCLASS = {90C08}, MRNUMBER = {667079}, DOI = {10.1016/0022-247X(82)90214-1}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1016/0022-247X(82)90214-1}, } @ARTICLE{Kort:77, AUTHOR = "K. KORTANEK", TITLE = "Constructing a perfect duality in infinite programming", JOURNAL = apmo, VOLUME = 3, NUMBER = 4, YEAR = 1977, PAGES = "357-372" } @BOOK{BiGr:74, AUTHOR = "A. Ben-Israel and T.N.E. Greville", TITLE = "Generalized Inverses: Theory and Applications", PUBLISHER = "Wiley-Interscience ", YEAR = 1974 } @BOOK{bestritter, AUTHOR = "M. J. Best and K. Ritter ", TITLE = "Quadratic Programming Active Set Analysis and Computer Programs", PUBLISHER = "Taylor and Francis", YEAR = "2016", } @book {MR3642293, AUTHOR = {Best, M.J.}, TITLE = {Quadratic programming with computer programs}, SERIES = {Advances in Applied Mathematics}, PUBLISHER = {CRC Press, Boca Raton, FL}, YEAR = {2017}, PAGES = {xiv+386}, ISBN = {978-1-4987-3575-9}, MRCLASS = {90-01 (90C20)}, MRNUMBER = {3642293}, MRREVIEWER = {Andrzej Stachurski}, } @book {MR2722272, AUTHOR = {Best, Michael J.}, TITLE = {Portfolio optimization}, SERIES = {Chapman \& Hall/CRC Finance Series}, NOTE = {With 1 CD-ROM (Windows, Macintosh and UNIX)}, PUBLISHER = {CRC Press, Boca Raton, FL}, YEAR = {2010}, PAGES = {xiv+222}, ISBN = {978-1-4200-8584-6}, MRCLASS = {91-01 (91G10)}, MRNUMBER = {2722272}, MRREVIEWER = {Youngna Choi}, } @BOOK{bha87, AUTHOR = "R. Bhatia ", TITLE = "Perturbation Bounds for Matrix Eigenvalues : Pitman Research Notes in Mathematics Series 162", PUBLISHER = "Longman", ADDRESS = {New York}, YEAR = 1987 } @book {MR98i:15003, AUTHOR = {Bhatia, R.}, TITLE = {Matrix analysis}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1997}, PAGES = {xii+347}, ISBN = {0-387-94846-5}, } @ARTICLE{blanks, AUTHOR = "J. B. BLANKS ", TITLE = "Near Optimal Quadratic-Based Placement for a Class of IC Layout Problems", JOURNAL = "IEEE Circuits and Devices", YEAR = 1985, PAGES = "31-373" } @BOOK{MR2061575, author = "S. Boyd and L. Vandenberghe", title = "Convex Optimization", publisher = "Cambridge University Press", year = "2004", URL= "http://www.stanford.edu\/\~{ }boyd\/cvxbook\/", address = "Cambridge"} @BOOK{ApplLinAlgBoydVand:18, author = "S. Boyd and L. Vandenberghe", title = "Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares", publisher = "Cambridge University Press", year = "2018", URL= "http://www.stanford.edu\/\~{ }boyd\/vmls\/", address = "Cambridge"} @PHDTHESIS{boyd, AUTHOR = "S.C. Boyd ", TITLE = "The Subtour Polytope of the Travelling Salesman Problem", SCHOOL = "University of Waterloo", YEAR = 1986 } @book {MR2353163, AUTHOR = {Burachik, R.S. and Iusem, A.N.}, TITLE = {Set-valued mappings and enlargements of monotone operators}, SERIES = {Springer Optimization and Its Applications}, VOLUME = {8}, PUBLISHER = {Springer, New York}, YEAR = {2008}, PAGES = {xvi+293}, ISBN = {978-0-387-69755-0}, MRCLASS = {47H04 (47H05 47H10 47J25 47N10 49J53 54C60)}, MRNUMBER = {2353163}, MRREVIEWER = {Qiji Jim Zhu}, } @ARTICLE{bru84, AUTHOR = "P. A. BRUIJS", TITLE = "On the quality of heuristic solutions to a 19 X 19 quadratic assignment problem", JOURNAL = "European Journal of Operational Research ", VOLUME = 17, YEAR = 1984, PAGES = "21-30" } @ARTICLE{bufav62, AUTHOR = "E.S. BUFFA and G.C. ARMOUR and T.E. VOLLMAN ", TITLE = "Allocating Facilities with CRAFT", JOURNAL = "Harvard Business Review ", VOLUME = 42, YEAR = 1962, PAGES = "136-158" } @ARTICLE{bur73, AUTHOR = "R.E. Burkard ", TITLE = "Die Storungsmethode zur Losung quadratischer Zuordnungsprobleme", JOURNAL = "Operations Research Verfahren", VOLUME = 16, YEAR = 1973, PAGES = "84-108" } @INCOLLECTION{bu:91, AUTHOR = "R.E. Burkard ", TITLE = " Locations with spatial interactions: the quadratic assignment problem", booktitle = " Discrete Location Theory", publisher = "John Wiley", editor = "P.B.\ Mirchandani and R.L.\ Francis", YEAR = 1991, } @ARTICLE{bur84, AUTHOR = "R.E. Burkard ", TITLE = "Quadratic assignment problems", JOURNAL = "European Journal of Operational Research ", VOLUME = 15, YEAR = 1984, PAGES = "283-289" } @ARTICLE{burbo83, AUTHOR = "R.E. Burkard and T. BONNIGER", TITLE = "A heuristic for quadratic {B}oolean programs with applications to quadratic assignment problems", JOURNAL = "European Journal of Operational Research ", VOLUME = 13, YEAR = 1983, PAGES = "374-386" } @BOOK{burde80, AUTHOR = "R.E. Burkard and U. DERIGS", TITLE = "Assignment and Matching Problems: Solution Methods with Fortran Programs", PUBLISHER = "Springer-Berlin", YEAR = 1980 } @ARTICLE{burfi83, AUTHOR = "R.E. Burkard and U. FINCKE", TITLE = "The asymptotic probabilistic behaviour of quadratic sum assignment problems", JOURNAL = "Z. Operations Res. ", VOLUME = 27, YEAR = 1983, PAGES = "73-81" } @ARTICLE{BuOf:77, AUTHOR = "R.E. Burkard and J.~OFFERMANN", TITLE = "Entwurf von Schreibmaschinentastaturen mittels quadratischer Zuordnungsprobleme", JOURNAL = "Z. Operations Res. ", VOLUME = 21, YEAR = 1977, PAGES = "B121-B132" } @ARTICLE{burre84, AUTHOR = "R.E. Burkard and F. Rendl", TITLE = "A thermodynamically motivated simulation procedure for combinatorial optimization problems", JOURNAL = "European Journal Operational Research ", VOLUME = 17, YEAR = 1984, PAGES = "169-174" } @article {CaMa:88, author = "P. CARRARESI and F.~MALUCELLI", TITLE = {A new lower bound for the quadratic assignment problem}, JOURNAL = {Oper. Res.}, FJOURNAL = {Operations Research. The Journal of the Operations Research Society of America}, VOLUME = {40}, YEAR = {1992}, NUMBER = {suppl. 1}, PAGES = {S22--S27}, ISSN = {0030-364X}, CODEN = {OPREAI}, MRCLASS = {90C35 (90B80)}, MRNUMBER = {92m:90051}, } @incollection {CaMa:92, author = "P. CARRARESI and F.~MALUCELLI", TITLE = {A reformulation scheme and new lower bounds for the {Q}{A}{P}}, BOOKTITLE = {Quadratic assignment and related problems (New Brunswick, NJ, 1993)}, PAGES = {147--160}, editor = {Pardalos, P and Wolkowicz, H.}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {1994}, MRCLASS = {90C27}, MRNUMBER = {1 290 350}, } @ARTICLE{chrge81, AUTHOR = "N. Christofides and M. Gerrard", TITLE = "A Graph Theoretic Analysis of Bounds for the Quadratic Assignment Problem", JOURNAL = "Annals of Discrete Mathematics ", VOLUME = 11, YEAR = 1971, PAGES = "61-68" } @ARTICLE{cmt80, AUTHOR = "N. Christofides and A. Mingozzi and P. Toth", TITLE = "Contributions to the Quadratic Assignment Problem", JOURNAL = "European Journal Operational Research ", VOLUME = 4, YEAR = 1980, PAGES = "243-247" } @BOOK{cla83, AUTHOR = "F.H. Clarke", TITLE = {Optimization and nonsmooth analysis}, SERIES = {Classics in Applied Mathematics}, VOLUME = {5}, EDITION = {Second}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {1990}, PAGES = {xii+308}, ISBN = {0-89871-256-4}, MRCLASS = {49-02 (01A75 49J52 58C20 90C48)}, MRNUMBER = {MR1058436 (91e:49001)}, } @ARTICLE{con71, AUTHOR = "K. Conrad", TITLE = "Das quadratische Zuweisungsproblem und zwei seiner Spezialfalle", JOURNAL = "Mohr-Siebeck, Tubingen ", YEAR = 1971 } @BOOK{ds, AUTHOR = "J. E. Dennis Jr. and Robert. B. Schnabel", TITLE = "Numerical Methods for Unconstrained Optimization and Nonlinear Equations", PUBLISHER = "Prentice-Hall ", YEAR = 1983 } @ARTICLE{dyfrm86, AUTHOR = "M.E. Dyer and A.M. Frieze and C.J.H. McDiarmid", TITLE = "On linear programs with random costs", JOURNAL = mprog, VOLUME = 35, YEAR = 1986, PAGES = "3-16" } @INPROCEEDINGS{edw77copy, AUTHOR = "C.S. Edwards", TITLE = "The Derivation of a Greedy Approximator for the {K}oopmans-{B}eckmann Quadratic Assignment Problem", BOOKTITLE = "Proceedings CP77 Combinatorial Programming Conference, Liverpool", YEAR = 1977, PAGES = "55-86" } @ARTICLE{Edw80master, AUTHOR = "C. S. Edwards ", TITLE = "A Branch and Bound Algorithm for the {K}oopmans-{B}eckmann Quadratic Assignment Problem", JOURNAL = mps, VOLUME = 13, YEAR = 1980, PAGES = "35-52" } @ARTICLE{els:77, AUTHOR = "A. N. ELSHAFEI", TITLE = "Hospital lay-out as a quadratic assignment problem", JOURNAL = "Operational Research Quarterly ", VOLUME = 28, YEAR = 1977, PAGES = "167-179" } @ARTICLE{FillWill:71, AUTHOR = "P.A. FILLMORE and J.P. WILLIAMS", TITLE = "Some convexity theorems for matrices", JOURNAL = glasgow, VOLUME = "10", YEAR = "1971", PAGES = "110-117" } @TECHREPORT{fmd87, AUTHOR = "G. Finke and E.B. Medova-Dempster ", TITLE = "Approximation Approach To Combinatorial Optimization Problems", INSTITUTION = "Technical University of Nova Scotia", YEAR = 1987 } @TECHREPORT{fvhrk85, AUTHOR = "J.C.B. Frenk and M. van Houweninge and A.H.G. Rinnooy Kan ", TITLE = "Asymptotic Properties of Assignment Problems ", INSTITUTION = "Erasmus University, Rotterdam", YEAR = 1982 } @ARTICLE{fletch85, AUTHOR = "R. Fletcher ", TITLE = "Semi-Definite Matrix Constraints In Optimization ", JOURNAL = "SIAM Journal of Control and Optimization", VOLUME = 23, YEAR = 1985, PAGES = "493-513" } @article {MR0187375, AUTHOR = {Fletcher, R. and Reeves, C.M.}, TITLE = {Function minimization by conjugate gradients}, JOURNAL = {Comput. J.}, FJOURNAL = {The Computer Journal}, VOLUME = {7}, YEAR = {1964}, PAGES = {149--154}, ISSN = {0010-4620}, MRCLASS = {65.30}, MRNUMBER = {0187375}, MRREVIEWER = {R. L. Graves}, DOI = {10.1093/comjnl/7.2.149}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1093/comjnl/7.2.149}, } @BOOK{fran74, AUTHOR = "R. L. Francis and J. A. White", TITLE = "Facility Layout and Location : An Analytical Approach", PUBLISHER = "Prentice-Hall ", YEAR = "1974", } @ARTICLE{FrYa:83, AUTHOR = "A. M. FRIEZE and J.~YADEGAR", TITLE = "On The Quadratic Assignment Problem", JOURNAL = "Discrete Applied Mathematics ", VOLUME = "5", YEAR = "1983", PAGES = "89-98" } @article {FriJer:94, AUTHOR = "A. FRIEZE and M. JERRUM", TITLE = {Improved approximation algorithms for {MAX} k-{CUT} and {MAX} {BISECTION}}, journal = "Algorithmica", year = 1997, pages = "67--81", volume = 18 } @TECHREPORT{ren, AUTHOR = "W. Gander and G. Golub and U. von Matt ", TITLE = "A Constrained Eigenvalue Problem", INSTITUTION = "Institut fur Informatik ETH-Zentrum, CH-8092 Zurich Switzerland", YEAR = 1988 } @BOOK{garjo, AUTHOR = "M. R. Garey and D. S. Johnson", TITLE = "Computers and Intractability ", PUBLISHER = "W. H. Freeman and Company ", ADDRESS = "San Francisco", YEAR = 1979 } @ARTICLE{gavpl66, AUTHOR = "J. W. Gavett and N. V. Plyter ", TITLE = "The optimal assignment of facilities to locations by branch and bound", JOURNAL = "Operations Research ", VOLUME = 14, YEAR = 1966, PAGES = "210-232" } @BOOK{gil81, AUTHOR = "P. E. GILL and W. MURRAY and M.H. Wright", TITLE = "Practical Optimization ", PUBLISHER = "Academic Press ", ADDRESS = "Toronto", YEAR = 1981 } @TECHREPORT{GSM:96, AUTHOR = "P.E. GILL and M.A. Saunders and W. MURRAY", TITLE = "{SNOPT}: An {SQP} algorithm for large-scale constrained optimization", INSTITUTION = "University of California, San Diego", NUMBER = "NA 96-2", YEAR = "1996" } @ARTICLE{gol87, AUTHOR = "B. Gollan ", TITLE = "Eigenvalue Perturbations And Nonlinear Parametric Optimization", JOURNAL = "Mathematical Programming Study ", VOLUME = 30, YEAR = 1987, PAGES = "67-81" } @book{golvl, AUTHOR = {Golub, G.H. and Van Loan, C.F.}, TITLE = {Matrix computations}, SERIES = {Johns Hopkins Studies in the Mathematical Sciences}, EDITION = {Fourth}, PUBLISHER = {Johns Hopkins University Press, Baltimore, MD}, YEAR = {2013}, PAGES = {xiv+756}, ISBN = {978-1-4214-0794-4; 1-4214-0794-9; 978-1-4214-0859-0}, MRCLASS = {65-02 (65Fxx)}, MRNUMBER = {3024913}, MRREVIEWER = {J\"org Liesen}, } @ARTICLE{gotokuh, AUTHOR = "S. Goto and E.S. Kuh ", TITLE = "An approach to the two-dimensional placement problem in circuit layout", JOURNAL = "IEEE Transactions on Circuits and Systems ", VOLUME ="CAS-25", NUMBER = "4", YEAR = "1978", PAGES = "208-214" } @article {MR1397251, AUTHOR = {Sebastiani, Paola}, TITLE = {On the derivatives of matrix powers}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {17}, YEAR = {1996}, NUMBER = {3}, PAGES = {640--648}, ISSN = {0895-4798}, CODEN = {SJMAEL}, MRCLASS = {15A54 (15A18)}, MRNUMBER = {MR1397251 (98a:15046)}, } @article {MR1397248, AUTHOR = {Mathias, Roy}, TITLE = {A chain rule for matrix functions and applications}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {17}, YEAR = {1996}, NUMBER = {3}, PAGES = {610--620}, ISSN = {0895-4798}, CODEN = {SJMAEL}, MRCLASS = {47A55 (47A56)}, MRNUMBER = {MR1397248 (97c:47015)}, } @article {MR1007171, AUTHOR = {Tracy, D. S. and Jinadasa, K. G.}, TITLE = {Patterned matrix derivatives}, JOURNAL = {Canad. J. Statist.}, FJOURNAL = {The Canadian Journal of Statistics. La Revue Canadienne de Statistique}, VOLUME = {16}, YEAR = {1988}, NUMBER = {4}, PAGES = {411--418}, ISSN = {0319-5724}, MRCLASS = {26B05 (15A69 62H99)}, MRNUMBER = {MR1007171 (90m:26019)}, MRREVIEWER = {Jan R. Magnus}, } @article {MR818112, AUTHOR = {Magnus, Jan R. and Neudecker, H.}, TITLE = {Matrix differential calculus with applications to simple, {H}adamard, and {K}ronecker products}, JOURNAL = {J. Math. Psych.}, FJOURNAL = {Journal of Mathematical Psychology}, VOLUME = {29}, YEAR = {1985}, NUMBER = {4}, PAGES = {474--492}, ISSN = {0022-2496}, CODEN = {JMTPAJ}, MRCLASS = {26B05 (92A25)}, MRNUMBER = {MR818112 (87a:26009)}, } @article {MR0488680, AUTHOR = {McMath, John S. and Sims, S. E. and Hallum, C. R.}, TITLE = {On the properties of a matrix valued derivative utilizing the {M}oore-{P}enrose inverse}, JOURNAL = {Linear Algebra and Appl.}, VOLUME = {18}, YEAR = {1977}, NUMBER = {3}, PAGES = {281--291}, MRCLASS = {65F20 (15A99)}, MRNUMBER = {MR0488680 (58 \#8201)}, MRREVIEWER = {I. Fennell Burns}, } @article {MR0272801, AUTHOR = {Vetter, W. J.}, TITLE = {Derivative operations on matrices}, JOURNAL = {IEEE Trans. Automatic Control}, FJOURNAL = {Institute of Electrical and Electronics Engineers. Transactions on Automatic Control}, VOLUME = {AC-15}, YEAR = {1970}, PAGES = {241--244}, ISSN = {0018-9286}, MRCLASS = {15.35 (93.00)}, MRNUMBER = {MR0272801 (42 \#7682)}, } @BOOK{gra81, AUTHOR = "A. Graham", TITLE = "Kronecker Products and Matrix Calculus: with Applications", PUBLISHER = "Halsted Press ", ADDRESS = "Toronto", YEAR = 1981 } @PHDTHESIS{hadphd, AUTHOR = "S.W. Hadley ", TITLE = "Continuous Optimization Approaches for the Quadratic Assignment Problem", SCHOOL = "University of Waterloo", YEAR = 1989 } @TECHREPORT{hei72, AUTHOR = "C.H. Heider ", TITLE = "A computationally simplified pair exchange algorithm for the quadratic assignment problem", INSTITUTION = "Center for Naval Analyses, Arlington, Va.", NUMBER = 101, YEAR = 1972 } @ARTICLE{hw53, AUTHOR = "A.J. Hoffman and H.W. Wielandt", TITLE = "The Variation of the Spectrum of a Normal Matrix", JOURNAL = "Duke Mathematics", VOLUME = 20, YEAR = 1953, PAGES = "37-39" } @TECHREPORT{kamot89, AUTHOR = "B.K. Kaku and T.E. Morton and G.L. Thompson ", TITLE = "A Heuristic Algorithm for the Facilities Layout Problem", INSTITUTION = "Carnegie Mellon University, Pittsburgh, Pa.", YEAR = 1989 } @ARTICLE{kak86, AUTHOR = "B. K. Kaku and G. L. Thompson ", TITLE = "An exact algorithm for the general quadratic assignment problem", JOURNAL = "European Journal of Operational Research ", VOLUME = 23, YEAR = 1986, PAGES = "382-390" } @ARTICLE{kaubr78, AUTHOR = "L. Kaufman and F. Broeckx ", TITLE = "An Algorithm for the Quadratic Assignment Problem Using Benders' Decomposition", JOURNAL = "European Journal of Operational Research ", VOLUME = 2, YEAR = 1978, PAGES = "204-211" } @BOOK{Kato:76, AUTHOR = "T. KATO", TITLE = {Perturbation theory for linear operators}, EDITION = {Second}, NOTE = {Grundlehren der Mathematischen Wissenschaften, Band 132}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1976}, PAGES = {xxi+619}, } @BOOK{kkato, AUTHOR = "T. KATO", TITLE = "Perturbation Theory for Linear Operators", PUBLISHER = "Springer-Verlag ", ADDRESS = "Berlin", YEAR = 1966 } @ARTICLE{kirgv83, AUTHOR = "S. KIRKPATRICK and C.D. GELATTI Jr. and M.P. VECCHI ", TITLE = "Optimization by simulated annealing", JOURNAL = "Science ", VOLUME = 220, YEAR = 1983, PAGES = "204-211" } @ARTICLE{kp78, AUTHOR = "J. Krarup and P. M. Pruzan ", TITLE = "Computer-aided layout design", JOURNAL = "Math. Programming Study ", VOLUME = 9, YEAR = 1978, PAGES = "85-94" } @BOOK{lan69, AUTHOR = "P. Lancaster", TITLE = "Theory of Matrices", PUBLISHER = "Academic Press ", ADDRESS = "New York", YEAR = 1969 } @article {MR0171375, AUTHOR = {LANCASTER, P.}, TITLE = {On eigenvalues of matrices dependent on a parameter}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {6}, YEAR = {1964}, PAGES = {377--387}, ISSN = {0029-599X}, MRCLASS = {65.40}, MRNUMBER = {MR0171375 (30 \#1606)}, MRREVIEWER = {W. W. Hooker}, } @ARTICLE{LaRo:05, AUTHOR = {P. Lancaster and L. Rodman}, TITLE = {Canonical forms for {H}ermitian matrix pairs under strict equivalence and congruence}, JOURNAL = {SIAM Rev.}, YEAR = {2005}, volume = {47}, number = {3}, pages = {407--443}, month = {}, note = {}, abstract = {}, keywords = {}, source = {}, } @BOOK{LanTis:85, AUTHOR = "P. LANCASTER and M.~TISMENETSKY", TITLE = {The theory of matrices}, EDITION = {Second}, SERIES = {Computer Science and Applied Mathematics}, PUBLISHER = {Academic Press Inc.}, ADDRESS = {Orlando, Fla.}, YEAR = {1985}, PAGES = {xv+570}, ISBN = {0-12-435560-9}, } @ARTICLE{land63, AUTHOR = "A. M. Land ", TITLE = "A problem of assignment with interrelated costs", JOURNAL = "Operational Research Quarterly ", VOLUME = 14, YEAR = 1963, PAGES = "185-198" } @ARTICLE{las80, AUTHOR = "R. S. Lashkari and S. C. Jaisingh ", TITLE = "An Heuristic Approach to Quadratic Assignment Problem", JOURNAL = "Journal of the Operational Research Society", VOLUME = 31, NUMBER = 9, YEAR = 1980, PAGES = "845-850" } @BOOK{lmw88, AUTHOR = "Robert F. Love and James G. Morris and George O. Wesolowsky", TITLE = "Facilities Location: Models and Methods ", PUBLISHER = "North-Holland ", YEAR = 1988 } @ARTICLE{lovwo76a, AUTHOR = "R. F. Love and J. Y. Wong ", TITLE = "Solving Quadratic Assignment Problems with Rectangular Distances and Integer Programming", JOURNAL = "Naval Research Logistics Quarterly", VOLUME = 23, YEAR = 1976, PAGES = "623-627" } @ARTICLE{lovwo76b, AUTHOR = "R. F. Love and J. Y. Wong ", TITLE = "On Solving A One-dimensional Space Allocation Problem with Integer Programming", JOURNAL = "INFOR", VOLUME = 14, YEAR = 1976, PAGES = "139-143" } @ARTICLE{mirsky, AUTHOR = "L. Mirsky ", TITLE = "The Spread of a Matrix", JOURNAL = "Mathematika", VOLUME = 3, YEAR = 1956, PAGES = "127-130" } @BOOK{mo79, AUTHOR = "A.W. MARSHALL and I. OLKIN", TITLE = "Inequalities:Theory of Majorization and its Applications", PUBLISHER = "Academic Press ", ADDRESS = "New York", YEAR = 1979 } @ARTICLE{max64, AUTHOR = "W.L. Maxwell ", TITLE = "The scheduling of economic lot sizes ", JOURNAL = "Naval Research Logistics Quarterly", VOLUME = 11, YEAR = 1964, PAGES = "89-124" } @BOOK{mc70, AUTHOR = "E. J. McCormick", TITLE = "Human Factors Engineering", PUBLISHER = "McGraw-Hill ", ADDRESS = "New York", YEAR = 1970 } @BOOK{mul70, AUTHOR = "H. Muller-Merbach", TITLE = "Optimale Reihenforgen", NOTE = "158-171", PUBLISHER = "Springer ", ADDRESS = "Berlin", YEAR = 1970 } @INPROCEEDINGS{noc83, AUTHOR = "J. Nocedal and M.L. Overton", TITLE = "Numerical Methods for Solving Inverse Eigenvalue Problems", BOOKTITLE = "Numerical Methods : Proceedings of the International Workshop held at Caracus, June 14-18, 1982", YEAR = 1982, PAGES = "55-86" } @misc{asl2020behavior, title={Behavior of Limited Memory BFGS when Applied to Nonsmooth Functions and their Nesterov Smoothings}, author={A. Asl and M.L. Overton}, year={2020}, eprint={2006.11336}, archivePrefix={arXiv}, primaryClass={math.OC} } @TECHREPORT{ove87, AUTHOR = "M.L. Overton ", TITLE = "On Minimizing the Maximum Eigenvalue of a Symmetric Matrix ", YEAR = 1987, INSTITUTION = "Centre for Mathematical Analysis, Australian National University", NUMBER = "CMA-R03-87" } @TECHREPORT{parcr89, AUTHOR = "P.M. Pardalos and J.V. Crouse ", TITLE = "A Parallel Algorithm for the Quadratic Assignment Problem ", YEAR = 1989, INSTITUTION = "The Pennsylvania State University, University Park, PA." } @ARTICLE{peg66, AUTHOR = "C.C. Pegels ", TITLE = "Plant Layout and Discrete Optimizing ", JOURNAL = "International Journal of Production Research", VOLUME = 5, YEAR = 1966, PAGES = "81-92" } @ARTICLE{pc71, AUTHOR = "J.F. Pierce and W.B. Crowston ", TITLE = "Tree Search Algorithms for Quadratic Assignment Problems ", JOURNAL = "Naval Research Logistics Quarterly", VOLUME = 18, YEAR = 1971, PAGES = "1-36" } @INBOOK{pulleyart, AUTHOR = "W.R. Pulleyblank ", TITLE = "Mathematical Programming The State of the Art ", PUBLISHER = "Springer-Verlag ", YEAR = 1982, PAGES = "312-345" } @ARTICLE{Rou:87, AUTHOR = "C. Roucairol ", TITLE = "A Parallel Branch and Bound Algorithm for the Quadratic Assignment Problem", JOURNAL = "Discrete Applied Mathematics", VOLUME = 15, YEAR = 1987, PAGES = "211-225" } @ARTICLE{roua79, AUTHOR = "C. Roucairol ", TITLE = "A Reduction Method for Quadratic Assignment Problems", JOURNAL = "Operations Research Verfahren ", VOLUME = 32, YEAR = 1979, PAGES = "183-187" } @ARTICLE{roub79, AUTHOR = "C. Roucairol ", TITLE = "Un nouvel algorithme pour le probleme d'affectation quadratique", JOURNAL = "R.A.I.R.O. ", VOLUME = 13, YEAR = 1979, PAGES = "275-301" } @ARTICLE{shera86, AUTHOR = "H.D. Sherali and P. Rajgopal ", TITLE = "A flexible polynomial-time, construction and improvement heuristic for the quadratic assignment problem ", JOURNAL = "Computers and Operations Research ", VOLUME = 13, NUMBER = 5, YEAR = 1986, PAGES = "587-600" } @ARTICLE{s61, AUTHOR = "L. Steinberg ", TITLE = "The Backboard Wiring Problem: A Placement Algorithm", JOURNAL = "SIAM Review ", VOLUME = 3, YEAR = 1961, PAGES = "37-50" } @ARTICLE{ugi79, AUTHOR = "I. Ugi and J. Bauer and J. Friedrich and J. Gasteiger and C. Jochum and W. Schubert ", TITLE = "Neue Anwendungsgebiete fur Computer in der Chemie", JOURNAL = "Angew. Chemie ", VOLUME = 91, YEAR = 1979, PAGES = "99-184" } @article {MR2672774, AUTHOR = {Vendramin, L. and Campello, R.J.G.B. and Hruschka, E.R.}, TITLE = {Relative clustering validity criteria: a comparative overview}, JOURNAL = {Stat. Anal. Data Min.}, FJOURNAL = {Statistical Analysis and Data Mining}, VOLUME = {3}, YEAR = {2010}, NUMBER = {4}, PAGES = {209--235}, ISSN = {1932-1864}, MRCLASS = {62H30 (65Y20)}, MRNUMBER = {2672774}, DOI = {10.1002/sam.10080}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1002/sam.10080}, } @INPROCEEDINGS{vanro, AUTHOR = "A. Vannelli and G. S. Rowan ", TITLE = "An eigenvector based approach for efficient multi-stack layout in VLSI design", BOOKTITLE = "29th Midwest Symposium on Circuits and Systems ", EDITOR = "M. Ismail", PUBLISHER = "Noth Holland, New York", YEAR = 1986, PAGES = "435-439" } @article {MR3133757, AUTHOR = {Vershik, A.M.}, TITLE = {Long history of the {M}onge-{K}antorovich transportation problem}, JOURNAL = {Math. Intelligencer}, FJOURNAL = {The Mathematical Intelligencer}, VOLUME = {35}, YEAR = {2013}, NUMBER = {4}, PAGES = {1--9}, ISSN = {0343-6993}, MRCLASS = {01A70 (49Q20 91B02)}, MRNUMBER = {3133757}, DOI = {10.1007/s00283-013-9380-x}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s00283-013-9380-x}, } @preamble{ "\def\udot#1{\ifmmode\oalign{$#1$\crcr\hidewidth.\hidewidth }\else\oalign{#1\crcr\hidewidth.\hidewidth}\fi} " } @article {MR3092770, AUTHOR = {Ernst, E. and Volle, M.}, TITLE = {Zero duality gap for convex programs: a generalization of the {C}lark-{D}uffin theorem}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {158}, YEAR = {2013}, NUMBER = {3}, PAGES = {668--686}, ISSN = {0022-3239}, MRCLASS = {90C25 (90C46)}, MRNUMBER = {3092770}, MRREVIEWER = {Costel M. B\u alc\u au}, DOI = {10.1007/s10957-013-0287-7}, URL = {https://doi.org/10.1007/s10957-013-0287-7}, } @article {MR945664, AUTHOR = {Volle, M.}, TITLE = {Concave duality: application to problems dealing with difference of functions}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {41}, YEAR = {1988}, NUMBER = {2, (Ser. A)}, PAGES = {261--278}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C48 (90C30)}, MRNUMBER = {MR945664 (90f:90156)}, MRREVIEWER = {Ho{\`a}ng T{\udot{u}}y}, } @ARTICLE{vb66, AUTHOR = "T. E. Vollman and E. S. Buffa ", TITLE = "The Facilities Layout Problem in Perspective", JOURNAL = "Management Science ", VOLUME = 12, YEAR = 1966, PAGES = "450-468" } % WWWWWWWWWWWWWW @ARTICLE{2017arXiv170600476W, author = {{Wang}, P.-W. and {Chang}, W.-C. and {Zico Kolter}, J.}, title = "{The Mixing method: low-rank coordinate descent for semidefinite programming with diagonal constraints}", journal = {ArXiv e-prints}, archivePrefix = "arXiv", eprint = {1706.00476}, primaryClass = "math.OC", keywords = {Mathematics - Optimization and Control, Computer Science - Machine Learning, Statistics - Machine Learning}, year = 2017, month = jun, adsurl = {http://adsabs.harvard.edu/abs/2017arXiv170600476W}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } @techreport{YingweiWang:13, author = "Y. Wang", title = "An interior point LP solver", institution = "Purdue University", number = "CS 52000", year = "2013", address = "Lafayette, IN" } @book {Wade:03, AUTHOR = {Wade, W.R.}, TITLE = {Introduction to Analysis}, NOTE = {Fourth editon}, PUBLISHER = {Prentice Hall}, YEAR = {2010}, PAGES = {696}, ISBN = {0132296381}, } @TECHREPORT {Wal:81, author = "D.A. WALMSLEY", title = "The {S}implex {M}ethod for minimization of a general function", institution = "Assessment Division, Transport Systems Department, Transport and Road Research Laboratory", year = "1981", type = "Supplementary Report", number = "686", address = "Crowthorne, Berkshire"} @article {MR97i:65055, AUTHOR = {WANG, X. and GALLIVAN, K.A. and BRAMLEY, R.}, TITLE = {C{I}{M}{G}{S}: an incomplete orthogonal factorization preconditioner}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {18}, YEAR = {1997}, NUMBER = {2}, PAGES = {516--536}, ISSN = {1064-8275}, CODEN = {SJOCE3}, MRCLASS = {65F10 (65F20 65F25 65Y20)}, MRNUMBER = {97i:65055}, } @book {MR2003a:65002, AUTHOR = {Watkins, David S.}, TITLE = {Fundamentals of matrix computations}, SERIES = {Pure and Applied Mathematics}, NOTE = {Second editon}, PUBLISHER = {Wiley-Interscience [John Wiley \& Sons]}, ADDRESS = {New York}, YEAR = {2002}, PAGES = {xiv+618}, ISBN = {0-471-21394-2}, MRCLASS = {65-01 (65Fxx)}, MRNUMBER = {2003a:65002}, } @ARTICLE {Wat:79, author = "G.A. WATSON", title = "The minimax solution of an overdetermined system of nonlinear equations", journal = "Journal Instit. Math. Appl.", year = "1979", volume = "23", pages = "167-180"} @article {MR0420435, AUTHOR = {Waksman, Z. and Epelman, M.}, TITLE = {On point classification in convex sets}, JOURNAL = {Math. Scand.}, FJOURNAL = {Mathematica Scandinavica}, VOLUME = {38}, YEAR = {1976}, NUMBER = {1}, PAGES = {83--96}, ISSN = {0025-5521}, MRCLASS = {52A20}, MRNUMBER = {MR0420435 (54 \#8449)}, MRREVIEWER = {R. Bantegnie}, } @TECHREPORT {Wed:74, author = "P.A. WEDIN", title = "On the {G}auss-{N}ewton method for the non-linear least squares problem", institution = "Inst. f{\"{o}}r Tell{\"{a}}mpad Matematik", year = "1974", type = "ITM Arbetsrapport", number = "4", address = "Stockholm"} @ARTICLE {Wen:79a, author = "Y. {WEN-CI}", title = "The convergence property of the simplex evolutionary techniques", journal = "Scientia Sinica", year = "1979", note = "Special issue of Mathematics (1)"} @ARTICLE {Wen:79b, author = "Y. {WEN-CI}", title = "Positive basis and a class of direct search techniques", journal = "Scientia Sinica", year = "1979", note = "Special issue of Mathematics (1)"} @ARTICLE {Whi:80, author = "D.J. WHITE", title = "Multi-objective interactive programming", journal = "J. Oper. Res. Soc.", year = "1980", pages = "517"} @INCOLLECTION {Whi:83, author = "D.J. WHITE", title = "A selection of multi-objective interactive programming methods", booktitle = "Multi-Objective Decision Making", publisher = "Academic Press", year = "1983", editor = "S. French and R. Hartley and L.C. Thomas and D.J. White", pages = "99", address = "London and New York"} @ARTICLE{wes83, AUTHOR = "D. H. West ", TITLE = "Approximate Solution of the Quadratic Assignment Problem", JOURNAL = "ACM Transactions on Mathematical Software", VOLUME = 9, NUMBER = 4, YEAR = 1983, PAGES = "461-466" } @ARTICLE{we64, AUTHOR = "B. Whitehead and M. Z. Elders ", TITLE = "An Approach to the Optimum Layout of Single-Story Buildings ", JOURNAL = "Architect's Journal ", VOLUME = 139, YEAR = 1964, PAGES = "1373-1380" } @article {MR2506479, AUTHOR = {Weiszfeld, E.}, TITLE = {On the point for which the sum of the distances to {$n$} given points is minimum}, NOTE = {Translated from the French original [Tohoku Math. J. {{\bf{4}}3} (1937), 355--386] and annotated by Frank Plastria}, JOURNAL = {Ann. Oper. Res.}, FJOURNAL = {Annals of Operations Research}, VOLUME = {167}, YEAR = {2009}, PAGES = {7--41}, ISSN = {0254-5330}, MRCLASS = {90B80}, MRNUMBER = {2506479}, DOI = {10.1007/s10479-008-0352-z}, URL = {http://dx.doi.org/10.1007/s10479-008-0352-z}, } @book {MR2223227, AUTHOR = {Wildberger, N.J.}, TITLE = {Divine proportions}, NOTE = {Rational trigonometry to universal geometry}, PUBLISHER = {Wild Egg, Kingsford}, YEAR = {2005}, PAGES = {xx+300}, ISBN = {0-9757492-0-X}, MRCLASS = {00-01 (51-01 97-01)}, MRNUMBER = {2223227}, } @incollection {springerlink:10.1007/11559887_18, author = {Winkler, Joab}, affiliation = {Department of Computer Science, The University of Sheffield, Regent Court, 211 Portobello Street, Sheffield S1 4DP United Kingdom}, title = {A Comparison of Condition Numbers for the Full Rank Least Squares Problem}, booktitle = {Deterministic and Statistical Methods in Machine Learning}, series = {Lecture Notes in Computer Science}, editor = {Winkler, Joab and Niranjan, Mahesan and Lawrence, Neil}, publisher = {Springer Berlin / Heidelberg}, isbn = {}, pages = {29318}, volume = {3635}, url = {http://dx.doi.org/10.1007/11559887_18}, note = {10.1007/11559887_18}, year = {2005} } @ARTICLE{wilwa87, AUTHOR = "M.R. Wilhelm and T.L. Ward ", TITLE = "Solving Quadratic Assignment Problems by Simulated Annealing ", JOURNAL = "IIE Transactions ", VOLUME = 19, YEAR = 1987, PAGES = "107-119" } @BOOK {Wilk:63, author = "J.H. WILKINSON", title = "Rounding Errors in Algebraic Processes", publisher = "Prentice-Hall", year = "1963", address = "Englewood Cliffs, NJ"} @BOOK {Wilk:65, author = "J.H. WILKINSON", title = "The Algebraic Eigenvalue Problem", publisher = "Oxford University Press", year = "1965", address = "London"} @article {MR0258458, AUTHOR = {WILLIAMS, A.C.}, TITLE = {Complementarity theorems for linear programming}, JOURNAL = {SIAM Rev.}, FJOURNAL = {SIAM Review}, VOLUME = {12}, YEAR = {1970}, PAGES = {135--137}, ISSN = {1095-7200}, MRCLASS = {90.50}, MRNUMBER = {MR0258458 (41 \#3105)}, MRREVIEWER = {W. F. Tyndall}, } @PHDTHESIS {Will:90, author = "K.A. WILLIAMSON", title = "Parameter identification in systems of ordinary differential equations", school = "Department of Mathematical Sciences, Rice University", year = "1990", address = "Houston, TX", note = "In preparation"} @PHDTHESIS {Will:90b, author = "K.A. Williamson", title = "A robust trust region algorithm for nonlinear programming", school = "Department of Mathematical Sciences, Rice University", year = "1990", number = "TR90-22", address = "Houston, TX"} @PHDTHESIS {Wils:63, author = "R.B. WILSON", title = "A simplicial algorithm for concave programming", school = "Harvard University", year = "1963"} @book {MR1994718, AUTHOR = {G{\"o}pfert, Alfred and Riahi, Hassan and Tammer, Christiane and Z{\u{a}}linescu, Constantin}, TITLE = {Variational methods in partially ordered spaces}, SERIES = {CMS Books in Mathematics/Ouvrages de Math\'ematiques de la SMC, 17}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {2003}, PAGES = {xiv+350}, ISBN = {0-387-00452-1}, MRCLASS = {90-02 (46N10 90C29 90C48)}, MRNUMBER = {MR1994718 (2004h:90001)}, MRREVIEWER = {George Isac}, } @book {MR830661, AUTHOR = {Jahn, Johannes}, TITLE = {Mathematical vector optimization in partially ordered linear spaces}, SERIES = {Methoden und Verfahren der Mathematischen Physik [Methods and Procedures in Mathematical Physics]}, VOLUME = {31}, PUBLISHER = {Verlag Peter D. Lang}, ADDRESS = {Frankfurt am Main}, YEAR = {1986}, PAGES = {viii+310}, ISBN = {3-8204-8940-1}, MRCLASS = {90C25 (90C31)}, MRNUMBER = {MR830661 (87f:90095)}, MRREVIEWER = {J. E. Spingarn}, } @book {MR0454581, AUTHOR = {Wong, Yau Chuen and Ng, Kung Fu}, TITLE = {Partially ordered topological vector spaces}, NOTE = {Oxford Mathematical Monographs}, PUBLISHER = {Clarendon Press, Oxford}, YEAR = {1973}, PAGES = {x+217}, MRCLASS = {46A40}, MRNUMBER = {MR0454581 (56 \#12830)}, MRREVIEWER = {M. Levin}, } @article {MR2002b:15002, AUTHOR = {Bostian, A.A. and Woerdeman, H.J.}, TITLE = {Unicity of minimal rank completions for tri-diagonal partial block matrices}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {325}, YEAR = {2001}, NUMBER = {1-3}, PAGES = {23--55}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A03 (15A09)}, MRNUMBER = {2002b:15002}, MRREVIEWER = {Shu An Hu}, } @article {MR90g:15039, AUTHOR = {Woerdeman, H.J.}, TITLE = {Minimal rank completions for block matrices}, NOTE = {Linear algebra and applications (Valencia, 1987)}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {121}, YEAR = {1989}, PAGES = {105--122}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A57 (93B20)}, MRNUMBER = {90g:15039}, MRREVIEWER = {Valeriu Prepeli{\c{t}}{\u{a}}}, } @ARTICLE {Wolf:69, author = "P. WOLFE", title = "Convergence conditions for ascent methods", journal = "SIAM Review", year = "1969", volume = "11", pages = "226-235"} @ARTICLE {Wolf:71, author = "P. WOLFE", title = "Convergence conditions for ascent methods: some corrections", journal = "SIAM Review", year = "1971", volume = "13", pages = "185-188"} @PHDTHESIS {Woo:85, author = "D.J. WOODS", title = "An interactive approach for solving multi-objective optimization problems", school = "Department of Mathematical Sciences, Rice University", year = "1985", number = "TR85-5", address = "Houston, TX"} @phdthesis{MWright:76, author = "M. Wright", year = 1976, title = "Numerical methods for nonlinearly constrained optimization", school = "Department of Computer Science, Stanford University" } @incollection {MWright:98, author = "M. Wright", TITLE = {The interior-point revolution in constrained optimization}, BOOKTITLE = {High performance algorithms and software in nonlinear optimization (Ischia, 1997)}, SERIES = {Appl. Optim.}, VOLUME = {24}, PAGES = {359--381}, PUBLISHER = {Kluwer Acad. Publ.}, ADDRESS = {Dordrecht}, YEAR = {1998}, MRCLASS = {90C51 (90-02)}, MRNUMBER = {2002f:90165}, } @article {MR99i:90093, AUTHOR = {Wright, M.H.}, TITLE = {Ill-conditioning and computational error in interior methods for nonlinear programming}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {9}, YEAR = {1999}, NUMBER = {1}, PAGES = {84--111 (electronic)}, ISSN = {1095-7189}, MRCLASS = {90C30}, MRNUMBER = {99i:90093}, MRREVIEWER = {Florian Jarre}, } @article {MR99g:90136, AUTHOR = {Wright, Stephen J.}, TITLE = {Superlinear convergence of a stabilized {SQP} method to a degenerate solution}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {11}, YEAR = {1998}, NUMBER = {3}, PAGES = {253--275}, ISSN = {0926-6003}, CODEN = {CPPPEF}, MRCLASS = {90C30 (65K05 90C31)}, MRNUMBER = {99g:90136}, MRREVIEWER = {Asen L. Dontchev}, } @article {MR91d:90062, AUTHOR = {Wright, S.J.}, TITLE = {Implementing proximal point methods for linear programming}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {65}, YEAR = {1990}, NUMBER = {3}, PAGES = {531--554}, ISSN = {0022-3239}, CODEN = {JOTABN}, MRCLASS = {90C05 (90C06 90C20)}, MRNUMBER = {91d:90062}, MRREVIEWER = {Christian Michelot}, } @article {MR1724782, AUTHOR = {Wright, S.J.}, TITLE = {Modified {C}holesky factorizations in interior-point algorithms for linear programming}, NOTE = {Dedicated to John E. Dennis, Jr., on his 60th birthday}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {9}, YEAR = {1999}, NUMBER = {4}, PAGES = {1159--1191 (electronic)}, ISSN = {1095-7189}, MRCLASS = {90Cxx}, MRNUMBER = {1 724 782}, } @article {MR97i:90039, AUTHOR = {Wright, S.J.}, TITLE = {Stability of augmented system factorizations in interior-point methods}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {18}, YEAR = {1997}, NUMBER = {1}, PAGES = {191--222}, ISSN = {0895-4798}, CODEN = {SJMAEL}, MRCLASS = {90C05 (65F05 65G05)}, MRNUMBER = {97i:90039}, MRREVIEWER = {Florian Jarre}, } @article {MR96f:65055, AUTHOR = {Wright, S.J.}, TITLE = {Stability of linear equations solvers in interior-point methods}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {16}, YEAR = {1995}, NUMBER = {4}, PAGES = {1287--1307}, ISSN = {0895-4798}, CODEN = {SJMAEL}, MRCLASS = {65F35 (90C05 90C33)}, MRNUMBER = {96f:65055}, MRREVIEWER = {Florian Jarre}, } @article {WrightS:85, AUTHOR = {Wright, S.J.}, TITLE = {AN INEXACT LEVENBERG-MARQUARDT METHOD FOR LARGE SPARSE NONLINEAR LEAST-SQUARES}, JOURNAL = {JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, SERIES B}, VOLUME = {26}, YEAR = {1985}, NUMBER = {Apr.}, PAGES = {387--403} } @article {MR1724780, AUTHOR = {Schnabel, Robert B. and Eskow, Elizabeth}, TITLE = {A revised modified {C}holesky factorization algorithm}, NOTE = {Dedicated to John E. Dennis, Jr., on his 60th birthday}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {9}, YEAR = {1999}, NUMBER = {4}, PAGES = {1135--1148 (electronic)}, ISSN = {1095-7189}, MRCLASS = {65Fxx (15A23 90Cxx)}, MRNUMBER = {1 724 780}, } @article {MR99e:65046, AUTHOR = {Cheng, Sheung Hun and Higham, N.J.}, TITLE = {A modified {C}holesky algorithm based on a symmetric indefinite factorization}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {19}, YEAR = {1998}, NUMBER = {4}, PAGES = {1097--1110 (electronic)}, ISSN = {1095-7162}, MRCLASS = {65F05 (15A23)}, MRNUMBER = {99e:65046}, } @article {MR92a:65133, AUTHOR = {Schnabel, Robert B. and Eskow, Elizabeth}, TITLE = {A new modified {C}holesky factorization}, JOURNAL = {SIAM J. Sci. Statist. Comput.}, FJOURNAL = {Society for Industrial and Applied Mathematics. Journal on Scientific and Statistical Computing}, VOLUME = {11}, YEAR = {1990}, NUMBER = {6}, PAGES = {1136--1158}, ISSN = {0196-5204}, CODEN = {SIJCD4}, MRCLASS = {65F30 (65K10)}, MRNUMBER = {92a:65133}, } @article {MR88d:65097, AUTHOR = {Hoy, A.}, TITLE = {Modified {C}holesky factorizations of the {H}essian matrix for minimizing nonlinear functions}, JOURNAL = {Z. Angew. Math. Mech.}, FJOURNAL = {Zeitschrift f\"ur Angewandte Mathematik und Mechanik. Ingenieurwissenschaftliche Forschungsarbeiten}, VOLUME = {66}, YEAR = {1986}, NUMBER = {11}, PAGES = {564--566}, ISSN = {0044-2267}, CODEN = {ZAMMAX}, MRCLASS = {65K10 (65H10)}, MRNUMBER = {88d:65097}, MRREVR = {R. P. Tewarson}, } @BOOK {SWright:96, author = "S. Wright", title = "Primal-Dual Interior-Point Methods", PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, year = "1996", address = "Philadelphia, Pa"} @TECHREPORT{SWright:97, author = "S. Wright", title = "Modifying {SQP} for degenerate problems", institution = "Argonne National Laboratory", keywords = "SQP, degeneracy", year = "1997"} @incollection{SWright:99, author = "S. Wright", title = "Recent developments in interior-point methods", booktitle = "Proceedings of 19th IFIP TC7 Conference on System Modelling and Optimization, July, 1999, Cambridge", editor = "M.J.D. Powell", Publisher="Kluwer Academic Publishers", ADDRESS = {Boston, MA}, note = "To appear", year = "2000"} @article {MR86k:65048, AUTHOR = {Wright, S.J. and HOLT, J.N.}, TITLE = {An inexact {L}evenberg-{M}arquardt method for large sparse nonlinear least squares}, JOURNAL = {J. Austral. Math. Soc. Ser. B}, FJOURNAL = {Australian Mathematical Society. Journal. Series B. Applied Mathematics}, VOLUME = {26}, YEAR = {1985}, NUMBER = {4}, PAGES = {387--403}, ISSN = {0334-2700}, CODEN = {JAMMDU}, MRCLASS = {65H10 (65F20 86-08)}, MRNUMBER = {86k:65048}, MRREVIEWER = {R.J. Plemmons}, } @article {MR3148498, AUTHOR = {Wu, C. and Li, C. and Long, Q.}, TITLE = {A {DC} programming approach for sensor network localization with uncertainties in anchor positions}, JOURNAL = {J. Ind. Manag. Optim.}, FJOURNAL = {Journal of Industrial and Management Optimization}, VOLUME = {10}, YEAR = {2014}, NUMBER = {3}, PAGES = {817--826}, ISSN = {1547-5816}, MRCLASS = {90B80 (90B10 90C22)}, MRNUMBER = {3148498}, DOI = {10.3934/jimo.2014.10.817}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.3934/jimo.2014.10.817}, } %XXXXXXXXXXXXXXXXXXXXXXXXXXX @article {int:Xu1, AUTHOR = {XU, X. and HUNG, P.-F. and YE, Y.}, TITLE = {A simplified homogeneous and self-dual linear programming algorithm and its implementation}, JOURNAL = {Ann. Oper. Res.}, FJOURNAL = {Annals of Operations Research}, VOLUME = {62}, YEAR = {1996}, PAGES = {151--171}, ISSN = {0254-5330}, } @ARTICLE{2015arXiv150904682X, author = {{Xu}, G. and {Burer}, S.}, title = "{Robust Sensitivity Analysis of the Optimal Value of Linear Programming}", journal = {ArXiv e-prints}, archivePrefix = "arXiv", eprint = {1509.04682}, primaryClass = "math.OC", keywords = {Mathematics - Optimization and Control}, year = 2015, month = sep, adsurl = {http://adsabs.harvard.edu/abs/2015arXiv150904682X}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } %YYYYYYYYYYYYYYY @phdthesis {yang:96, AUTHOR = {YANG, T.}, year = 1996, title = "Iterative Methods for Least Squares and Total Least Squares Problems", school = { Link{\"o}ping University, Sweden}, } @article {MR2000b:65062, AUTHOR = {YANG, T. and LIN, H.X.}, TITLE = {Solving sparse least squares problems with preconditioned {CGLS} method on parallel distributed memory computers}, JOURNAL = {Parallel Algorithms Appl.}, FJOURNAL = {Parallel Algorithms and Applications}, VOLUME = {13}, YEAR = {1999}, NUMBER = {4}, PAGES = {289--305}, ISSN = {1063-7192}, CODEN = {PAAPEC}, MRCLASS = {65F10 (65Y05)}, MRNUMBER = {2000b:65062}, } @incollection {MR1476009, AUTHOR = {YANG, T.}, TITLE = {New {IMGS}-based preconditioners for least squares problems}, BOOKTITLE = {Numerical analysis and its applications (Rousse, 1996)}, SERIES = {Lecture Notes in Comput. Sci.}, VOLUME = {1196}, PAGES = {581--588}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1997}, MRCLASS = {65F30 (65K10)}, MRNUMBER = {1 476 009}, } @article{YaVa:93, AUTHOR = {Vanderbei, R.J. and Yang, B.}, TITLE = {The simplest semidefinite programs are trivial}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {20}, YEAR = {1995}, NUMBER = {3}, PAGES = {590--596}, ISSN = {0364-765X}, MRCLASS = {90C08 (65K05 90C25)}, MRNUMBER = {1354771}, MRREVIEWER = {Henry Wolkowicz}, DOI = {10.1287/moor.20.3.590}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1287/moor.20.3.590}, } @INPROCEEDINGS {Yan92, author = "M. YANNAKAKIS", title = "On the approximation of maximum {S}atisfiability", booktitle = "Proceedings of the Third ACM-SIAM Symposium on Discrete Algorithms", pages = "1--9", year = "1992"} @ARTICLE{Ye:94, AUTHOR = "Y. YE", TITLE = "Combining binary search and {N}ewton's method to compute real roots for a class of real functions", JOURNAL = "Journal of Complexity", VOLUME = 10, YEAR = 1994, PAGES = "271-280" } @book {MR98m:90002, AUTHOR = {YE, Y.}, TITLE = {Interior point algorithms}, SERIES = {Wiley-Interscience Series in Discrete Mathematics and Optimization}, NOTE = {Theory and analysis, A Wiley-Interscience Publication}, PUBLISHER = {John Wiley \& Sons Inc.}, ADDRESS = {New York}, YEAR = {1997}, PAGES = {xvi+418}, ISBN = {0-471-17420-3}, MRCLASS = {90-02 (65K05 90Cxx)}, MRNUMBER = {98m:90002}, MRREVIEWER = {Tam{\'a}s Terlaky}, } @TECHREPORT{YuaByr:91, author = "Y. YUAN and R.H. Byrd", title = "Non-quasi-{N}ewton updates for unconstrained optimization", institution = "Department of Computer Science, University of Colorado at Boulder", year = "1991"} @ARTICLE {Ye:92, author = "Y. YE", title = "On affine scaling algorithms for nonconvex quadratic programming", journal = mprog, year = "1992", volume = "56", pages = "285-300"} @ARTICLE {int:Ye55, author = "Y. YE and M.J. Todd and S. MIZUNO", title = "An {${\cal O}(\sqrt{n} L)$}--iteration homogeneous and self--dual linear programming algorithm", journal = mor, year = "1994", volume = "19", pages = "53-67"} @incollection {Ye:92b, author = "Y. YE", title = "A new complexity result on minimization of a quadratic function with a sphere constraint", booktitle = "Recent Advances in Global Optimization", editors = "C.A. Floudas & P.M. Pardalos", year = "1992", publisher = "Princeton University Press", pages = "19-31"} @article{YeZhang:01, AUTHOR = {Ye, Y. and Zhang, S.}, TITLE = {New results on quadratic minimization}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {14}, YEAR = {2003}, NUMBER = {1}, PAGES = {245--267 (electronic)}, ISSN = {1052-6234}, MRCLASS = {90C20 (90C26)}, MRNUMBER = {2005943 (2004i:90100)}, MRREVIEWER = {Franz Rendl}, DOI = {10.1137/S105262340139001X}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/S105262340139001X}, } @article {MR2447891, AUTHOR = {John, E. and Y{\i}ld{\i}r{\i}m, E.A.}, TITLE = {Implementation of warm-start strategies in interior-point methods for linear programming in fixed dimension}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {41}, YEAR = {2008}, NUMBER = {2}, PAGES = {151--183}, ISSN = {0926-6003}, MRCLASS = {90C05 (90C51)}, MRNUMBER = {2447891 (2009j:90064)}, DOI = {10.1007/s10589-007-9096-y}, URL = {http://dx.doi.org/10.1007/s10589-007-9096-y}, } @article {MR1884918, AUTHOR = {Yildirim, E.A. and Wright, S.J.}, TITLE = {Warm-start strategies in interior-point methods for linear programming}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {12}, YEAR = {2002}, NUMBER = {3}, PAGES = {782--810 (electronic)}, ISSN = {1052-6234}, MRCLASS = {90C51 (90C05)}, MRNUMBER = {1884918 (2003b:90137)}, MRREVIEWER = {Carla Durazzi}, DOI = {10.1137/S1052623400369235}, URL = {http://dx.doi.org/10.1137/S1052623400369235}, } @BOOK {Youn:71, author = "D.M. Young", title = "Iterative Solution of Large Linear Systems", publisher = "Academic Press", year = "1971", address = "New York, NY"} @INCOLLECTION {Youn:76, author = "D.M. Young", title = "Optimization in the presence of noise", booktitle = "Optimization in Action", publisher = "Academic Press", year = "1976", editor = "L.C.W. Dixon", pages = "517", address = "London"} @incollection {MR2002a:90076, AUTHOR = {Yuan, Ya-xiang}, TITLE = {A review of trust region algorithms for optimization}, BOOKTITLE = {ICIAM 99 (Edinburgh)}, PAGES = {271--282}, PUBLISHER = {Oxford Univ. Press}, ADDRESS = {Oxford}, YEAR = {2000}, MRCLASS = {90C30 (65K05 90-02)}, MRNUMBER = {2002a:90076}, } @TECHREPORT {Yuan:83a, author = "Y. YUAN", title = "Global convergence of trust region algorithms for nonsmooth optimization", institution = "Department of Applied Mathematics and Theoretical Physics, University of Cambridge", year = "1983", number = "DAMTP 1983/NA13", address = "Cambridge, England"} @TECHREPORT {Yuan:83b, author = "Y. YUAN", title = "Some properties of trust region algorithms for nonsmooth optimization", institution = "Department of Applied Mathematics and Theoretical Physics, University of Cambridge", year = "1983", number = "DAMTP 1983/NA14", address = "Cambridge, England"} @article {MR91e:90078, AUTHOR = {Yuan, Y.}, TITLE = {On a subproblem of trust region algorithms for constrained optimization}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {47}, YEAR = {1990}, NUMBER = {1 (Ser. A)}, PAGES = {53--63}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C20}, MRNUMBER = {91e:90078}, MRREVR = {Kang Hoh Phua}, } @article {MR86i:90100, AUTHOR = {Yuan, Y.}, TITLE = {On the superlinear convergence of a trust region algorithm for nonsmooth optimization}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {31}, YEAR = {1985}, NUMBER = {3}, PAGES = {269--285}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C30}, MRNUMBER = {86i:90100}, MRREVR = {Bernard Lemaire}, } @article {MR86f:90141, AUTHOR = {Yuan, Y.}, TITLE = {Conditions for convergence of trust region algorithms for nonsmooth optimization}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {31}, YEAR = {1985}, NUMBER = {2}, PAGES = {220--228}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C30}, MRNUMBER = {86f:90141}, } @TECHREPORT {Yuan:83c, author = "Y. YUAN", title = "An example of only linear convergence of trust region algorithms for nonsmooth optimization", institution = "Department of Applied Mathematics and Theoretical Physics, University of Cambridge", year = "1983", number = "DAMTP 1983/NA15", address = "Cambridge, England"} @ARTICLE {Yuan:90, author = "Y. YUAN", title = "On a subproblem of trust region algorithms for constrained optimization", journal = mprog, year = "1990", volume = "47", pages = "53-63"} @ARTICLE {Yuan:91, author = "Y. YUAN", title = "A dual algorithm for minimizing a quadratic function with two quadratic constraints", journal = "Journal of Computational Mathematics", year = "1991", volume = "9", pages = "348-359"} %ZZZZZZZZZZZZZ @article{zhang1988quasi, title={Quasi-{N}ewton algorithms with updates from the preconvex part of Broyden's family}, author={Zhang, Y. and Tewarson, R.P.}, journal={IMA Journal of Numerical Analysis}, volume={8}, number={4}, pages={487--509}, year={1988}, publisher={Oxford University Press} } @incollection {MR95b:90133, AUTHOR = {Z{\u{A}}LINESCU, C.}, TITLE = {On a new stability condition in mathematical programming}, BOOKTITLE = {Nonsmooth optimization: methods and applications (Erice, 1991)}, PAGES = {429--438}, PUBLISHER = {Gordon and Breach}, ADDRESS = {Montreux}, YEAR = {1992}, } @article {MR93b:90095, AUTHOR = {Z{\u{A}}LINESCU, C.}, TITLE = {A note on $d$-stability of convex programs and limiting {L}agrangians}, JOURNAL = mprog, FJOURNAL = {Mathematical Programming}, VOLUME = {53}, YEAR = {1992}, NUMBER = {3, Ser. A}, PAGES = {267--277}, ISSN = {0025-5610}, CODEN = {MHPGA4}, } @article {MR2015542, AUTHOR = {Zhan, X.}, TITLE = {On some matrix inequalities}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {376}, YEAR = {2004}, PAGES = {299--303}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A42 (15A15)}, MRNUMBER = {2015542 (2004i:15014)}, DOI = {10.1016/j.laa.2003.08.008}, URL = {http://dx.doi.org/10.1016/j.laa.2003.08.008}, } @book {MR1927396, AUTHOR = {Zhan, X.}, TITLE = {Matrix inequalities}, SERIES = {Lecture Notes in Mathematics}, VOLUME = {1790}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {2002}, PAGES = {viii+116}, ISBN = {3-540-43798-3}, MRCLASS = {15A45 (47A30 47A63)}, MRNUMBER = {1927396 (2003h:15030)}, MRREVIEWER = {T. Ando}, } @article {MR1777462, AUTHOR = {ZHANG, Y.}, TITLE = {User's guide to {LIPSOL}: linear-programming interior point solvers {V}0.4}, NOTE = {Interior point methods}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods and Software}, VOLUME = {11/12}, YEAR = {1999}, NUMBER = {1-4}, PAGES = {385--396}, ISSN = {1055-6788}, CODEN = {OMSOE2}, MRCLASS = {90C05 (90-04)}, MRNUMBER = {MR1777462}, } @PHDTHESIS {Zh:92, author = "Q. ZHAO", title = "Measures for least change secant methods", school = "University of Waterloo", year = "1992", address = "Waterloo, Ont, Canada"} @article{DBLP:journals/corr/ZhaoP16, author = {H. Zhao and P. Poupart and G. Gordon}, title = {A Unified Approach for Learning the Parameters of Sum-Product Networks}, journal = {CoRR}, volume = {abs/1601.00318}, year = {2016}, url = {http://arxiv.org/abs/1601.00318}, timestamp = {Wed, 07 Jun 2017 14:42:30 +0200}, biburl = {http://dblp.uni-trier.de/rec/bib/journals/corr/ZhaoP16}, bibsource = {dblp computer science bibliography, http://dblp.org} } @article{ZhangHuang:03, AUTHOR = "Z. ZHANG and Y. HUANG", TITLE = "A Projection Method for Least Squares Problems with a Quadratic Equality Constraint", JOURNAL = simax, VOLUME = "25", NUMBER ="1", YEAR = "2003", PAGES = "188--212", } @techreport{JiaLi:jan11, author = "Z. Jia and B. Li", title = "A contribution to the condition number of the total least squares problem", institution = "Northeast Normal University", number = "arXiv:1101.2342v1", year = "2011", address = "Cangchun 130024, China" } @incollection{ziembamulvey, title = "Assect/liability management under uncertanity for fixed income securities", author = "ZENIOS, S.A.", editor = "W.T ZIEMBA, J.M. MULVEY", booktitle = "Worldwide Asset and Liability Modeling", publisher = "Cambridge University Press", note="Publications of the {N}ewton Institute series", year = "1998", } @article{malyshev:03, AUTHOR = "A.N. MALYSHEV", TITLE = "A Unified Theory of Conditioning for Linear Least Squares and Tikhonov Regularization Solutions", JOURNAL = simax, VOLUME = "24", NUMBER ="4", YEAR = "2003", PAGES = "1186--1196", } @incollection{MR2160825, TITLE = {Eigenvalue and singular value inequalities of {S}chur complements}, AUTHOR = {Liu, J.}, SERIES = {Numerical Methods and Algorithms}, VOLUME = {4}, booktitle = {The {S}chur complement and its applications}, EDITOR = {ZHANG, F.}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {2005}, PAGES = {xvi+295}, ISBN = {0-387-24271-6}, MRCLASS = {15-06 (62-06 62H20 65-03 65-06)}, MRNUMBER = {MR2160825}, MRREVIEWER = {Daniel Kressner}, } @article {MR1629451, AUTHOR = {Zhang, Xin-Min}, TITLE = {Optimization of {S}chur-convex functions}, JOURNAL = {Math. Inequal. Appl.}, FJOURNAL = {Mathematical Inequalities \& Applications}, VOLUME = {1}, YEAR = {1998}, NUMBER = {3}, PAGES = {319--330}, ISSN = {1331-4343}, MRCLASS = {26B25 (26D07)}, MRNUMBER = {MR1629451 (99f:26017)}, MRREVIEWER = {Ion Cojocaru}, } @ARTICLE{Zha:92, AUTHOR = "Y. Zhang", TITLE = {Computing a {C}elis-{D}ennis-{T}apia trust-region step for equality constrained optimization}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {55}, YEAR = {1992}, NUMBER = {1, Ser. A}, PAGES = {109--124}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C30 (65K05)}, MRNUMBER = {MR1163297 (93c:90086)}, MRREVIEWER = {Bernd Luderer}, } % % % ref.bib % @article {kn:nick, author = "N.I.M. Gould", title = "On solving three classes of nonlinear programming problems via simple differentiable penalty functions", journal = jota, year = 1988, volume = 56, pages = "89-126" } @article{GratMoufToin09, author = {S. Gratton and M. Mouffe and Ph.L. Toint}, title = {Stopping rules and backward error analysis for bound-constrained optimization}, journal = "Numerische Mathematik", note = {DOI: 10.1007/s00211-011-0376-1}, volume = {(to appear)}, year = 2011} @article {MR2072928, AUTHOR = {Gould, N.I.M. and Toint, Ph.L.}, TITLE = {Preprocessing for quadratic programming}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming. A Publication of the Mathematical Programming Society}, VOLUME = {100}, YEAR = {2004}, NUMBER = {1, Ser. B}, PAGES = {95--132}, ISSN = {0025-5610}, MRCLASS = {90C20}, MRNUMBER = {2072928 (2005e:90084)}, MRREVIEWER = {Eugenia Duca}, } @techreport{kn:cl3, author = "A. R. Conn and Y. Li ", title = "An approach to nonlinear $l_\infty$ approximation", institution = "Department of Computer Science", year = 1989, number = "CS-89-21", address = " University of Waterloo, Waterloo, Ontario N2L 3G1, Canada" } @inproceedings{kn:cl4, author = "A. R. Conn and Y. Li", year = "To appear", editor = "J. P. Hennart " , booktitle = "Proceedings of the Fifth Mexican Workshop on Numerical Analysis", publisher = " Springer Verlag " } @article{cp, author = "Andrew Roger Conn and Tomasz Pietrzykowski", title = {A Penalty Function Method Converging Directly to a Constrained Optimum}, journal = sinum, volume = 14, number = 2, month = Apr, year = 1977, pages = "348-375" } @article{ kn:tc1, author =" T. F. COLEMAN and A. R. Conn", year = 1984, title = "On the Local Convergence of a Quasi-{N}ewton Method for the Nonlinear Programming Problem", journal = " Siam J. Numer. Anal.", volume = 21, pages =" 755-769" } @book{kn:vanloan, author = "G.H. Golub and C.F. {Van Loan}", title = "Matrix Computations", publisher = "The Johns Hopkins University Press", year = 1983 } @book{kn:maga, author = "Mangasarian, O. L.", title = "Nonlinear Programming", publisher = "McGraw-Hill", year = 1969 } @book{kn:kowalik, author = "J. S. Kowalik and M. R. Osborne", title = "Methods for Unconstrained Optimization", year = 1968, publisher = "American Elsevier Publishing Co." } @article{kn:rosen, author = "J. B. Rosen and S. Suzuki", title = "Construction of the Nonlinear Programming Test Problems", journal = "Communications of the Association of Computing Machinery", volume = 8, year = 1965, pages = 113 } @article{kn:rosenbrock, author = "H. H. Rosenbrock", title = " An Automatic Method for Finding the Greatest or Least Value of a Function", journal = "Comp. J.", volume = 3, year = 1960, pages = "175-184" } @article{kn:BPR, author = "I. Barrodale and M. J. D. Powell and F. D. K. Roberts ", title = "The differential Correction Algorithm for Rational $L_\infty$-Approximation", journal = "SIAM J. Num. Anal.", volume = 7, year = 1972, pages = "493-504" } @article{kn:elattar, author = "El-Attar and M. Vidyasagar and S. R. K. Dutta", title = "An Algorithm for $l_1$-Approximation", journal = "SIAM J. Num. Anal.", volume = 16, year = 1979, pages = "70-86" } @article{kn:davidon, author = "Davidon", title = "New Least Square Algorithm", journal = "J. Opt. Theory and Applics.", volume = 18, year = 1976, pages = "187-198" } @article{kn:3, author = "Barrodale, I and Roberts, {F. D. K.}", title = "An Improved Algorithm for Discrete $ l_1 $ Linear Approximation", journal = "SIAM J. Num. Anal.", volume = 10, year = 1972, pages = "839-848" } @article{kn:4, author = "Barrodale, I. and Young, A.", title = "Algorithms for best $ L_1 $ and $ L_{\infty} $ Linear Approximations on a Discrete Set", journal = "Numer. Math.", volume = 8, year = 1966, pages = "295-306" } @article{kn:chris, author = "C. Charalambous and J. W. Bandler", title = " Nonlinear Minimax Optimisation as a Sequence of Least pth Optimization with Finite Values of p", journal = "International Journal of System Science", year= 1976, pages ="377-394", volume = 7 } @article{kn:5, author = "R. H. Bartels and A. R. Conn", title = " Linearly Constrained Discrete $ l_1 $ Problems", journal = "ACM Trans. on Math. Software", year= 1980, number = 4, pages ="594-608", volume = 6 } @techreport{kn:6, author = "R. H. Bartels and A. R. Conn", title = "A Primal, Penalty Linear Programming Method for Solving Overdetermined Linear Systems in the $ L_{\infty} $ Sense", number = "Tech. Rept. CORR 77/143", year = 1977, institution = "Univ. of Waterloo", address = "Dept. of Combinatorics and Optimization, Waterloo, Ontario, Canada, N2L 3G1" } @article{kn:8, author = "R. H. Bartels and A. R. Conn and J. W. Sinclair", title =" Minimization Techniques for Piecewise Differentiable Functions: the $ l_1 $ Solution to an Overdetermined Linear System", journal = "SIAM J. Numer. Anal.", volume = 15, year = 1978, pages= "224-241" } @article{kn:9, author = "R. H. Bartels and G. H. Golub", title = "Stable Numerical Methods for Obtaining the Chebychev Solution to an Overdetermined System of Equations", journal = "Comm. ACM ", volume = 11, year = 1968, pages =" 401-406 " } @incollection {MR0272396, AUTHOR = {Bartels, R.H. and Golub, G.H. and Saunders, M.A.}, TITLE = {Numerical techniques in mathematical programming}, BOOKTITLE = {Nonlinear {P}rogramming ({P}roc. {S}ympos., {U}niv. of {W}isconsin, {M}adison, {W}is., 1970)}, PAGES = {123--176}, PUBLISHER = {Academic Press}, ADDRESS = {New York}, YEAR = {1970}, MRCLASS = {90.58 (65.00)}, MRNUMBER = {0272396 (42 \#7277)}, } @article {MR0240957, AUTHOR = {Bartels, R.H. and Golub, G.H.}, TITLE = {Stable numerical methods for obtaining the {C}hebyshev solution to an overdetermined system of equations}, JOURNAL = {Comm. ACM}, FJOURNAL = {Communications of the Association for Computing Machinery}, VOLUME = {11}, YEAR = {1968}, PAGES = {401--406}, ISSN = {0001-0782}, MRCLASS = {65.35}, MRNUMBER = {0240957 (39 \#2302)}, } @article {MR0321519, AUTHOR = {Gill, Philip E. and Murray, Walter}, TITLE = {A numerically stable form of the simplex algorithm}, JOURNAL = {Linear Algebra and Appl.}, VOLUME = {7}, YEAR = {1973}, PAGES = {99--138}, MRCLASS = {90C05}, MRNUMBER = {0321519 (47 \#10052)}, MRREVIEWER = {Romesh Saigal}, } @article{bartelsgolub:69, author = "R.H. Bartels and G.H. Golub", title = "The simplex method of linear programming using {LU} decomposition", journal = "Comm. ACM ", volume = 12, number = "5", year = 1969, pages =" 4266-268 " } @article{kn:11, author = "A. R. Conn", title = " Linear Programming via a Nondifferentiable Penalty Function", journal = "SIAM J. Numer. Anal.", volume = 13, year =1976, pages = "145-154" } @article{kn:12, author = "B. Joe and R. H. Bartels", title = "An Exact Penalty Method for Constrained, Discrete,Linear $ l_{\infty} $ Data Fitting", journal = "SIAM J. Sci. Stat. Comput.", volume = 4 , year =1983, pages = "69-84" } @book{kn:13, author = "Osborne, {M. R.}", title = "Finite Algorithms in Optimization and Data Analysis", publisher = "John Wiley", year = 1985 } @book{kn:14, author = "Powell, {M. J. D.}", title = "Approximation Theory and Methods", publisher = "Cambridge University Press", year =1981 } @article{kn:15, author = "Stiefel, {E. L.}", title = "Note on Jordan Elimination, Linear Programming and Tschebyscheff Approximation", journal="SIAM J. Numer. Math.", volume = 2, year = 1960, pages = "1-17" } @article{kn:anderson, author= "D. H. ANDERSON and M. R. OSBORNE ", title="Discrete, Nonlinear Approximations in Polyhedral Norms: a {Levenberg}-like Algorithm", journal = "Numerische Mathematik", pages = "167-170", volume = 28, year = 1977 } @article{kn:bdch, author = "J. W. Bandler and C. Charalambous", title = " Practical Least pth Optimization of Networks", journal = " IEEE Trans. Micro. Theory and Techniques", pages = "834-840", volume = "MTT-20", year = 1972 } @article{kn:bandler, author = "J. W. Bandler and C. Charalambous", title = " Nonlinear Programming Using Minimax Techniques", journal = jota, pages = "607-619", volume = 13, year = 1974 } @inproceedings{kn:bp, author ="Barrodale, I. and Phillips, C.", title ="An Improved Algorithm for Discrete {Chebychev} Linear Approximation", booktitle =" Proc. 4th Manitoba Conf. on Numer. Math.", address = " U. of Manitoba, Winnipeg, Canada", year= 1974, pages = "177-190" } @article{kn:bp1, author = "I. Barrodale and C. Phillips", title = "Algorithm 495; Solutions of an Overdetermined System of Linear Equations in the {Chebyshev} Norm", journal = toms, year = "1975", volume = "1", pages = "264-270" } @article{kn:bcc, author = "R. H. Bartels and A. R. Conn and C. Charalambous", title = "On {Cline's} Direct Method for Solving Overdetermined Linear Systems in the $ l_{\infty} $ Sense", journal = "SIAM J. Numer. Anal.", volume = 15, year =1978, pages = "255-270" } @article{ kn:bcl, author = "R. H. Bartels and A. R. Conn and Y. Li", title = "Primal Methods are Better Than Dual Methods for Solving Overdetermined Linear Systems in the $l_{\infty}$ Sense?", journal = "SIAM J. Numer. Anal.", year = "To appear" } @article{kn:ben, author = "BEN-TAL and ZOWE", year = "1982", title = "Necessary and Sufficient Optimality Conditions for a Class of Nonsmooth Minimization Problems", journal = "Math. Prog.", volume = "24", pages ="70-91" } @article{ kn:mich, author = "M. Brannigan", year = "1985", title = "Discrete {Chebyshev} Approximation with Linear Constraints", journal = "SIAM J. Numer. Anal.", volume = 22, pages ="1-14" } @techreport{kn:Senad, author = "Busova\v{c}a, S.", title = "Handling Degeneracy in a Nonlinear $ L_1 $ Algorithm", number = "Tech. Rept. CS-85-34", institution = "Univ. of Waterloo", address = "Dept. of Computer Science, Univ. of Waterloo, Waterloo, Ontario N2L 3G1", year= 1985 } @techreport{kn:colville, author = "A. R. Colville", title = "A Comparative Study on Nonlinear Programming Codes", number = "320-2949", year = 1968, institution= " IBM Thomas J. Watson Research Center, Yorktown Heights, New York " } @techreport{kn:charal, author = "C. Charalambous", title = "Acceleration of the Least pth Algorithm for Minimax Optimization", number = "28-0-28067", year = 1977, institution= "University of Waterloo, Department of System Design" } @article{kn:cc, author = "C. Charalambous and A. R. Conn", title = "An Efficient Method to Solve the Minimax Problem Directly", journal = "SIAM J. Numer. Anal.", volume = "15", year = "1978", pages = "162-187" } @phdthesis{kn:chamber, author = "R. M. Chamberlain", year = 1980, title = "The Theory and Application of Variable Metric Methods to Constrained Optimization Problems", school = { Corpus Christi College, Cambridge} } @phdthesis{kn:lithesis, author = "Yuying Li", year = 1988, title = "An Efficient Algorithm for Nonlinear Minimax Problems", school = { University of Waterloo } } @phdthesis{kn:watsonthesis, author = "G. A. Watson", year = 1969, title = "Chebyshev approximation with applicatons to the numerical solution of differntial equations", school = {Australian National University} } @phdthesis{kn:madsen, author = "K. Madsen", year = 1985, title = "Minimization of Nonlinear Approximation Functions", school = "Technical University of Denmark" } @article{kn:clpp, author = "R. M. Chamberlain, C. Lemarechal, H. C. Pedersen and M. J. D. Powell", year = 1982, title = " The Watchdog Technique for Forcing Convergence in Algorithms for Constrained Optimization", journal = "Math. Prog. Study", volume = 16, pages = "1-17" } @inproceedings{kn:char, author = "C. Charalambous", year = 1978, title = "Some Recent Advances in Nonlinear Programming", journal = " Large Engineering Systems 2", pages = "133-?", editor = "G. J. Savage and P. H. Roe Ed." } @article{kn:chen, author = "Chen", title = "Solution of minmax problems using equivalent differentiable functions", journal = "Comp. \& Math. with Appl.", volume = 11, year = 1985, pages = "1165-1169" } @book{kn:chny1, author = "E. W. Cheney", year = 1966, title = "Introduction to Approximation Theory", publisher = "Mc Graw-Hill" } @article{kn:cg, author = "E. W. Cheney and A. A. Goldstein", title = "{N}ewton's Method for Convex Programming and {Tchebycheff} Approximation", journal = "Numer. Mathe.", volume = 1, pages = "253-268", year = 1959 } @article{kn:tc, author = "T. F. COLEMAN and A. R. Conn", year = 1982, title = "Nonlinear Programming Via An Exact Penalty Function: Asymptotic Analysis", journal = "Math. Prog.", volume = 24, pages = "123-136" } @misc{kn:conn2, author = "Conn, A. R.", title = "Private communication", year = "1985" } @techreport{kn:cl1, author = "A. R. Conn and Y. Li ", title = " Structure and Characterization of Discrete {C}hebyshev Problems ", institution = "Department of Computer Science", year = 1988, number = "CS-88-39", address = " University of Waterloo, Waterloo, Ontario N2L 3G1, Canada" } @techreport{kn:cl2, author = "A. R. Conn and Y. Li ", title = " An Efficient Algorithm for nonlinear Minimax Problems ", institution = "Department of Computer Science", year = 1988, number = "CS-88-41", address = " University of Waterloo, Waterloo, Ontario N2L 3G1, Canada" } @techreport{kn:conn, author = "Conn, A. R. ", title = "An Efficient Second Order Method to Solve the (Constrained) Minimax Problem", number = "CORR 79-5", year = 1979, institution = " Dept. of Combinatorics and Optimization, University of Waterloo, Ontario, Canada" } @article{kn:gorge, author = "Dennis, Jr., J. E. and J. J. Mor\'{e}", year = 1977, title = "Quasi-{N}ewton Methods, Motivation and Theory", journal = "SIAM Review", volume = 19, pages = "46-89" } @book{kn:dennis, author = "Dennis, Jr., J. E. and R.E. Schnable", year = 1983, title = " Numerical Methods for Unconstrained Optimization and Nonlinear Equations", publisher = "Prentice-Hall, Englewood Cliff" } @article{kn:descloux, author = "J. Descloux", year = 1961, title = " D\'{e}g\'{e}n\'{e}resence Dans Les Approximations de {Tschebysheff} Lin\'{e}aries et Discr\`{e}tes", journal = "Numerische Mathematik", volume = 3, pages = "180-187" } @book{kn:dem, author = "DEM'YANOV and MALOZEMOV", year = 1974, title = " Introduction to Minimax", publisher = "Keter Publishing House", address = "Jerusalem" } @article{kn:Drez, author = "Drezner", year = 1982, title = { On Minimax Optimization Problems}, journal = " Math. Prog.", volume = 22, pages = "227-230" } @inproceedings{kn:flt1, author = "R. Fletcher", year = 1981, title = {Second Order Corrections for Non-differentiable Optimization}, editor = { G.A. Watson }, booktitle = "Lecture Notes in Mathematics 912", publisher = " Springer Verlag", pages = "85-114" } @article{kn:flt2, author = "R. Fletcher", year = 1982, title = {A Model Algorithm for Composite Nondifferentiable Optimization Problems}, journal = "Math. Prog. Study", volume = 17, pages = "67-76" } @techreport{kn:gm1, author = "P. E. Gill and W. Murray", year = 1974, title = {Safeguarded Steplength Algorithms for Optimization Using Descent Methods}, institution = " National Physical Laboratory", number =" Report NAC 37" } @article{kn:gm, author = "P. E. Gill and W. Murray", year = "1978", title = {Numerically Stable Methods for Quadratic Programming}, journal = "Math. Prog.", volume = "14", pages = "349-372" } @article{erwaygillgriffin:09, author = "J.B. Erway and P.E. Gill and J.D. Griffin", year = "2009", title = {Iterative Methods for Finding a Trust-region Step}, journal = "siopt", volume = "20", number="2", pages = "1110-1131" } @book{kn:gm3, author = "P. E. Gill and W. Murray", year = 1974, title = { Numerical Methods for Constrained Optimization}, publisher = "Academic Press" } @book{kn:gmw, author = "P.E. GILL and W. MURRAY and M.H. Wright", year = 1981, title = { Practical Optimizations}, publisher = " Academic Press" } @article{kn:hdmd, author = "J. Hald and K. Madsen", year = 1981, title = { Combined {LP} and {Quasi-{N}ewton} methods for Minimax Optimization}, journal = "Math. Prog.", volume = 20, pages = "49-62" } @article{kn:han1, author = "S. P. Han", year = 1976, title = { Superlinearly Convergent Variable Metric Algorithms for General Nonlinear Programming Problems}, journal = "Math. Prog.", volume = 11, pages ="?" } @techreport{kn:han3, author = "S. P. Han", year = 1978, title = { Superlinear Convergence of a Minimax Method }, institution = "Cornell Tech. Report", number = "$\sharp$TR78-336" } @article{kn:han2, author = "S. P. Han", title = {Variable Metric Methods for Minimizing a Class of Nondifferentiable Functions}, journal = " Math. Prog.", volume = 20, year = 1981, pages = "1-13" } @inproceedings{kn:hettich, author = "Hettich", year = 1976, title = {A {N}ewton-Method for Nonlinear {Chebyshev} Approximation}, booktitle =" Lecture Notes in Mathematics 556", editor="Schaback, R. and Scherer, K", publisher = " Springer Verlag", pages = "222-236" } @book {MR1349828, AUTHOR = {Lawson, C.L. and Hanson, R.J.}, TITLE = {Solving least squares problems}, SERIES = {Classics in Applied Mathematics}, VOLUME = {15}, NOTE = {Revised reprint of the 1974 original}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA}, YEAR = {1995}, PAGES = {xii+337}, ISBN = {0-89871-356-0}, MRCLASS = {65F20}, MRNUMBER = {1349828}, DOI = {10.1137/1.9781611971217}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/1.9781611971217}, } @book {MR0366019, AUTHOR = {Lawson, C.L. and Hanson, R.J.}, TITLE = {Solving least squares problems}, SERIES = {Prentice-Hall Series in Automatic Computation}, PUBLISHER = {Prentice-Hall, Inc., Englewood Cliffs, N.J.}, YEAR = {1974}, PAGES = {xii+340}, MRCLASS = {65F20}, MRNUMBER = {0366019}, MRREVIEWER = {R. P. Tewarson}, } @book{kn:hanson, author = "C.L. Lawson and R.J. Hanson", year = 1974, title = { Solving Least Square Problems}, publisher = " Prentice-Hall" } @article {MR1167883, AUTHOR = {HANSON, R.J. and KROGH, F.T.}, TITLE = {A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints}, JOURNAL = {ACM Trans. Math. Software}, FJOURNAL = {Association for Computing Machinery. Transactions on Mathematical Software}, VOLUME = {18}, YEAR = {1992}, NUMBER = {2}, PAGES = {115--133}, ISSN = {0098-3500}, CODEN = {ACMSCU}, MRCLASS = {65Y10 (49M30)}, MRNUMBER = {1 167 883}, } @article{kn:man1, author = "K. Madsen", year = 1975, title = { Minimax Solution of Nonlinear Equations Without Calculating Derivatives}, journal = "Mathematical Programming Study", volume = 3, pages = "110-126" } @inproceedings{kn:may, author = "Mayne, D. Q. ", year = 1979, title = {On the Use of Exact Penalty Functions to Determine Steplength in Optimization Algorithms}, editor = "G. A. Watson", booktitle = "Lecture Notes in Mathematics 773", publisher = " Springer Verlag", pages = "98-109" } @book{kn:gn, author = "G. Meinardus", year = 1967, title ={ Approximation of Functions: Theory and Numerical Methods}, note ="translated by Larry, L. Schumaker", publisher = "Springer Verlag" } @article{kn:mt, author = "T. S. Motzkin", year = 1949, title ={Approximation by Curves of a Unisolvent Family}, journal = "Bull. Amer. Math. Soc.", volume = 55, pages = "789-793" } @article{kn:gm2, author = "W. MURRAY and M.L. Overton", year = 1979, title = { Steplength Algorithms for Minimizing a Class of Nondifferentiable Functions}, journal = "Computing", volume = 23, pages = "309-331" } @article{kn:water, author = "W. MURRAY and M.H. Wright", year = 1982, title = {Computation of the Search Direction in Constrained Optimization Algorithms}, journal = "Math. Prog. Study", volume = 16, pages = "62-83" } @article{kn:nocedal, author = "J. Nocedal and M.L. Overton", year = 1985, title = { Projected {H}essian Updating Algorithms For Nonlinearly Constrained Optimization}, journal = "SIAM J. Numer. Anal.", volume =22, pages = "821-850" } @book {MR2001b:90002, AUTHOR = {Nocedal, J. and Wright, S.J.}, TITLE = {Numerical optimization}, SERIES = {Springer Series in Operations Research and Financial Engineering}, EDITION = {Second}, PUBLISHER = {Springer, New York}, YEAR = {2006}, PAGES = {xxii+664}, ISBN = {978-0387-30303-1; 0-387-30303-0}, MRCLASS = {90-01 (49Mxx 65K05 90-02 90C30)}, MRNUMBER = {2244940 (2007a:90001)}, MRREVIEWER = {Michael C. Ferris}, } @article{kn:ow, author = "M. R. Osborne and G. A. Watson", year = 1968, title = {An Algorithm for Minimax Approximation in the Nonlinear Case}, journal = "Computing J.", volume = 12, pages = " 63-68 " } @article{kn:ow2, author = "M. R. Osborne and G. A. Watson", year = 1969, title = {A Note on Singular Minimax Approximation Problem}, journal = "J. Math. Anal. and Appl.", volume = 25, pages = "692-709" } @incollection{kn:overton, author = "M.L. Overton", year = 1982, title = {Algorithms for Nonlinear $l_1$ and $l_{\infty}$ Fitting}, booktitle= "Nonlinear Optimization 1981", editor = " M. J. D. Powell.", publisher ="Academic Press, New York", note = "NATO conference series II" } @article{kn:pow1, author = "M. J. D. Powell", year = 1978, title = { Algorithms for Nonlinear Constraints That Use {Lagrangian} Functions}, journal = "Math. Prog.", volume = 14 } @incollection{kn:pow2, author = "Powell, M. J. D.", year = 1978, title = {The Convergence of Variable Metric Methods for Nonlinearly Constrained Optimization Calculations}, booktitle = "Nonlinear Programming 3", editor = "O.L. Mangasrian, R. R. Meyer and S. M. Robinson", publisher ="Academic Press, London and New York", pages = "27-63" } @incollection{kn:powell2, author = "Powell, M. J. D.", year = 1978, title = { A Fast Algorithm for Nonlinearly Constrained Optimization Calculations, }, editor = "G.A. Watson" , booktitle = " Numerical Analysis, Lecture Notes in Mathematics, no. 630", publisher = " Springer Verlag", pages ="144-157" } @book{kn:powell, author = "Powell, M. J. D.", year = 1981, title = {Approximation Theory and Methods}, publisher =" Cambridge University Press" } @article{kn:rice1, author = "J. R. Rice", year = 1964, title = {On the Existence and Characterisation of Best Nonlinear {Tchebyshev} Approximation}, journal = "Tran. Am. Math. Soc.", volume = 110, pages = "88-97" } @book{kn:rice0, author = "J. R. Rice", year = 1964, title = { The Approximation of Functions 1, Linear Theory}, publisher = "Addison-Wesley" } @book{kn:rice2, author = "J. R. Rice", year = 1969, title = {The Approximation of Functions 2, Nonlinear Theory}, publisher = "Addison-Wesley" } @inproceedings{kn:stf, author = "Stiefel, E. L. ", year = 1959, title = { Numerical Methods of {Tchebycheff} Approximation}, booktitle = "Proceedings of a symposium", organization= " math. research center", publisher = "Univ. of Wisconsin Press" } @article{kn:torn, author = "L. Tornheim", year = 1950, title = {On N-parameter Families of Functions and Associated Convex Functions}, journal = "Trans. Amer. Math. Soc.", volume = 69, pages = "457-467" } @book{kn:val, author = "S. Vajda", year = 1961, title = mprog, publisher = " Addison-Wesley" } @article{kn:bdmd, author = "J. W. Bandler and P. A. McDobald", year = 1969, title = {Optimization of Microwave Networks by Razor Research}, journal = "IEEE Trans. Microwave Theory Tech.", volume = 17, pages = "552-562" } @article{kn:watson76, author = "Watson, G. A.", year = 1976, title = {A Method for Calculating Best Non-linear {Chebyshev} Approximations}, journal = "J. Inst. Math. Appl.", volume = 18, pages = "351-360" } @article{kn:wat, author = " Watson, G. A.", year = 1979, title = {The Minimax Solution of an Overdetermined System of Non-linear Equations}, journal = "J. Inst. Math. Appl.", volume = 23, pages = "167-180" } @article{kn:wmf, author = "R. S. Womersley and R. Fletcher", title = {An Algorithm for Composite Nonsmooth Optimization Problems}, journal = "J. Opt. Theory and Applis.", volume = 48, year = 1986, pages ="493-523" } @article{kn:cheby, author = "Chebyshev", title = " \em Sur les questions de minimum qui se rattachent \`{a} la r\'{e}pr\'{e}sentation approximative des fonctions", journal = " Oeuvres", volume = 1, address = " St. Petersburg", year = 1899, pages = "273-378" } @article{kn:mo, author = "W. Murray and M.L. Overton", title = {A Projected {Lagrangian} Algorithm for Nonlinear Minimax Optimization}, journal = "SIAM. J. Sci. Stat. Comput.", volume = 1, year = 1980, pages = " 345-370" } @book{kn:watson3, author = "G. A. Watson", title = " Approximation Theory and Numerical Methods", publisher = "John Wiley", year = 1980 } @book{f, author = "R. Fletcher", year = 1987, title = "Practical Methods of Optimization", edition = "second", publisher = "Wiley-Interscience" } @article{w, author = "P. Wolfe", title = {A technique for resolving degeneracy in linear programming}, journal = "SIAM Journal", volume = 11, year = 1963, pages = "205-211" } @article{ro, author = "D. M. Ryan and M. R. Osborne", title = {On the solution of highly degenerate linear programmes}, journal = mprog, volume = 41, year = 1988, pages = "385-392" } % addbib - additions from Serge Kruk for China proceedings @TECHREPORT {St:93, author = "G.W. Stewart", title = "On Infinitely Many Algorithms for Solving Equations", institution = "University of Maryland", year = "1993", number = "TR-92-121", note = "Translation of the 1870 Schr{\"o}der paper"} @TECHREPORT {PY:86, author = "M.J.D. Powell and Y. YUAN", title = "A trust region algorithm for equality constrained optimization", institution = "Department of Applied Mathematics and Theoretical Physics, University of Cambridge", year = "1986", number = "DAMTP 1986/NA2", address = "Cambridge, England"} @ARTICLE {VM:90, author = "G.G. VINING and R.H. MYERS", title = "Combining Taguchi and Response Surface Philosophies: A Dual Response Approach" , journal = "Journal of Quality Technology", year = "1990", volume = "22", pages = "38-45"} @article {MR1885208, AUTHOR = {Dantzig, G.B.}, TITLE = {Linear programming}, NOTE = {50th anniversary issue of Operations Research}, JOURNAL = {Oper. Res.}, FJOURNAL = {Operations Research}, VOLUME = {50}, YEAR = {2002}, NUMBER = {1}, PAGES = {42--47}, ISSN = {0030-364X}, CODEN = {OPREAI}, MRCLASS = {90C05 (90-03)}, MRNUMBER = {1885208}, DOI = {10.1287/opre.50.1.42.17798}, URL = {http://dx.doi.org/10.1287/opre.50.1.42.17798}, } @ARTICLE {Da:49, author = "G.B. Dantzig", title = "Programming in a linear structure", journal = "Econometrica", year = "1949", volume = "17"} @ARTICLE {KuTu:51, author = "H.W. Kuhn and A.W. Tucker", title = "Nonlinear programming", journal = "Econometrica", year = "1951", volume = "19"} @BOOK{Be:95, AUTHOR = "M. J. BEST and K. RITTER ", TITLE = "Quadratic Programming Active Set Analysis and Computer Programs", publisher = "University of Waterloo", YEAR = 1995 } @ARTICLE {Best1, author = "M.J. BEST and J. HLOUSKOVA", title = "An algorithm for portfolio optimization with transaction costs", journal = "Management Science", year = "2005", pages = "1676--1688", volume = "51"} @article {MR2312254, author = "M.J. BEST and J. HLOUSKOVA", TITLE = {Quadratic programming with transaction costs}, JOURNAL = {Comput. Oper. Res.}, FJOURNAL = {Computers \& Operations Research}, VOLUME = {35}, YEAR = {2008}, NUMBER = {1}, PAGES = {18--33}, ISSN = {0305-0548}, CODEN = {CMORAP}, MRCLASS = {91B28 (90C20)}, MRNUMBER = {MR2312254}, } @article {MR1954028, author = "M.J. BEST and J. HLOUSKOVA", TITLE = {Portfolio selection and transactions costs}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {24}, YEAR = {2003}, NUMBER = {1}, PAGES = {95--116}, ISSN = {0926-6003}, CODEN = {CPPPEF}, MRCLASS = {90C20 (90C31 91B28)}, MRNUMBER = {MR1954028 (2003m:90084)}, } @ARTICLE {ElAl:91, author = "M. EL-ALEM", title = "A Global convergence theory for the {CDT} trust-region algorithm for constrained optimization" , journal = sinum, year = "1991", volume = "28", pages = "266-290"} @ARTICLE {FuKo:95b, author = "T. Fujie and M. Kojima", title = "Semidefinite Programming Relaxation for Nonconvex Quadratic Programs" , journal = "Technical report", institution = "Dept. of Information Sciences", address= "Tokyo Institute of Technology, Tokyo, Japan", year = "1995", volume = "", pages = ""} @ARTICLE {LySz:94, author = "S. Lyle and M. Szularz", title = "Local Minima of the Trust Region Problem" , journal = jota, year = "1994", volume = "80", pages = "117-134"} @ARTICLE {Dr:63, author = "N.R. DRAPER", title = "Ridge analysis of surface response" , journal = "Technometrics", year = "1959", volume = "5", pages = "469-479"} @ARTICLE {Ho:59, author = "A.E. HOERL", title = "Optimal solution of many-variable equations" , journal = "Chemical engineering progress", year = "1959", volume = "55", pages = "69-78"} @ARTICLE {MyCa:73, author = "R.H. MYERS and W.H. CARTER", title = "Response surface techniques for Dual Response Systems", journal = "Technometrics", year = "1973", volume = "15", pages = "301-317"} @ARTICLE {PoYu:86, author = "M.J.D. Powell and Y. YUAN", title = "A recursive quadratic programming algorithm that uses differentiable penalty functions", journal = "Math. Prog.", year = "1986", volume = "7", pages = "265-278"} @ARTICLE {Rocka:73, author = "R.T. Rockafellar", title = "Augmented Lagrange Multipliers Functions and Duality in Nonconvex Programming", journal = "SIAM Journal on Control", year = "1973", volume = "12", pages = "268-285"} @ARTICLE {Han:77b, author = "S.P. HAN", title = "A globally convergent method for nonlinear programming", journal = jota, year = "1977", volume = "22", pages = "297-309"} @article {MaMa:95, AUTHOR = {MATHIS, F.H. and MATHIS, L.J.}, TITLE = {A nonlinear programming algorithm for hospital management}, JOURNAL = {SIAM Rev.}, FJOURNAL = {SIAM Review. A Publication of the Society for Industrial and Applied Mathematics}, VOLUME = {37}, YEAR = {1995}, NUMBER = {2}, PAGES = {230--234}, ISSN = {0036-1445}, CODEN = {SIREAD}, } @incollection {MR96m:90100, AUTHOR = {SCHAIBLE, S.}, TITLE = {Fractional programming}, BOOKTITLE = {Handbook of global optimization}, PAGES = {495--608}, SERIES = {Nonconvex Optim. Appl.}, VOLUME = {2}, PUBLISHER = {Kluwer Acad. Publ.}, ADDRESS = {Dordrecht}, YEAR = {1995}, } @article {MR84m:90122, AUTHOR = {SCHAIBLE, S.}, TITLE = {Fractional programming}, JOURNAL = {Z. Oper. Res. Ser. A-B}, FJOURNAL = {Zeitschrift f\"ur Operations Research. Serie A. Serie B}, VOLUME = {27}, YEAR = {1983}, NUMBER = {1}, PAGES = {39--54}, ISSN = {0340-9422}, MRCLASS = {90C32}, MRNUMBER = {84m:90122}, } @article {MR84c:90091, AUTHOR = {SCHAIBLE, S.}, TITLE = {Bibliography in fractional programming}, JOURNAL = {Z. Oper. Res. Ser. A-B}, FJOURNAL = {Zeitschrift f\"ur Operations Research. Serie A. Serie B}, VOLUME = {26}, YEAR = {1982}, NUMBER = {7}, PAGES = {A211--A241}, ISSN = {0340-9422}, MRCLASS = {90C32 (00A15)}, MRNUMBER = {84c:90091}, } @incollection {MR83e:90153, AUTHOR = {SCHAIBLE, S.}, TITLE = {Fractional programming---state of the art}, BOOKTITLE = {Operational research '81 (Hamburg, 1981)}, PAGES = {479--493}, PUBLISHER = {North-Holland}, ADDRESS = {Amsterdam}, YEAR = {1981}, MRCLASS = {90C32}, MRNUMBER = {83e:90153}, } @article {Sc:77, AUTHOR = {SCHAIBLE, S.}, TITLE = {A Note on the Sum of a Linear and a Linear-Fractional Function}, JOURNAL = {Naval Research Logistics Quarterly}, VOLUME = {24}, YEAR = {1977}, PAGES = {691--693}, } @proceedings {MR83g:90075, TITLE = {Generalized Concavity in Optimization and Economics}, BOOKTITLE = {Proceedings of the NATO Advanced Study Institute held at the University of British Columbia, Vancouver, B.C., August 4--15, 1980}, EDITOR = {SCHAIBLE, S. and ZIEMBA, W.T.}, PUBLISHER = {Academic Press Inc. [Harcourt Brace Jovanovich Publishers]}, ADDRESS = {New York}, YEAR = {1981}, PAGES = {xiv+767}, ISBN = {0-12-621120-5}, } @incollection {MR95g:90004, AUTHOR = {SCHAIBLE, S.}, TITLE = {Generalized monotonicity---a survey}, BOOKTITLE = {Generalized convexity (P\'ecs, 1992)}, PAGES = {229--249}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1994}, MRCLASS = {90-02 (47N10 49J40 90C33)}, MRNUMBER = {95g:90004}, MRREVR = {Michel Th{\'e}ra}, } @book {MR89e:90155, AUTHOR = {AVRIEL, M. and DIEWERT, W.E. and SCHAIBLE, S. and ZANG, I.}, TITLE = {Generalized concavity}, PUBLISHER = {Plenum Press}, ADDRESS = {New York}, YEAR = {1988}, PAGES = {x+332}, ISBN = {0-306-42656-0}, MRCLASS = {90C25 (26B25 90A10 90A11 90C32)}, MRNUMBER = {89e:90155}, MRREVR = {Jean-Pierre Crouzeix}, } # The following strings from V. Balakrishnan on SDP and systems control ## were moved to top of file @book{ Lya:47, author={A.M. LYAPUNOV}, title={Probl\`eme g\'en\'eral de la stabilit\'e du mouvement}, publisher={Princeton University Press}, year={1947}, volume={17}, series={Annals of Mathematics Studies}, address= {Princeton} } @book{ Lur:57, author={A.I. LUR'E}, title={Some Nonlinear Problems in the Theory of Automatic Control}, publisher={H. M. Stationery Off.}, year={1957}, note={In Russian, 1951.}, address= {London} } @article{ Wil:71a, author="J. C. WILLEMS", title="Least Squares Stationary Optimal Control and the Algebraic {R}iccati Equation", journal=tac, year=1971, pages= "621-634", volume="AC-16", number=6, month=dec } @article{ PyS:82, author= {E. S. PYATNITSKII and V. I. SKORODINSKII}, title= {Numerical Methods of {L}yapunov Function Construction and Their Application to the Absolute Stability Problem}, journal= scl, year= {1982}, volume= {2}, number= {2}, pages= {130-135}, month= aug } @article{ HoB:76, author= {H. P. HORISBERGER and P. R. B\'ELANGER}, title= {Regulators for Linear, Time Invariant Plants with Uncertain Parameters}, journal= tac, year= {1976}, volume= {AC-21}, pages= {705-708} } @BOOK{Vid:93, author = {M. VIDYASAGAR}, year = 1993, title = {Nonlinear Systems Analysis}, edition = {second}, publisher = {Prentice-Hall}, address = {Englewood Cliffs} } @book{ DeV:75, author= {C.A. DESOER and M. VIDYASAGAR}, title= {Feedback Systems: {I}nput-Output Properties}, publisher= {Academic Press}, address= {New York}, year= {1975}, } # Now from Jon lee @article {Pad:89, AUTHOR = {PADBERG, M. W.}, TITLE = {The {B}oolean quadric polytope: {S}ome characteristics, facets and relatives}, JOURNAL = mprog, FJOURNAL = {Mathematical Programming}, VOLUME = {Ser. B, 45}, YEAR = {1989}, NUMBER = {1}, PAGES = {139--172}, ISSN = {0025-5610}, CODEN = {MHPGA4}, } @incollection {AFLW:96, AUTHOR = {K.M. ANSTREICHER and FAMPA, M. and LEE, J. and WILLIAMS, J.}, TITLE = {Continuous relaxations for constrained maximum-entropy sampling}, BOOKTITLE = {Integer Programming and Combinatorial Optimization (Vancouver, BC, 1996)}, editor = {W.H. Cunningham and T. McCormick and M. Queyranne}, PAGES = {234--248}, SERIES = {Lecture Notes in Comput. Sci.}, VOLUME = {1084}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1996}, } @article {AFLW:97, AUTHOR = {K.M. ANSTREICHER and FAMPA, M. and LEE, J. and WILLIAMS, J.}, title = {Using continuous nonlinear relaxations to solve constrained maximum-entropy sampling problems}, JOURNAL = mprog, FJOURNAL = {Mathematical Programming}, VOLUME = {Ser. A, 85}, YEAR = {1999}, NUMBER = {2}, PAGES = {221-240}, } @article {KLQ:95, AUTHOR = {KO, C.-W. and LEE, J. and QUEYRANNE, M.}, TITLE = {An exact algorithm for maximum entropy sampling}, JOURNAL = {Oper. Res.}, FJOURNAL = {Operations Research. The Journal of the Operations Research Society of America}, VOLUME = {43}, YEAR = {1995}, NUMBER = {4}, PAGES = {684--691}, ISSN = {0030-364X}, CODEN = {OPREAI}, } @article {Lee:98, AUTHOR = {LEE, J.}, TITLE = {Constrained maximum-entropy sampling}, JOURNAL = {Oper. Res.}, FJOURNAL = {Operations Research. The Journal of the Operations Research Society of America}, VOLUME = {46}, pages = "655-664", YEAR = {1998}, } @incollection {KLW:98, AUTHOR = {KO, C.-W. and LEE, J. and WAYNE, K.}, title = {A spectral bound for {D}-optimality}, BOOKTITLE = {MODA 5 - Advances in Model-Oriented Data Analysis and Experimental Design (Marseilles, 1998)}, SERIES = {Contributions to Statistics}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, year = {1998}, editor = {A.C. Atkinson and L. Pronzato and H.P. Wynn}, } @article {Wel:82b, AUTHOR = {WELCH, W.J.}, TITLE = {Branch-and-bound search for experimental designs based on {D}-optimality and other criteria}, JOURNAL = {Technometrics}, FJOURNAL = {Technometrics. A Journal of Statistics for the Physical, Chemical and Engineering Sciences}, VOLUME = {24}, YEAR = {1982}, NUMBER = {1}, PAGES = {41--48}, ISSN = {0040-1706}, CODEN = {TCMTA2}, } @article {Wel:82a, AUTHOR = {WELCH, W.J.}, TITLE = {Algorithmic complexity: {T}hree {N}{P}-hard problems in computational statistics}, JOURNAL = {J. Statist. Comput. Simulation}, FJOURNAL = {Journal of Statistical Computation and Simulation}, VOLUME = {15}, YEAR = {1982}, NUMBER = {1}, PAGES = {17--25}, ISSN = {0094-9655}, CODEN = {JSCSAT}, } %%% from F. Jarre - start @incollection{so85, AUTHOR = "G.\ SONNEVEND", TITLE = "An {`analytical centre'} for polyhedrons and new classes of global algorithms for linear {(smooth, convex)} programming", BOOKTITLE = "System Modelling and Optimization", NOTE = "Lecture Notes in Control and Information Sciences No. 84", PUBLISHER = "Springer", ADDRESS = "Berlin", YEAR = "1986", PAGES = "866--875", } @techreport{utl, AUTHOR = " URBAN, T. and TITS, A.L. and LAWRENCE, C.T. ", TITLE = "A primal-dual interior-point method for nonconvex optimization with multiple logarithmic barrier parameters and with strong convergence properties", TYPE = "Report", INSTITUTION = "University of Maryland", ADDRESS = "College Park", YEAR = "1998", } @techreport{vs, AUTHOR = "R.J.\ Vanderbei and D.F.\ SHANNO", TITLE = "An interior point algorithm for nonconvex nonlinear programming", TYPE = "Report", NUMBER = "SOR-97-21", INSTITUTION = "Dept.\ of Statistics and OR, Princeton University", YEAR = "1997", } #%%% from F. Jarre - end # some from Serge @article {MR2093387, AUTHOR = {OBUCHOWSKA, WIES{\L}AWA T.}, TITLE = {Remarks on the analytic centers of convex sets}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {29}, YEAR = {2004}, NUMBER = {1}, PAGES = {60--90}, ISSN = {0926-6003}, CODEN = {CPPPEF}, MRCLASS = {52A41 (90C25 90C30)}, MRNUMBER = {MR2093387}, } @article {MR2031625, AUTHOR = {OBUCHOWSKA, W.T.}, TITLE = {On the minimizing trajectory of convex functions with unbounded level sets}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {27}, YEAR = {2004}, NUMBER = {1}, PAGES = {37--52}, ISSN = {0926-6003}, CODEN = {CPPPEF}, MRCLASS = {90C25}, MRNUMBER = {MR2031625 (2004m:90114)}, } @incollection {MR1482247, AUTHOR = {Caron, R.J. and Boneh, A. and Boneh, S.}, TITLE = {Redundancy}, BOOKTITLE = {Advances in sensitivity analysis and parametric programming}, SERIES = {Internat. Ser. Oper. Res. Management Sci.}, VOLUME = {6}, PAGES = {13.1--13.41}, PUBLISHER = {Kluwer Acad. Publ.}, ADDRESS = {Boston, MA}, YEAR = {1997}, MRCLASS = {90C08 (90C15)}, MRNUMBER = {1482247 (98k:90058)}, } @article {MR95j:90054, AUTHOR = {OBUCHOWSKA, W.T. and Caron, R.J.}, TITLE = {Minimal representation of quadratically constrained convex feasible regions}, JOURNAL = mprog, FJOURNAL = {Mathematical Programming}, VOLUME = {68}, YEAR = {1995}, NUMBER = {2, Ser. A}, PAGES = {169--186}, ISSN = {0025-5610}, CODEN = {MHPGA4}, } @article {MR1761152, AUTHOR = {OBUCHOWSKA, W.T.}, TITLE = {Minimal representation of convex regions defined by analytic functions}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {246}, YEAR = {2000}, NUMBER = {1}, PAGES = {100--121}, ISSN = {0022-247X}, CODEN = {JMANAK}, MRCLASS = {90Cxx (52A41)}, MRNUMBER = {1 761 152}, } @article {MR2000f:90049, AUTHOR = {OBUCHOWSKA, W.T.}, TITLE = {Convex constrained programmes with unattained infima}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {234}, YEAR = {1999}, NUMBER = {2}, PAGES = {675--694}, ISSN = {0022-247X}, CODEN = {JMANAK}, MRCLASS = {90C25 (52A41)}, MRNUMBER = {2000f:90049}, MRREVR = {Jean-Pierre Crouzeix}, } @article {MR2000e:90083, AUTHOR = {OBUCHOWSKA, W.T.}, TITLE = {On infeasibility of systems of convex analytic inequalities}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {234}, YEAR = {1999}, NUMBER = {1}, PAGES = {223--245}, ISSN = {0022-247X}, CODEN = {JMANAK}, MRCLASS = {90C31 (90C08 90C25)}, MRNUMBER = {2000e:90083}, MRREVR = {Henry Wolkowicz}, } @article {MR99i:90098, AUTHOR = {ISAC, G. and OBUCHOWSKA, W.T.}, TITLE = {Functions without exceptional family of elements and complementarity problems}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {99}, YEAR = {1998}, NUMBER = {1}, PAGES = {147--163}, ISSN = {0022-3239}, CODEN = {JOTABN}, MRCLASS = {90C33}, MRNUMBER = {99i:90098}, MRREVR = {Siegfried Schaible}, } @article {MR97c:90111, AUTHOR = {OBUCHOWSKA, W.T. and Caron, R.J.}, TITLE = {Improving the rate of convergence of the logarithmic barrier function method}, JOURNAL = {Optimization}, FJOURNAL = {Optimization. A Journal of Mathematical Programming and Operations Research}, VOLUME = {35}, YEAR = {1995}, NUMBER = {4}, PAGES = {317--332}, ISSN = {0233-1934}, MRCLASS = {90C30 (65K05)}, MRNUMBER = {97c:90111}, } @article {MR85d:90073, AUTHOR = {OBUCHOWSKA, W.T.}, TITLE = {Certain relations between the global and the conditional extremum in convex programming}, JOURNAL = {Przeglpolhk ad Statyst.}, FJOURNAL = {Polska Akademia Nauk. Komitet Statystyki i Ekonometrii. Przeglpolhk ad Statystyczny}, VOLUME = {29}, YEAR = {1982}, NUMBER = {1-2}, PAGES = {231--238 (1983)}, ISSN = {0033-2372}, CODEN = {PZSTAD}, MRCLASS = {90C25}, MRNUMBER = {85d:90073}, } @article {MR84h:62093, AUTHOR = {OBUCHOWSKA, WIES{\L}AWA}, TITLE = {Some properties of a correlation matrix which is majorized and minorized by a neutral matrix}, JOURNAL = {Przeglpolhk ad Statyst.}, FJOURNAL = {Polska Akademia Nauk. Komitet Statystyki i Ekonometrii. Przeglpolhk ad Statystyczny}, VOLUME = {27}, YEAR = {1980}, NUMBER = {3-4}, PAGES = {271--278 (1982)}, ISSN = {0033-2372}, CODEN = {PZSTAD}, MRCLASS = {62H20 (62H05)}, MRNUMBER = {84h:62093}, MRREVR = {M. Hu{\v{s}}kov{\'a}}, } @book {MR56:17985, AUTHOR = {Jacobson, David H.}, TITLE = {Extensions of linear-quadratic control, optimization and matrix theory}, NOTE = {Mathematics in Science and Engineering, Vol. 133}, PUBLISHER = {Academic Press [Harcourt Brace Jovanovich Publishers]}, ADDRESS = {London}, YEAR = 1977, PAGES = {x+217}, } @book {MR2515104, AUTHOR = {Dontchev, Asen L. and Rockafellar, R. Tyrrell}, TITLE = {Implicit functions and solution mappings}, SERIES = {Springer Monographs in Mathematics}, NOTE = {A view from variational analysis}, PUBLISHER = {Springer}, ADDRESS = {Dordrecht}, YEAR = {2009}, PAGES = {xii+375}, ISBN = {978-0-387-87820-1}, MRCLASS = {49J53 (26B10 47J30 47N10 49K40 58C15 90C31)}, MRNUMBER = {2515104 (2010g:49027)}, MRREVIEWER = {Stephen M. Robinson}, DOI = {10.1007/978-0-387-87821-8}, URL = {http://dx.doi.org/10.1007/978-0-387-87821-8}, } @article {MR88e:49045, AUTHOR = {Rockafellar, R. T.}, TITLE = {Linear-quadratic programming and optimal control}, JOURNAL = {SIAM J. Control Optim.}, FJOURNAL = {Society for Industrial and Applied Mathematics. Journal on Control and Optimization}, VOLUME = 25, YEAR = 1987, NUMBER = 3, PAGES = {781--814}, ISSN = {0363-0129}, CODEN = {SJCODC}, } @incollection {MR91j:93083, AUTHOR = {Rapoport, L. B.}, TITLE = {Positive definiteness of a quadratic form under quadratic constraints and absolute stability of nonlinear control systems}, BOOKTITLE = {Qualitative theory of differential equations (Szeged, 1988)}, PAGES = {567--576}, SERIES = {Colloq. Math. Soc. J\'anos Bolyai}, VOLUME = 53, PUBLISHER = {North-Holland}, ADDRESS = {Amsterdam}, YEAR = 1990, } @article {MR97d:90069, AUTHOR = {Preisig, J. C.}, TITLE = {Copositivity and the minimization of quadratic functions with nonnegativity and quadratic equality constraints}, JOURNAL = {SIAM J. Control Optim.}, FJOURNAL = {SIAM Journal on Control and Optimization}, VOLUME = 34, YEAR = 1996, NUMBER = 4, PAGES = {1135--1150}, ISSN = {0363-0129}, CODEN = {SJCODE}, } @article {MR96m:49066, AUTHOR = {Matveev, A.S.}, TITLE = {Lagrangian duality in the theory of nonconvex optimization, and modifications of the {T}oeplitz-{H}ausdorff theorem}, JOURNAL = {Algebra i Analiz}, FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Algebra i Analiz}, VOLUME = 7, YEAR = 1995, NUMBER = 5, PAGES = {143--181}, ISSN = {0234-0852}, } @Article{Park:1988:RNG, author = "Stephen K. Park and Keith W. Miller", title = "Random Number Generators: Good Ones are Hard to Find", journal = "Communications of the ACM", volume = "31", number = "10", pages = "1192--1201", month = oct, year = "1988", coden = "CACMA2", ISSN = "0001-0782", mrclass = "65C10 (11K45)", mrnumber = "91h:65012", bibdate = "Sat Apr 06 08:06:30 1996", url = "http://www.acm.org/pubs/toc/Abstracts/0001-0782/63042.html", acknowledgement = ack-nhfb, annote = "Practical and theoretical issues are presented concerning the design, implementation, and use of a good, minimal standard random number generator that will port to virtually all systems.", country = "USA", descriptors = "Random number; random number testing; Pseudo-random generator", keywords = "algorithms; design; performance; standardization; theory", language = "English", references = "47", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation. {\bf D.2.0}: Software, SOFTWARE ENGINEERING, General, Standards. {\bf K.6.2}: Computing Milieux, MANAGEMENT OF COMPUTING AND INFORMATION SYSTEMS, Installation Management.", } @article {MR1651750, AUTHOR = {Dedieu, J.P. and Shub, M.}, TITLE = {{N}ewton's method for overdetermined systems of equations}, JOURNAL = {Math. Comp.}, FJOURNAL = {Mathematics of Computation}, VOLUME = {69}, YEAR = {2000}, NUMBER = {231}, PAGES = {1099--1115}, ISSN = {0025-5718}, MRCLASS = {65Y10 (65J15 65Y20)}, MRNUMBER = {1651750}, MRREVIEWER = {Erich Novak}, DOI = {10.1090/S0025-5718-99-01115-1}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1090/S0025-5718-99-01115-1}, } @Article{BlBlSh86, author = "M. Blum and L. Blum and M. Shub", title = "A simple and secure pseudo-random number generator", journal = "SIAM Journal on Computing", year = "1986", pages = "364--383", volume = "15", note = "Two pseudo-random sequence generators are presented which, from small seeds, generate long well-distributed sequences. The first, $1/P$ generator, is completely predictable from a small segment of its output. The second, $x^2 \pmod N$ generator, is {\it cryptographically secure} as its sequence is polynomial-time unpredictable (if quadratic residuacity problem is indeed hard).", } @Article{BlMi84, author = "M. Blum and S. Micali", title = "How to generate cryptographically strong sequence of pseudo-random bits", journal = "SIAM Journal on Computing", year = "1984", pages = "850--864", volume = "13", note = "This paper introduces the notion of cryptographically secure pseudo-random number generator.", } @Article{Marsaglia93, author = "G. Marsaglia", title = "Remarks on choosing and implementing random number generators.", journal = "Comm. A.C.M.", volume = "36", number = "7", pages = "105--110", month = jul, year = "1993", keywords = "random number generator, RNG, pseudo PRNG", abstract = "via enews", } @article {MR52:5711, AUTHOR = {MARSAGLIA, G. and STYAN, G.P.H.}, TITLE = {Equalities and inequalities for ranks of matrices}, JOURNAL = {Linear and Multilinear Algebra}, VOLUME = {2}, YEAR = {1974/75}, PAGES = {269--292}, MRCLASS = {15A45}, MRNUMBER = {52 \#5711}, MRREVIEWER = {A. R. Amir-Moez}, } @article {MR52:5699, AUTHOR = {Marsaglia, George and Styan, George P. H.}, TITLE = {Rank conditions for generalized inverses of partitioned matrices}, JOURNAL = {Sankhy\=a Ser. A}, VOLUME = {36}, YEAR = {1974}, NUMBER = {4}, PAGES = {437--442}, MRCLASS = {15A09}, MRNUMBER = {52 \#5699}, MRREVIEWER = {Thomas L. Boullion}, } @article {MR47:236, AUTHOR = {Marsaglia, G. and Styan, G. P. H.}, TITLE = {When does ${\rm rank}\ ({A}+{B})={\rm rank}({A})+{\rm rank}({B})$?}, JOURNAL = {Canad. Math. Bull.}, VOLUME = {15}, YEAR = {1972}, PAGES = {451--452}, MRCLASS = {15A03}, MRNUMBER = {47 \#236}, MRREVIEWER = {A. R. Amir-Moez}, } @Article{Mitchell93a, author = "Mitchell", title = "A Nonlinear Random Number Generator with Known, Long Cycle Length", journal = "CRYPTOLOGIA: Cryptologia", volume = "17", year = "1993", } @proceedings {MR97k:94002, TITLE = {Advances in cryptology---{C}{R}{Y}{P}{T}{O} '95}, BOOKTITLE = {Proceedings of the 15th Annual International Cryptology Conference held at the University of California, Santa Barbara, CA, August 27--31, 1995}, EDITOR = {Coppersmith, Don}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {963}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1995}, PAGES = {xii+467}, ISBN = {3-540-60221-6}, } @incollection {MR91d:68051, AUTHOR = {Micali, S. and Schnorr, C.-P.}, TITLE = {Efficient, perfect random number generators}, BOOKTITLE = {Advances in cryptology---CRYPTO '88 (Santa Barbara, CA, 1988)}, PAGES = {173--198}, SERIES = {Lecture Notes in Comput. Sci.}, VOLUME = {403}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1990}, } @incollection {MR85i:94017, AUTHOR = {Sloane, N. J. A.}, TITLE = {Encrypting by random rotations}, BOOKTITLE = {Cryptography (Burg Feuerstein, 1982)}, PAGES = {71--128}, SERIES = {Lecture Notes in Comput. Sci.}, VOLUME = {149}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1983}, } @article {MR90g:94015, AUTHOR = {Matthews, Robert}, TITLE = {On the derivation of a ``chaotic'' encryption algorithm}, JOURNAL = {Cryptologia}, FJOURNAL = {Cryptologia}, VOLUME = {13}, YEAR = {1989}, NUMBER = {1}, PAGES = {29--42}, ISSN = {0161-1194}, } @article {MR92b:94035, AUTHOR = {Ritter, Terry}, TITLE = {The efficient generation of cryptographic confusion sequences}, JOURNAL = {Cryptologia}, FJOURNAL = {Cryptologia}, VOLUME = {15}, YEAR = {1991}, NUMBER = {2}, PAGES = {81--139}, ISSN = {0161-1194}, } @Book{knut:81, author = "D. E. Knuth", year = "1981", title = "The Art of Computer Programming {II}: Seminumerical Algorithms", edition = "Second", publisher = "Addison--Wesley", address = "Reading, Massachusetts", kwds = "cs, na, book, random numbers, computer arithmetic", } @InProceedings{Plumstead83b, oldtag = "Plumstead83", author = "Joan B. Plumstead", title = "Inferring a Sequence Produced by a Linear Congruence", pages = "317--319", booktitle = "Proc.\ CRYPTO 82", editor = "R. L. Rivest and A. Sherman and D. Chaum", publisher = "Plenum Press", address = "New York", year = "1983", comment = "Abstract of the FOCS '82 paper", } @Article{Shamir83, author = "A. Shamir", title = "On the Generation of Cryptographically Strong Pseudorandom Sequences", journal = "ACM Trans. on Computer Sys.", volume = "1", number = "1", pages = "38", month = feb, year = "1983", keywords = "TOCS", } @InCollection{KnuYao76, author = "Knuth and Yao", title = "The Complexity of Nonuniform Random Number Generation", booktitle = "Algorithms and Complexity: New Directions and Recent Results, Ed. J. F. Traub, Academic Press", year = "1976", } @incollection {MR780384, AUTHOR = {Yao, Andrew C.}, TITLE = {Theory and applications of trapdoor functions}, BOOKTITLE = {23rd annual symposium on foundations of computer science (Chicago, Ill., 1982)}, PAGES = {80--91}, PUBLISHER = {IEEE}, ADDRESS = {New York}, YEAR = {1982}, } @TechReport{BeYeZh:98, author = {Benson, S. J. and Ye, Y. and Zhang, X.}, title = {Solving Large-Scale Semidefinite Programs for Combinatorial Optimization}, institution = {University of Iowa}, year = {1998}, month = {May}, } @article{Monteiro-Svaiter-2010a, doi = {10.1137/110849468}, url = {https://doi.org/10.1137/110849468}, year = {2013}, month = jan, publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})}, volume = {23}, number = {1}, pages = {475--507}, author = {R.D.C. Monteiro and B.F. Svaiter}, title = {Iteration-Complexity of Block-Decomposition Algorithms and the Alternating Direction Method of Multipliers}, journal = {{SIAM} Journal on Optimization} } @TechReport{MoTs:98, author = {Monteiro, R and Tsuchiya T}, title = {Polynomial Convergence of a New Family of Primal-Dual Algorithms for Semidefinite Programming}, institution = {Georgia Institute of Technology}, year = {1998}, month = {January}, } @ARTICLE{GAC:96, author = {P. GAHINET and P. APKARIAN and M. CHILALI}, month = mar, year = 1996, title = {Affine Parameter-Dependent {L}yapunov Functions for Real Parameter Uncertainty}, journal = tac, volume = 41, number = 3, pages = {436-442} } @article{AGB:95, author={P. APKARIAN and P. GAHINET and G. BECKER}, title={Self-Scheduled {${\cal H}_{\infty}$} Control of Linear Parameter-Varying Systems: A Design Example}, journal=aut, mon=sep, year=1995, volume=31, number=9, pages={1251-1261} } @phdthesis{Bec:93, author= {G. BECKER}, title= { Quadratic Stability and Performance of Linear Parameter Dependent Systems}, school= {University of California, Berkeley}, year= {1993} } @ARTICLE{YuS:97, author = {{J. YU and A. SIDERIS}}, year = 1997, title = {{$H_\infty$ control with parametric {L}yapunov functions}}, journal = scl, volume = 30, pages = {57-69} } @ARTICLE{ElS:96, author = {L.~EL~GHAOUI and G. SCORLETTI}, month = sep, year = 1996, title = {Control of Rational Systems using {L}inear-{F}ractional {R}epresentations and {L}inear {M}atrix {I}nequalities}, journal = {Automatica}, volume = 32, number = 9 } @phdthesis{You:93, author={P. M. Young}, title= {{R}obustness with {P}arametric and {D}ynamic {U}ncertainty}, school={California Institute of Technology}, year={1993}, address={Pasadena, CA 91125}, month=may } @article{ Pac:94, author={A. PACKARD}, title={Gain Scheduling via Linear Fractional Transformations}, journal=scl, volume = {22}, pages={79-92}, year={1994} } @manual{mutools, author= {G. BALAS and J. C. DOYLE and K. GLOVER and A. PACKARD and R. SMITH}, title= {$\mu$-analysis and synthesis}, organization= {MUSYN, inc., and The Mathworks, Inc.}, year= {1991} } @ARTICLE{MeR:97, author = {A. MEGRETSKI and A. RANTZER}, month = Jun, year = 1997, title = {System Analysis via Integral Quadratic Constraints}, journal = tac, volume = {42}, number = {6}, pages = {819-830}, } @article {ElGhaoui03, AUTHOR = {El Ghaoui, L. and Oks, M. and Oustry, F.}, TITLE = {Worst-case value-at-risk and robust portfolio optimization: a conic programming approach}, JOURNAL = {Oper. Res.}, FJOURNAL = {Operations Research}, VOLUME = {51}, YEAR = {2003}, NUMBER = {4}, PAGES = {543--556}, ISSN = {0030-364X}, CODEN = {OPREAI}, MRCLASS = {91B28 (90C15)}, MRNUMBER = {1991970}, DOI = {10.1287/opre.51.4.543.16101}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1287/opre.51.4.543.16101}, } @article {Ghaoui1997, AUTHOR = {El Ghaoui, L. and Lebret, H.}, TITLE = {Robust solutions to least-squares problems with uncertain data}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {18}, YEAR = {1997}, NUMBER = {4}, PAGES = {1035--1064}, ISSN = {0895-4798}, CODEN = {SJMAEL}, MRCLASS = {65F20 (15A06)}, MRNUMBER = {1472008 (99c:65075)}, MRREVIEWER = {Ching-Tsuan Pan}, DOI = {10.1137/S0895479896298130}, URL = {http://dx.doi.org/10.1137/S0895479896298130}, } @inproceedings{EBFB:92, author={L. {El~Ghaoui} and V. Balakrishnan and E. Feron and S. Boyd}, title={On Maximizing a Robustness Measure for Structured Nonlinear Perturbations}, booktitle=acc, year={1992}, pages={2923-2924}, volume = {4}, address={Chicago}, month=jun } @ARTICLE{Bal:95, author = {V. Balakrishnan}, year = 1995, title = {Linear Matrix Inequalities in Robustness Analysis with Multipliers}, journal = scl, volume = 25, number = 4, pages = {265-272} } @techreport{CTB1:97, author={Y.S. CHOU and A.L. TITS and V. Balakrishnan}, title= {Absolute Stability Theory, Theory, and State-Space Verification of Frequency-Domain Conditions: Connections and Implications for Computation}, institution={Institute for Systems Research, University of Maryland}, number = {TR 97-23}, note = {Accepted for publication in {\it IEEE Trans.\ Aut.\ Control}, 1998.}, year=1997 } @article{ShA:90, author={J. S. SHAMMA and M. ATHANS}, title={Analysis of Gain Scheduled Control for Nonlinear Plants}, journal=tac, number = 8, volume=35, pages = {898-907}, year = 1990, month = Aug } @article{ShA:92, author={J. S. SHAMMA and M. ATHANS}, title={Gain Scheduling: Potential Hazards and Possible Remedies}, journal= csm, pages = {101-107}, year = {1992}, month = "June" } @article{ WYPB:94, author={F. WU and X. H. YANG and A. PACKARD and G. BECKER}, title={Induced {${\bf L}_2$}-Norm Control for {LPV} System with Bounded Parameter Variation Rates}, journal=ijrnc, month=dec, year=1994, } @article{ AG:95, author={P. APKARIAN and P. GAHINET}, title={A Convex Characterization of Gain-Scheduled {${\cal H}_{\infty}$} Controllers}, journal=tac, volume={AC-40}, number=5, pages={853-864}, mon=may, year=1995 } @manual{ Kmtools, author= {R. CHIANG and M.G. SAFONOV}, title= {Robust Control Toolbox}, organization= {The Mathworks, Inc.}, year= {1992} } @article{ FTD:91, author={M.K. H. FAN and A.L. TITS and J.C. DOYLE}, title={Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics}, journal=tac, year={1991}, volume={AC-36}, number={1}, pages={25-38}, month=jan } @book{ Wu:95, author={F. WU}, title={Control of Linear Parameter Varying Systems}, publisher={Engineering-Mechanical Eng.\ Dept., University of California Berkeley}, series={Doctoral Dissertation}, year={1995} } @ARTICLE{FAG:96, author = {E. Feron, P. APKARIAN and P. GAHINET}, month = jul, year = 1996, title = {Analysis and Synthesis of Robust Control Systems via Parameter-Dependent {L}yapunov Functions}, journal = tac, volume = 41, number = 7, pages = {1041-1046} } @incollection{ SaC:93, author="M.G. SAFONOV and R. Y. CHIANG", title="Real/Complex {$K_m$}-Synthesis without Curve Fitting", booktitle="Control and Dynamic Systems", volume="56", part="2", pages="303--324", editor="C.T. Leondes", publisher="Academic Press", address="New York", year="1993", } @article{ Sch:96, author= {C. SCHERER}, title= {Mixed {$H_2$/$H_\infty$} control for time-varying and linear para\-metrically-varying systems}, journal= ijrnc, year=1996, volume = 6, month = {Nov--Dec}, number = {9/10}, pages = {929-952} } @ARTICLE{GaA:94, author = {P. GAHINET and P. APKARIAN}, year = 1994, title = {A Linear Matrix Inequality Approach to ${H}^\infty$ Control}, journal = ijrnc, volume = 4, pages = {421-448}, note = {} } @BOOK{ZDG:96, author = {{K. ZHOU with J. DOYLE} and K. GLOVER}, year = 1996, title = {Robust and Optimal Control}, note = {}, publisher = {Prentice Hall} } @article{Ran:96, author = {A. RANTZER}, title = {On the {Kalman}-{Yakubovich}-{Popov} {L}emma}, journal = scl, year = 1996, volume = 28, number = 1, pages = {7-10} } @article{ApA:98, author = {P. APKARIAN and R.J. ADAMS}, title = {Advanced Gain-Scheduled Techniques for Uncertain Systems}, journal = tcst, year = 1998, month = jan, volume = {6}, number = 1, pages = {21-32} } @inproceedings{Sch:96a, author = {C. SCHERER}, title = {Robust generalized ${H}_2$ control for uncertain and {LPV} systems with general scalings}, booktitle = cdc, year = 1996, month = dec, address = { }, pages = {3970-3975} } @article{ChG:95, author = {M. CHILALI and P. GAHINET}, title = {${H}_\infty$ design with pole placement constraints: An LMI approach}, journal = tac, year = 1995, month = mar, volume = 40, number = 3, pages = {358-367} } @book{AnV:73, author={B. ANDERSON and S. VONGPANITLERD}, title={Network analysis and synthesis: a modern systems theory approach}, publisher={Prentice-Hall}, year={1973} } @book{ GrL:95, author={M. GREEN and D. J. N. LIMEBEER}, title={Linear Robust Control}, publisher={Prentice Hall}, year={1995}, notes={}, volume={}, series={Information and System sciences}, address={Englewood Cliffs, NJ}, edition={}, month={} } @article{ Yak:62, author={V.A. YAKUBOVICH}, title={The solution of certain matrix inequalities in automatic control theory}, journal={Soviet Math. Dokl.}, year={1962}, note={In Russian, 1961.}, volume={3}, pages={620-623} } @article{ Yak:64, author={V.A. YAKUBOVICH}, title={Solution of certain matrix inequalities encountered in nonlinear control theory}, journal={Soviet Math. Dokl.}, year={1964}, volume={5}, pages={652-656} } @article{ Kal:63, author= {R.E. KALMAN}, title= { {L}yapunov Functions for the Problem of {L}ur'e in Automatic Control}, journal= {Proc. Nat. Acad. Sci., USA}, volume= {49}, pages= {201-205}, year= {1963} } @inproceedings{ Kal:63a, author= {R.E. KALMAN}, title= {On a New Characterization of Linear Passive Systems}, booktitle= { Proc. First Annual Allerton Conf. on Communication, Control and Computing}, pages= {456-470}, year= {1963} } @article{ Doy:82, author= {J. DOYLE}, title= {Analysis of Feedback Systems with Structured Uncertainties}, journal= ieep, volume= {129-D}, number= {6}, year= {1982}, pages= {242-250}, month= nov } @article{ Saf:82, author= {M.G. SAFONOV}, title= {Stability margins of diagonally perturbed multivariable feedback systems}, journal= ieep, volume= {129-D}, number= {6}, year= {1982}, month= nov, pages= {251-256} } # Gauss-Seidel related papers follow @article {MR2001a:90061, AUTHOR = {GRIPPO, L. and SCIANDRONE, M.}, TITLE = {On the convergence of the block nonlinear {G}auss-{S}eidel method under convex constraints}, JOURNAL = {Oper. Res. Lett.}, FJOURNAL = {Operations Research Letters}, VOLUME = {26}, YEAR = {2000}, NUMBER = {3}, PAGES = {127--136}, ISSN = {0167-6377}, CODEN = {ORLED5}, MRCLASS = {90C30 (65K05)}, MRNUMBER = {2001a:90061}, MRREVIEWER = {Zun Quan Xia}, } @article {MR2001a:65118, AUTHOR = {KORSAWE, J. and STARKE, G.}, TITLE = {Multilevel projection methods for nonlinear least-squares finite element computations}, NOTE = {Multilevel methods (Copper Mountain, CO, 1999)}, JOURNAL = {Electron. Trans. Numer. Anal.}, FJOURNAL = {Electronic Transactions on Numerical Analysis}, VOLUME = {10}, YEAR = {2000}, PAGES = {56--73 (electronic)}, ISSN = {1068-9613}, MRCLASS = {65M60 (65M55)}, MRNUMBER = {2001a:65118}, } @book {MR1931309, AUTHOR = {Auslender, A. and Teboulle, M.}, TITLE = {Asymptotic cones and functions in optimization and variational inequalities}, SERIES = {Springer Monographs in Mathematics}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {2003}, PAGES = {xii+249}, ISBN = {0-387-95520-8}, MRCLASS = {49-02 (49J53 49K40 90C46)}, MRNUMBER = {MR1931309 (2003i:49002)}, MRREVIEWER = {Constantin Z{\u{a}}linescu}, } @incollection {MR2000m:90027, AUTHOR = {AUSLENDER, A. and TEBOULLE, M. and BEN-TIBA, S.}, TITLE = {Coupling the logarithmic-quadratic proximal method and the block nonlinear {G}auss-{S}eidel algorithm for linearly constrained convex minimization}, BOOKTITLE = {Ill-posed variational problems and regularization techniques (Trier, 1998)}, SERIES = {Lecture Notes in Econom. and Math. Systems}, VOLUME = {477}, PAGES = {35--47}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1999}, MRCLASS = {90C25 (90C08)}, MRNUMBER = {2000m:90027}, MRREVIEWER = {K. Zimmermann}, } @article {MR99e:65049, AUTHOR = {BAI, Z.Z}, TITLE = {Asynchronous parallel nonlinear symmetric {G}auss-{S}eidel iteration methods}, JOURNAL = {Math. Numer. Sin.}, FJOURNAL = {Mathematica Numerica Sinica. Jisuan Shuxue}, VOLUME = {20}, YEAR = {1998}, NUMBER = {2}, PAGES = {187--200}, ISSN = {0254-7791}, MRCLASS = {65F10}, MRNUMBER = {99e:65049}, } #################################start student papers################## @inproceedings{chKruklip:02a, AUTHOR = "E. CHENG and S. Kruk and M. LIPMAN", TITLE = "Flow Formulations for the Student Scheduling Problem", bookTITLE = " Proceedings of the 4th international conference on the Practice and Theory of Automated Timetabling", publisher = "-", NUMBER = "298-308", YEAR = "2002", } @article{chKruklip:02b, AUTHOR = "E. CHENG and S. Kruk and M. LIPMAN", title="An Optimization Formulation for the existence of Complete Spheres-of-Influence graphs", journal="Congressus Numerantium", year="2002", } @TECHREPORT {DrorKruk:02, author = "M. DROR and S. Kruk", title = "Semidefinite Models of Centralized Inventory", institution = "Department of Mathematics and Statistics", address ="Oakland University, Rochester MI", year = "2002", number = "2002-3"} @techreport{2022_BaMaoMo, author = {Bauschke, H.H. and Mao, D. and Moursi, W.M.}, title = {How to project onto the intersection of a closed affine subspace and a hyperplane}, publisher = {arXiv}, year = {2022}, copyright = {Creative Commons Attribution Non Commercial Share Alike 4.0 International} } @article {MR3233066, AUTHOR = {Bauschke, H.H. and Bello Cruz, J.Y. and Nghia, T.T.A. and Phan, H.M. and Wang, X.}, TITLE = {The rate of linear convergence of the {D}ouglas-{R}achford algorithm for subspaces is the cosine of the {F}riedrichs angle}, JOURNAL = {J. Approx. Theory}, FJOURNAL = {Journal of Approximation Theory}, VOLUME = {185}, YEAR = {2014}, PAGES = {63--79}, ISSN = {0021-9045}, MRCLASS = {47J25 (49J53 49M27)}, MRNUMBER = {3233066}, MRREVIEWER = {Patrick L. Combettes}, DOI = {10.1016/j.jat.2014.06.002}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/j.jat.2014.06.002}, } @article {MR3227480, AUTHOR = {Bauschke, H. H. and Noll, D.}, TITLE = {On the local convergence of the {D}ouglas-{R}achford algorithm}, JOURNAL = {Arch. Math. (Basel)}, FJOURNAL = {Archiv der Mathematik}, VOLUME = {102}, YEAR = {2014}, NUMBER = {6}, PAGES = {589--600}, ISSN = {0003-889X}, MRCLASS = {47J25 (52A20 90C26)}, MRNUMBER = {3227480}, MRREVIEWER = {Shoham Sabach}, DOI = {10.1007/s00013-014-0652-2}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s00013-014-0652-2}, } @TECHREPORT {BausKruk:02, author = "H. Bauschke and S. Kruk", title = "The method of reflection-projection for convex feasibility problems with an obtuse cone", institution = "Department of Mathematics and Statistics", address ="Oakland University, Rochester MI", note = "to appear in JOTA", year = "2002", number = "2002-4"} @article {MR4115560, AUTHOR = {B\`ui, M.N. and Combettes, P.L.}, TITLE = {Warped proximal iterations for monotone inclusions}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {491}, YEAR = {2020}, NUMBER = {1}, PAGES = {124315, 21}, ISSN = {0022-247X}, MRCLASS = {47J25 (47H05 47J22)}, MRNUMBER = {4115560}, DOI = {10.1016/j.jmaa.2020.124315}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1016/j.jmaa.2020.124315}, } @techreport{bui2021multivariate, title={Multivariate Monotone Inclusions in Saddle Form}, author={M.N. Bui and P.L. Combettes}, year={2021}, eprint={2002.06135}, archivePrefix={arXiv}, primaryClass={math.OC} } @article {MR3767763, AUTHOR = {Combettes, P.L. and Eckstein, J.}, TITLE = {Asynchronous block-iterative primal-dual decomposition methods for monotone inclusions}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming}, VOLUME = {168}, YEAR = {2018}, NUMBER = {1-2, Ser. B}, PAGES = {645--672}, ISSN = {0025-5610}, MRCLASS = {47H05 (49M27 65K05 90C25)}, MRNUMBER = {3767763}, MRREVIEWER = {Radu Ioan Bo\c{t}}, DOI = {10.1007/s10107-016-1044-0}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10107-016-1044-0}, } @article {MR4088377, AUTHOR = {B\`ui, M.N. and Combettes, P.L.}, TITLE = {The {D}ouglas-{R}achford algorithm converges only weakly}, JOURNAL = {SIAM J. Control Optim.}, FJOURNAL = {SIAM Journal on Control and Optimization}, VOLUME = {58}, YEAR = {2020}, NUMBER = {2}, PAGES = {1118--1120}, ISSN = {0363-0129}, MRCLASS = {47H05 (47H09 49J40 49M29)}, MRNUMBER = {4088377}, DOI = {10.1137/19M1308451}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/19M1308451}, } @article {MR2222249, AUTHOR = {Bauschke, H.H. and Combettes, P.L. and Kruk, S.G.}, TITLE = {Extrapolation algorithm for affine-convex feasibility problems}, JOURNAL = {Numer. Algorithms}, FJOURNAL = {Numerical Algorithms}, VOLUME = {41}, YEAR = {2006}, NUMBER = {3}, PAGES = {239--274}, ISSN = {1017-1398}, MRCLASS = {90C25}, MRNUMBER = {2222249}, MRREVIEWER = {J. Borwein}, DOI = {10.1007/s11075-005-9010-6}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s11075-005-9010-6}, } @article {MR2063324, AUTHOR = {Bauschke, H.H. and Kruk, S.G.}, TITLE = {Reflection-projection method for convex feasibility problems with an obtuse cone}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {120}, YEAR = {2004}, NUMBER = {3}, PAGES = {503--531}, ISSN = {0022-3239}, MRCLASS = {90C25 (90C46)}, MRNUMBER = {2063324}, MRREVIEWER = {Wies\l awa T. Obuchowska}, DOI = {10.1023/B:JOTA.0000025708.31430.22}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1023/B:JOTA.0000025708.31430.22}, } @TECHREPORT {BausCombKruk:02, author = "H. Bauschke and P.L. Combettes and S. Kruk", title = "Solving large, sparse linear programs using projections", institution = "Department of Mathematics and Statistics", address ="Oakland University, Rochester MI", note = "to appear in JOTA", year = "2002", number = "2002-6"} @book {MR2798533, AUTHOR = {Bauschke, H.H. and Combettes, P.L.}, TITLE = {Convex analysis and monotone operator theory in {H}ilbert spaces}, SERIES = {CMS Books in Mathematics/Ouvrages de Math\'ematiques de la SMC}, NOTE = {With a foreword by H{\'e}dy Attouch}, PUBLISHER = {Springer, New York}, YEAR = {2011}, PAGES = {xvi+468}, ISBN = {978-1-4419-9466-0}, MRCLASS = {49-02 (41A65 46B20 46C05 47H05 90C25 90C30 90C48)}, MRNUMBER = {2798533 (2012h:49001)}, MRREVIEWER = {Simeon Reich}, DOI = {10.1007/978-1-4419-9467-7}, URL = {http://dx.doi.org/10.1007/978-1-4419-9467-7}, } @book {MR3616647, AUTHOR = {Bauschke, H.H. and Combettes, P.L.}, TITLE = {Convex analysis and monotone operator theory in {H}ilbert spaces}, SERIES = {CMS Books in Mathematics/Ouvrages de Math\'{e}matiques de la SMC}, EDITION = {Second}, NOTE = {With a foreword by H\'{e}dy Attouch}, PUBLISHER = {Springer, Cham}, YEAR = {2017}, PAGES = {xix+619}, ISBN = {978-3-319-48310-8; 978-3-319-48311-5}, MRCLASS = {49-02 (41A65 46B20 46C05 47H05 90C25)}, MRNUMBER = {3616647}, DOI = {10.1007/978-3-319-48311-5}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/978-3-319-48311-5}, } #################################end student papers################## #################################procrustes references################## @article {MR2003f:65114, AUTHOR = {Del Buono, N. and Lopez, L.}, TITLE = {Geometric integration on manifold of square oblique rotation matrices}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {23}, YEAR = {2002}, NUMBER = {4}, PAGES = {974--989 (electronic)}, ISSN = {1095-7162}, MRCLASS = {65L05 (34A34 34C40 37M99 65F99)}, MRNUMBER = {2003f:65114}, } @article {MR2003b:90071, AUTHOR = {Trendafilov, Nickolay T. and Lippert, Ross A.}, TITLE = {The multimode {P}rocrustes problem}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {349}, YEAR = {2002}, PAGES = {245--264}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {90C25 (65K10)}, MRNUMBER = {2003b:90071}, } @article {MR95f:65072, AUTHOR = {Watson, G. A.}, TITLE = {The solution of orthogonal {P}rocrustes problems for a family of orthogonally invariant norms}, JOURNAL = {Adv. Comput. Math.}, FJOURNAL = {Advances in Computational Mathematics}, VOLUME = {2}, YEAR = {1994}, NUMBER = {4}, PAGES = {393--405}, ISSN = {1019-7168}, MRCLASS = {65F10 (65F25)}, MRNUMBER = {95f:65072}, MRREVIEWER = {Hongyuan Zha}, } @article {MR93e:62140, AUTHOR = {Kiers, Henk A. L. and ten Berge, Jos M. F.}, TITLE = {Minimization of a class of matrix trace functions by means of refined majorization}, JOURNAL = {Psychometrika}, FJOURNAL = {Psychometrika. A Journal of Quantitative Psychology}, VOLUME = {57}, YEAR = {1992}, NUMBER = {3}, PAGES = {371--382}, ISSN = {0033-3123}, CODEN = {PSYKA2}, MRCLASS = {62H05 (62P15)}, MRNUMBER = {93e:62140}, } @article {MR93g:65055, AUTHOR = {Arun, K. S.}, TITLE = {A unitarily constrained total least squares problem in signal processing}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {13}, YEAR = {1992}, NUMBER = {3}, PAGES = {729--745}, ISSN = {0895-4798}, CODEN = {SJMAEL}, MRCLASS = {65F20 (15A18)}, MRNUMBER = {93g:65055}, MRREVIEWER = {Zden{\v{e}}k Strako{\v{s}}}, } @article {MR89g:15016, AUTHOR = {Shapiro, A. and Botha, J. D.}, TITLE = {Dual algorithms for orthogonal {P}rocrustes rotations}, JOURNAL = {SIAM J. Matrix Anal. Appl.}, FJOURNAL = {SIAM Journal on Matrix Analysis and Applications}, VOLUME = {9}, YEAR = {1988}, NUMBER = {3}, PAGES = {378--383}, ISSN = {0895-4798}, CODEN = {SJMAEL}, MRCLASS = {15A42 (15A15 93B60)}, MRNUMBER = {89g:15016}, MRREVIEWER = {M. M. Konstantinov}, } #################################end procrustes references################## #################################partial separability @article {MR2089056, AUTHOR = {Altangerel, L. and Bo{\c{t}}, R.I. and Wanka, G.}, TITLE = {Duality for convex partially separable optimization problems}, JOURNAL = {Mong. Math. J.}, FJOURNAL = {Mongolian Mathematical Journal}, VOLUME = {7}, YEAR = {2003}, PAGES = {1--18}, MRCLASS = {90C25 (90C46)}, MRNUMBER = {MR2089056 (2005d:90089)}, MRREVIEWER = {Teemu Pennanen}, } @article {MR1480634, AUTHOR = {Dayd{\'e}, M.J. and L'Excellent, J.Y. and Gould, N.I.M.}, TITLE = {Element-by-element preconditioners for large partially separable optimization problems}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {18}, YEAR = {1997}, NUMBER = {6}, PAGES = {1767--1787}, ISSN = {1064-8275}, CODEN = {SJOCE3}, MRCLASS = {90C30}, MRNUMBER = {MR1480634 (98j:90070)}, MRREVIEWER = {K. Schittkowski}, } @incollection {MR1307166, AUTHOR = {Conn, A.R. and Gould, N.I.M. and Toint, Ph.L.}, TITLE = {Improving the decomposition of partially separable functions in the context of large-scale optimization: a first approach}, BOOKTITLE = {Large scale optimization (Gainesville, FL, 1993)}, PAGES = {82--94}, PUBLISHER = {Kluwer Acad. Publ.}, ADDRESS = {Dordrecht}, YEAR = {1994}, MRCLASS = {90C30 (90C25)}, MRNUMBER = {MR1307166}, } @incollection {MR1282736, AUTHOR = {Conn, A.R. and Gould, N.I.M. and Lescrenier, M. and Toint, Ph.L.}, TITLE = {Performance of a multifrontal scheme for partially separable optimization}, BOOKTITLE = {Advances in optimization and numerical analysis (Oaxaca, 1992)}, SERIES = {Math. Appl.}, VOLUME = {275}, PAGES = {79--96}, PUBLISHER = {Kluwer Acad. Publ.}, ADDRESS = {Dordrecht}, YEAR = {1994}, MRCLASS = {90C30}, MRNUMBER = {MR1282736 (95a:90118)}, } @article {MR1152480, AUTHOR = {Schmidt, J.W.}, TITLE = {Dual algorithms for solving convex partially separable optimization problems}, JOURNAL = {Jahresber. Deutsch. Math.-Verein.}, FJOURNAL = {Jahresbericht der Deutschen Mathematiker-Vereinigung}, VOLUME = {94}, YEAR = {1992}, NUMBER = {1}, PAGES = {40--62}, ISSN = {0012-0456}, CODEN = {JDMVA7}, MRCLASS = {90C30 (41A15 49N15 65D07)}, MRNUMBER = {MR1152480 (93c:90084)}, MRREVIEWER = {Blagun Kalchev}, } @techreport{GrattonGurolToint:11, AUTHOR = "S. Gratton and S. Gurol Ph.L. Toint", TITLE = "Preconditioning and Globalizing Conjugate Gradients in Dual Space for Quadratically Penalized Nonlinear-Least Squares Problems", TYPE = "Technical Report", NUMBER = "NAXYS-10-2010", INSTITUTION = "Namur Center for Complex Systems", YEAR = "2010", URL = {http://www.optimization-online.org/DB_HTML/2010/12/2855.html}, } @article {MR866412, AUTHOR = {Toint, Ph.L.}, TITLE = {Global convergence of the partitioned {BFGS} algorithm for convex partially separable optimization}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {36}, YEAR = {1986}, NUMBER = {3}, PAGES = {290--306}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C25 (65K05)}, MRNUMBER = {MR866412 (88a:90160)}, MRREVIEWER = {Pierre Loridan}, } @article {MR3523420, AUTHOR = {Cao, H. and Yao, L.}, TITLE = {A partitioned {PSB} method for partially separable unconstrained optimization problems}, JOURNAL = {Appl. Math. Comput.}, FJOURNAL = {Applied Mathematics and Computation}, VOLUME = {290}, YEAR = {2016}, PAGES = {164--177}, ISSN = {0096-3003}, MRCLASS = {90C53 (65K10 90C06)}, MRNUMBER = {3523420}, DOI = {10.1016/j.amc.2016.06.009}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1016/j.amc.2016.06.009}, } @incollection {MR3446850, AUTHOR = {Mare\v{c}ek, J. and Richt\'{a}rik, P. and Tak\'{a}\v{c}, M.}, TITLE = {Distributed block coordinate descent for minimizing partially separable functions}, BOOKTITLE = {Numerical analysis and optimization}, SERIES = {Springer Proc. Math. Stat.}, VOLUME = {134}, PAGES = {261--288}, PUBLISHER = {Springer, Cham}, YEAR = {2015}, MRCLASS = {65K10 (90C25)}, MRNUMBER = {3446850}, DOI = {10.1007/978-3-319-17689-5_11}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/978-3-319-17689-5_11}, } @article {MR3217221, AUTHOR = {Sun, Y. and Andersen, M.S. and Vandenberghe, L.}, TITLE = {Decomposition in conic optimization with partially separable structure}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {24}, YEAR = {2014}, NUMBER = {2}, PAGES = {873--897}, ISSN = {1052-6234}, MRCLASS = {90C22 (90C25 90C51)}, MRNUMBER = {3217221}, MRREVIEWER = {Gyeong-Mi Cho}, DOI = {10.1137/130926924}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/130926924}, } #################################end partial separability #################################start from Forbes Burkowski @article{Olszewskietal:00, author = {K.A. Olszewski and L. Yan and D. Edwards and T. Yeh}, title = {From fold recognition to homology modeling: an analysis of protein modeling challenges at different levels of prediction complexity}, journal = {Computers and Chemistry}, year = "2000", volume = {24}, number = {}, pages = {499-510} } @article{Shapovalovetal:11, author = {M.S. Shapovalov and R.L. Dunbrack Jr}, title = {A smoothed backbone-dependent rotamer library for proteins derived from adaptive kernel density estimates and regressions}, journal = {Structure}, year = "2011", volume = {19}, number = {}, pages = {844-858} } @article{Lovelletal:00, author = {S.C. Lovell and J.M. Word and J.S. Richardson and D.C. Richardson}, title = {The Penultimate Rotamer Library}, journal = {Proteins: Structure Function and Genetics}, year = "2000", volume = {40}, number = {}, pages = {389-408} } @article{Desmetetal:92, author = {J. Desmet and M. de Maeyer and B. Hazes and I. Lasters}, title = {The dead-end elimination theorem and its use in protein side-chain positioning}, journal = {Nature}, year = "1992", volume = {356}, number = {}, pages = {539-542} } #################################end from Forbes Burkowski %----------------------------------------------------------- % Protein Data Bank @article{Berman00theprotein, author = {Berman, H.M. and Westbrook, J. and Feng, Z. and Gilliland, G. and Bhat, T.N. and Weissig, H. and Shindyalov, I.N. and Bourne, P.E.}, title = {The Protein Data Bank}, journal = {Nucleic Acids Res}, year = {2000}, volume = {28}, pages = {235--242}, url = {http://www.pdb.org} } @article{banner1976ato, title={Atomic coordinates for triose phosphate isomerase from chicken muscle.}, author={Banner, D.W. and Bloomer, A. and Petsko, G.A. and Phillips, D.C. and Wilson, I.A.}, journal={Biochem Biophys Res Commun}, volume={72}, number={1}, pages={146-55}, year={1976}, } @article{Pettersen598414, address = {Computer Graphics Laboratory, Department of Pharmaceutical Chemistry, University of California, 600 16th Street, San Francisco, California 94143-2240}, author = {Pettersen, E.F. and Goddard, T.D. and Huang, C.C. and Couch, G.S. and Greenblatt, D.M. and Meng, E.C. and Ferrin, T.E.}, doi = {10.1002/jcc.20084}, issn = {0192-8651}, journal = {Journal of computational chemistry}, keywords = {2read}, month = oct, number = {13}, pages = {1605--1612}, pmid = {15264254}, posted-at = {2010-10-30 03:33:07}, priority = {2}, publisher = {John Wiley \& Sons, Inc.}, title = {{UCSF Chimera--a visualization system for exploratory research and analysis.}}, url = {http://dx.doi.org/10.1002/jcc.20084}, volume = {25}, year = {2004} } @article{Dunbrack341254, author = {Dunbrack, Jr., R.L. and Karplus, M.}, doi = {10.1006/jmbi.1993.1170}, journal = {Journal of Molecular Biology}, keywords = {rotamers}, month = mar, number = {2}, pages = {543--574}, posted-at = {2007-10-08 07:25:18}, priority = {2}, title = {Backbone-dependent Rotamer Library for Proteins Application to Side-chain Prediction}, url = {http://dx.doi.org/10.1006/jmbi.1993.1170}, volume = {230}, year = {1993} } @article{Cornell3740715, author = {Cornell, W.D. and Cieplak, P. and Bayly, C.I. and Gould, I.R. and Merz, Jr., K.M. and Ferguson, D.M. and Spellmeyer, D.C. and Fox, T. and Caldwell, J.W. and Kollman, P.A.}, journal = {J. Am. Chem. Soc.}, keywords = {coletta, molecular\_dynamics, resp}, number = {19}, pages = {5179--5197}, posted-at = {2008-12-03 15:12:07}, priority = {2}, title = {A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules}, url = {http://pubs.acs.org/wls/journals/query/citationFindResults.html?op=findCitation\&\#38;cit\_qjrn=jacsat\&\#38;vol=117\&\#38;spn=5179\&\#38;mscid=\&\#38;submit.x=10\&\#38;submit.y=5\&\#38;submit=FIND}, volume = {117}, year = {1995} } @phdthesis{Kingsford:2005:CAP:1123937, author = {Kingsford, C.L.}, advisor = {Singh, M.}, title = {Computational approaches to problems in protein structure and function}, year = {2005}, isbn = {0-542-30656-5}, note = {AAI3188669}, school = {Princeton University}, address = {Princeton, NJ, USA}, url={http://www.cbcb.umd.edu/~carlk/papers/carlk-puthesis.pd} } #####################added by Dima march/2014 @incollection{Floudas:2001aa, Author = {Laurent, M.}, Booktitle = {Encyclopedia of Optimization}, Da = {2001/01/01}, Date-Added = {2014-02-27 18:53:49 -0500}, Date-Modified = {2014-02-27 19:00:43 -0500}, La = {English}, Pages = {1311-1319}, Publisher = {Springer US}, Se = {271}, Title = {Matrix completion problems}, Ty = {CHAP}, Year = {2001}, Bdsk-Url-1 = {http://dx.doi.org/10.1007/0-306-48332-7_271}, Bdsk-Url-2 = {http://dx.doi.org/10.1007/0-306-48332-7%7B%5C_%7D271}} @article {MR2600247, AUTHOR = {Netzer, T. and Plaumann, D. and Schweighofer, M.}, TITLE = {Exposed faces of semidefinitely representable sets}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {20}, YEAR = {2010}, NUMBER = {4}, PAGES = {1944--1955}, ISSN = {1052-6234}, MRCLASS = {90C22 (14P10 15A39 93D09)}, MRNUMBER = {2600247}, DOI = {10.1137/090750196}, URL = {http://dx.doi.org/10.1137/090750196}, } @book{Netzer:2012aa, Author = {Netzer, T.}, Date-Added = {2014-02-28 11:12:21 -0500}, Date-Modified = {2014-02-28 11:16:06 -0500}, Doi = {10.1.1.297.5105}, Publisher = {Habilitationsschrift, Universit{\"a}t Leipzig}, Title = {Spectrahedra and Their Shadows}, Year = {2012}, Bdsk-Url-1 = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.297.5105}} @article{MR3062007, Author = {Gouveia, J. and Parrilo, P.A. and Thomas, R.R.}, Date-Added = {2014-02-28 10:55:17 -0500}, Date-Modified = {2014-02-28 10:55:41 -0500}, Doi = {10.1287/moor.1120.0575}, Fjournal = {Mathematics of Operations Research}, Issn = {0364-765X}, Journal = {Math. Oper. Res.}, Mrclass = {90C25 (52A20)}, Mrnumber = {3062007}, Mrreviewer = {Franz Rendl}, Number = {2}, Pages = {248--264}, Title = {Lifts of convex sets and cone factorizations}, Url = {http://dx.doi.org/10.1287/moor.1120.0575}, Volume = {38}, Year = {2013}, Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=3062007}} @article{MR2515796, Author = {Helton, J.W. and Nie, J.}, Date-Added = {2014-02-28 11:04:52 -0500}, Date-Modified = {2014-02-28 11:07:38 -0500}, Doi = {10.1137/07070526X}, Fjournal = {SIAM Journal on Optimization}, Issn = {1052-6234}, Journal = {SIAM J. Optim.}, Mrclass = {14P10 (14P25 52A99 65K10 90C22 90C25 90C60)}, Mrnumber = {2515796 (2010i:14105)}, Mrreviewer = {Aris Daniilidis}, Number = {2}, Pages = {759--791}, Title = {Sufficient and necessary conditions for semidefinite representability of convex hulls and sets}, Url = {http://dx.doi.org/10.1137/07070526X}, Volume = {20}, Year = {2009}, Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=2515796}} @article{MR2533752, Author = {Helton, J.W. and Nie, J.}, Date-Added = {2014-02-28 11:04:53 -0500}, Date-Modified = {2014-02-28 11:07:29 -0500}, Doi = {10.1007/s10107-008-0240-y}, Fjournal = {Mathematical Programming. A Publication of the Mathematical Programming Society}, Issn = {0025-5610}, Journal = {Math. Program.}, Mrclass = {90C22 (90C25)}, Mrnumber = {2533752 (2010j:90103)}, Mrreviewer = {Alexander Engau}, Number = {1, Ser. A}, Pages = {21--64}, Title = {Semidefinite representation of convex sets}, Url = {http://dx.doi.org/10.1007/s10107-008-0240-y}, Volume = {122}, Year = {2010}, Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=2533752}} @article{MR1404832, Author = {Auslender, A.}, Coden = {NFADOL}, Date-Added = {2014-02-28 14:51:01 -0500}, Date-Modified = {2014-02-28 14:51:08 -0500}, Doi = {10.1080/01630569608816707}, Fjournal = {Numerical Functional Analysis and Optimization. An International Journal}, Issn = {0163-0563}, Journal = {Numer. Funct. Anal. Optim.}, Mrclass = {47N10 (47A99 49J27 54A10 57N17)}, Mrnumber = {1404832 (97j:47091)}, Mrreviewer = {Xian Zhi George Yuan}, Number = {5-6}, Pages = {503--515}, Title = {Closedness criteria for the image of a closed set by a linear operator}, Url = {http://dx.doi.org/10.1080/01630569608816707}, Volume = {17}, Year = {1996}, Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=1404832}} %%%%%%%%%%%%%%%%%%%%%quantum references CK Li et al @article {Kraus:83, AUTHOR = {Kraus, K.}, TITLE = {States, Effects, and Operations: Fundamental Notions of Quantum Theory}, JOURNAL = {Lecture Notes in Physics, Springer-Verlag, Berlin}, VOLUME = {190}, YEAR = {1983}, } @book {NC:00, editor = "M.A. Nielsen and I.L. Chuang", Publisher="Cambridge University Press", booktitle ="Quantum Computation and Quantum Information", title ="Quantum Computation and Quantum Information", year="2000" } @article {CJW:04, AUTHOR = {Chefles, A. and Jozsa, R. and Winter, A.}, TITLE = {On the existence of physical transformations between sets of quantum states}, JOURNAL = {Int. J. Quant. Inf.}, FJOURNAL = {International Journal Quantum Information}, VOLUME = {2}, YEAR = {2004}, PAGES = {11--21}, } @book{watrous_2018, place={Cambridge}, title={The Theory of Quantum Information}, DOI={10.1017/9781316848142}, publisher={Cambridge University Press}, author={Watrous, J.}, year={2018} } @techreport{Watrous:1207.5726, AUTHOR = {Watrous, J}, TITLE = {Simpler semidefinite programs for completely bounded norms}, YEAR = {2012}, institution = "School of Computer Sciences, University of Waterloo", URL = {http://arxiv.org/abs/1207.5726} } @article{Watrous:0901.4709, AUTHOR = {Watrous, J}, TITLE = {Semidefinite programs for completely bounded norms}, JOURNAL = {Theory of Computing}, VOLUME = {5}, YEAR = {2009}, PAGES={217-238}, URL = {http://arxiv.org/abs/0901.4709} } @article{Watrous:0710.0902, AUTHOR = {Watrous, J.}, TITLE = {Distinguishing quantum operations having few Kraus operators}, JOURNAL={Quant. Inf. Comp.}, FJOURNAL = {Quantum Information & Computation}, VOLUME = {8}, YEAR = {2008}, PAGES={819-833}, URL = {http://arxiv.org/abs/0710.0902} } @article{NJKr:0909.3907, AUTHOR = {Johnston, N. and Kribs, W.}, TITLE = {A Family of Norms With Applications In Quantum Information Theory}, JOURNAL = {Journal of Mathematical Physics}, VOLUME = {51}, YEAR = {2010}, URL = {http://arxiv.org/abs/0909.3907 } } @article{NJKr:1006.0898, AUTHOR = {Johnston, N. and Kribs, W.}, TITLE = {A Family of Norms With Applications In Quantum Information Theory II}, JOURNAL = {Quantum Information and Computation}, VOLUME = {11}, YEAR = {2011}, PAGES= {104-123}, URL = {http://arxiv.org/abs/1006.0898 } } @article{NJKr:1304.2328, AUTHOR = {Johnston, N. and Kribs, W.}, TITLE = {Duality of Entanglement Norms}, JOURNAL = {Linear and Multilinear Algebra}, VOLUME = {62}, YEAR = {2014}, PAGES= {648-658}, URL = {http://arxiv.org/abs/1304.2328 } } @article{Watrous:0411077, AUTHOR = {Watrous, J.}, TITLE = {Notes on super-operator norms induced by Schatten norms}, JOURNAL = {Quantum Information \& Computation}, VOLUME = {5}, YEAR = {2005}, PAGES={58-68}, URL = {http://arxiv.org/abs/quant-ph/0411077} } #######################added paper by Greg Reid 2014 @article{Faugere99, title={A new efficient algorithm for computing Gr{\"o}bner bases (< i> F< sub> 4)}, author={Faugere, Jean-Charles}, journal={Journal of pure and applied algebra}, volume={139}, number={1}, pages={61--88}, year={1999}, publisher={Elsevier} } @article{GerdtBlinkov:1998, title={Involutive bases of polynomial ideals}, author={Gerdt, V.P. and Blinkov, Y.A.}, journal={Mathematics and Computers in Simulation}, volume={45}, number={5}, pages={519--541}, year={1998}, publisher={Elsevier} } @article{GTZ88, title = {Gröbner bases and primary decomposition of polynomial ideals}, journal = {Journal of Symbolic Computation }, volume = {6}, number = {2��?}, pages = {149 - 167}, year = {1988}, author = {Patrizia Gianni and Barry Trager and Gail Zacharias}, } @article{GrigorevVorobjov92, title={Counting connected components of a semialgebraic set in subexponential time}, author={Grigor'ev, D Yu and Vorobjov Jr, NN}, journal={Computational Complexity}, volume={2}, number={2}, pages={133--186}, year={1992}, publisher={Springer} } @article{Hauenstein12, title={Numerically computing real points on algebraic sets}, author={Hauenstein, Jonathan D}, journal={Acta applicandae mathematicae}, volume={125}, number={1}, pages={105--119}, year={2013}, publisher={Springer} } @phdthesis{Hong90, author = {Hong, Hoon}, advisor = {Collins, George E.}, title = {Improvements in Cad-based Quantifier Elimination}, year = {1990}, note = {AAI9111716}, publisher = {The Ohio State University}, } @article{Kuranishi:1957, title={On E. Cartan's prolongation theorem of exterior differential systems}, author={Kuranishi, M.}, journal={American Journal of Mathematics}, pages={1--47}, year={1957}, publisher={JSTOR} } @article{LasserreLaurentRostalski09, title={A prolongation--projection algorithm for computing the finite real variety of an ideal}, author={Lasserre, J.B. and Laurent, M. and Rostalski, P.}, journal={Theoretical Computer Science}, volume={410}, number={27}, pages={2685--2700}, year={2009}, publisher={Elsevier} } @article {MR3023755, AUTHOR = {Sorber, L. and Van B.M. and De Lathauwer, L.}, TITLE = {Unconstrained optimization of real functions in complex variables}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {22}, YEAR = {2012}, NUMBER = {3}, PAGES = {879--898}, ISSN = {1052-6234}, MRCLASS = {90C06 (90C53)}, MRNUMBER = {3023755}, MRREVIEWER = {Ning Ruan}, DOI = {10.1137/110832124}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/110832124}, } @article {MR3544118, AUTHOR = {Anjos, M.F. and Vieira, M.V.C.}, TITLE = {An improved two-stage optimization-based framework for unequal-areas facility layout}, JOURNAL = {Optim. Lett.}, FJOURNAL = {Optimization Letters}, VOLUME = {10}, YEAR = {2016}, NUMBER = {7}, PAGES = {1379--1392}, ISSN = {1862-4472}, MRCLASS = {90B85 (90C25)}, MRNUMBER = {3544118}, DOI = {10.1007/s11590-016-1008-6}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s11590-016-1008-6}, } @article {MR2812889, AUTHOR = {Jankovits, I. and Luo, C. and Anjos, M.F. and Vannelli, A.}, TITLE = {A convex optimisation framework for the unequal-areas facility layout problem}, JOURNAL = {European J. Oper. Res.}, FJOURNAL = {European Journal of Operational Research}, VOLUME = {214}, YEAR = {2011}, NUMBER = {2}, PAGES = {199--215}, ISSN = {0377-2217}, MRCLASS = {90B85 (90C22 90C25)}, MRNUMBER = {2812889}, MRREVIEWER = {Frank Plastria}, DOI = {10.1016/j.ejor.2011.04.013}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1016/j.ejor.2011.04.013}, } @article {MR2155512, AUTHOR = {Anjos, M.F. and Kennings, A. and Vannelli, A.}, TITLE = {A semidefinite optimization approach for the single-row layout problem with unequal dimensions}, JOURNAL = {Discrete Optim.}, FJOURNAL = {Discrete Optimization}, VOLUME = {2}, YEAR = {2005}, NUMBER = {2}, PAGES = {113--122}, ISSN = {1572-5286}, MRCLASS = {90C22 (90B85)}, MRNUMBER = {2155512}, DOI = {10.1016/j.disopt.2005.03.001}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1016/j.disopt.2005.03.001}, } @article{Bingane2018TightandCheapCR, title={Tight-and-Cheap Conic Relaxation for the AC Optimal Power Flow Problem}, author={C. Bingane and M.F. Anjos and S. Le Digabel}, journal={IEEE Transactions on Power Systems}, year={2018}, volume={33}, pages={7181-7188} } @incollection{LaurentRostalski:12, author = "Laurent, M. and Rostalski, P.", title = "The approach of moments for polynomial equations", booktitle = {Handbook on semidefinite, conic and polynomial optimization}, EDITOR = {Anjos, Miguel F. and Lasserre, Jean B.}, SERIES = {International Series in Operations Research \& Management Science, 166}, PUBLISHER = {Springer, New York}, pages = "25--60", YEAR = {2012}, MRCLASS = {90-06 (90C22 90C30)}, MRNUMBER = {2894661 (2012j:90006)}, DOI = {10.1007/978-1-4614-0769-0}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/978-1-4614-0769-0}, } @phdthesis{Lu06, title={Finding all real solutions of polynomial systems}, author={Lu, Ye}, year={2006}, school={University of Notre Dame} } @book{Macaulay:1916, title={The algebraic theory of modular systems}, author={Macaulay, F.S. and Roberts, P.}, number={19}, year={1916}, publisher={University press Cambridge} } @inproceedings{MaZhi12, title={Computing real solutions of polynomial systems via low-rank moment matrix completion}, author={Ma, Y. and Zhi, L.}, booktitle={Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation}, pages={249--256}, year={2012}, organization={ACM} } @article{MWZ:2012, title = {A certificate for semidefinite relaxations in computing positive dimensional real varieties}, author={Ma, Y. and Wang, C. and Zhi, L.}, institution = "KLMM, Academy of Mathematics and Systems Science, CAS", eprint = {math/1212.4924}, journal = "Journal of Symbolic Computation ", volume = "72", number = "", pages = "1 - 20", year = "2016", issn = "0747-7171", doi = "http://dx.doi.org/10.1016/j.jsc.2014.12.002 [dx.doi.org]", url = "http://www.sciencedirect.com/science/article/pii/S0747717114001291" } @article{MollerSauer:2000, title={H-bases for polynomial interpolation and system solving}, author={M{\"o}ller, H.M. and Sauer, T.}, journal={Advances in Computational Mathematics}, volume={12}, number={4}, pages={335--362}, year={2000}, publisher={Springer} } @article{Mourrain:1996, title={Isolated points, duality and residues}, author={Mourrain, B.}, journal={Journal of Pure and Applied Algebra}, volume={117}, pages={469--493}, year={1997}, publisher={Elsevier} } @incollection{Mourrain:1999, title={A new criterion for normal form algorithms}, author={Mourrain, B.}, booktitle={Applied algebra, algebraic algorithms and error-correcting codes}, pages={430--442}, year={1999}, publisher={Springer} } @inproceedings{{MourrainTrebuchet:2000, title={Solving projective complete intersection faster}, author={Mourrain, B. and Trebuchet, P.}, booktitle={Proceedings of the 2000 international symposium on Symbolic and algebraic computation}, pages={234--241}, year={2000}, organization={ACM} } @inproceedings{Mourrain:2002, title={Algebraic methods for numerical solving}, author={Mourrain, B. and Tr{\'e}buchet, P.}, booktitle={Proc. of the 3rd International Workshop on Symbolic and Numeric Algorithms for Scientific Computing}, volume={1}, pages={42--57}, year={2002} } @book{Pommaret:1978, title={Systems of partial differential equations and Lie pseudogroups}, author={Pommaret, Jean-Fran{\c{c}}ois}, volume={14}, year={1978}, publisher={CRC Press} } @article{RRS00, title={Finding at least one point in each connected component of a real algebraic set defined by a single equation}, author={Rouillier, Fabrice and Roy, M-F and Safey El Din, M}, journal={Journal of Complexity}, volume={16}, number={4}, pages={716--750}, year={2000}, publisher={Elsevier} } @incollection{SRWZ2010, title={Geometric involutive bases and applications to approximate commutative algebra}, author={Scott, R. and Reid, G.J. and Wu, W. and Zhi, L.}, pages = {99--124}, editor = {Robbiano, Lorenzo and Abbott, John}, booktitle = {Approximate Commutative Algebra}, year={2010}, publisher={Springer} } @article{ReidLinWittkopf:2001, title={Differential elimination--completion algorithms for DAE and PDAE}, author={Reid, G.J. and Lin, P. and Wittkopf, A.D.}, journal={Studies in Applied Mathematics}, volume={106}, number={1}, pages={1--45}, year={2001}, publisher={Wiley Online Library} } @book{GottliebOrszag:77, AUTHOR = {Gottlieb, D. and Orszag, S.A.}, TITLE = {Numerical analysis of spectral methods: theory and applications}, NOTE = {CBMS-NSF Regional Conference Series in Applied Mathematics, No. 26}, PUBLISHER = {Society for Industrial and Applied Mathematics, Philadelphia, Pa.}, YEAR = {1977}, PAGES = {v+172}, MRCLASS = {65MXX (65-02 65P05)}, MRNUMBER = {0520152 (58 \#24983)}, MRREVIEWER = {O. Widlund} } @article{ReidWittkopf:2001, title={Fast differential elimination in C: The CDiffElim environment}, author={Wittkopf, A.D. and Reid, G.J.}, journal={Computer Physics Communications}, volume={139}, number={2}, pages={192--217}, year={2001}, publisher={Elsevier} } @article{ReidSmithVerschelde:2002, title={Geometric completion of differential systems using numeric-symbolic continuation}, author={Reid, G.J. and Smith, C. and Verschelde, J.}, journal={ACM SIGSAM Bulletin}, volume={36}, number={2}, pages={1--17}, year={2002}, publisher={ACM} } @inproceedings{ReidTangZhi:2003, title={A complete symbolic-numeric linear method for camera pose determination}, author={Reid, G.J. and Tang, J. and Zhi, L.}, booktitle={Proceedings of the 2003 international symposium on Symbolic and algebraic computation}, pages={215--223}, year={2003}, organization={ACM} } @techreport{ReidWangWu:14, title = {Geometric involutive bases for positive dimensional polynomial ideals and SDP methods}, author={Reid, G.J. and Wang, F. and Wu, W.}, date = {2014-05-28}, eprinttype = {arXiv}, eprint = {math/1405.7115}, year = {2014}, institution = "Department of Appl. Math., University of Western Ontario", } @article{ReidZhi2009, title={Solving polynomial systems via symbolic-numeric reduction to geometric involutive form}, author={Reid, G.J. and Zhi, L.}, journal={Journal of Symbolic Computation}, volume={44}, number={3}, pages={280--291}, year={2009}, publisher={Elsevier} } @article{Seidenberg54, title={A new decision method for elementary algebra}, author={Seidenberg, Abraham}, journal={Annals of Mathematics}, pages={365--374}, year={1954}, publisher={JSTOR} } @book{Seiler2010, title={Involution: The formal theory of differential equations and its applications in computer algebra}, series={Algorithms and Computation in Mathematics}, author={Seiler, Werner M}, volume={24}, year={2010}, publisher={Springer} } @incollection {MR2389242, AUTHOR = {Lu, Y. and Bates, D.J. and Sommese, A.J. and Wampler, C.W.}, TITLE = {Finding all real points of a complex curve}, BOOKTITLE = {Algebra, geometry and their interactions}, SERIES = {Contemp. Math.}, VOLUME = {448}, PAGES = {183--205}, PUBLISHER = {Amer. Math. Soc., Providence, RI}, YEAR = {2007}, MRCLASS = {65H10 (14Q99)}, MRNUMBER = {2389242 (2009c:65120)}, DOI = {10.1090/conm/448/08665}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1090/conm/448/08665}, } @book {MR3155500, AUTHOR = {Bates, Daniel J. and Hauenstein, Jonathan D. and Sommese, Andrew J. and Wampler, Charles W.}, TITLE = {Numerically solving polynomial systems with {B}ertini}, SERIES = {Software, Environments, and Tools}, VOLUME = {25}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA}, YEAR = {2013}, PAGES = {xx+352}, ISBN = {978-1-611972-69-6}, MRCLASS = {13-04 (13P15 65D99 68W30)}, MRNUMBER = {3155500}, MRREVIEWER = {Jan M. Verschelde}, } @book{SommeseWampler05, title={The Numerical solution of systems of polynomials arising in engineering and science}, author={Sommese, A.J. and Wampler, C.W.}, volume={99}, year={2005}, publisher={World Scientific} } @book {Stetter:2004, AUTHOR = {Stetter, Hans J.}, TITLE = {Numerical polynomial algebra}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {2004}, PAGES = {xvi+472}, ISBN = {0-89871-557-1}, MRCLASS = {65-02 (13P10)}, MRNUMBER = {MR2048781 (2006a:65004)}, MRREVIEWER = {Andrzej Kozlowski}, } @article{Tarski31, title={A decision method for elementary algebra and geometry}, author={Tarski, A.}, year={1951}, publisher={Rand Corporation} } @article{WuZhi12, title={Determining singular solutions of polynomial systems via symbolic--numeric reduction to geometric involutive forms}, author={Wu, X. and Zhi, L.}, journal={Journal of Symbolic Computation}, volume={47}, number={3}, pages={227--238}, year={2012}, publisher={Elsevier} } @inproceedings{WuReid13, title={Finding points on real solution components and applications to differential polynomial systems}, author={Wu, W. and Reid, G.J.}, booktitle={Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation}, pages={339--346}, year={2013}, organization={ACM} } @inproceedings{YZZ13, title={Verified error bounds for real solutions of positive-dimensional polynomial systems}, author={Yang, Z. and Zhi, L. and Zhu, Y.}, booktitle={Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation}, pages={371--378}, year={2013}, organization={ACM} } @Book{BPT2012, Editor ={G. Blekherman and P.A. Parrilo and R.R. Thomas}, TITLE = {Semidefinite optimization and convex algebraic geometry}, SERIES = {MOS-SIAM Series on Optimization}, VOLUME = {13}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA; Mathematical Optimization Society, Philadelphia, PA}, YEAR = {2013}, PAGES = {xx+476}, ISBN = {978-1-611972-28-3}, MRCLASS = {90-06 (14-06)}, MRNUMBER = {3075433}, MRREVIEWER = {Franz Rendl}, } @article{BLRSZ:2004, title={Determination of approximate symmetries of differential equations}, author={Bonasia, J. and Lemaire, F. and Reid, G.J. and Zhi, L.}, journal={Group Theory and Numerical Analysis}, volume={39}, pages={249}, year={2005}, publisher={American Mathematical Soc.} } @article{CurtoFialkow96, title={Solution of the truncated complex moment problem for flat data-Introduction}, author={Curto, RE and Fialkow, LA}, journal={Memoirs of the American Mathematical Society}, volume={119}, number={568}, pages={1}, year={1996}, publisher={AMER MATHEMATICAL SOC} } @article{DavenportHeintz88, title={Real quantifier elimination is doubly exponential}, author={Davenport, James H and Heintz, Joos}, journal={Journal of Symbolic Computation}, volume={5}, number={1}, pages={29--35}, year={1988}, publisher={Elsevier} } @book{BasuPollackRoy06, Author ={S. Basu and R. Pollack and M.-F. Roy}, TITLE = {Algorithms in Real Algebraic Geometry}, PUBLISHER = {Springer-Verlag}, SERIES = {Algorithms and Computation in Math}, EDITION = {2}, VOLUME = {10}, YEAR = {2006} } @book {MR1059481, TITLE = {Matrix theory and applications}, SERIES = {Proceedings of Symposia in Applied Mathematics}, VOLUME = {40}, EDITOR = {Johnson, C.R.}, NOTE = {Lecture notes prepared for the American Mathematical Society Short Course held in Phoenix, Arizona, January 10--11, 1989, AMS Short Course Lecture Notes}, PUBLISHER = {American Mathematical Society, Providence, RI}, YEAR = {1990}, PAGES = {x+260}, ISBN = {0-8218-0154-6}, MRCLASS = {15-02 (05-02 15-06 60J10 62H05)}, MRNUMBER = {1059481}, MRREVIEWER = {Kent Kidman}, DOI = {10.1090/psapm/040}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1090/psapm/040}, } @article {MR2014037, AUTHOR = {Harrison, K.J.}, TITLE = {Matrix completions and chordal graphs}, NOTE = {International Workshop on Operator Algebra and Operator Theory (Linfen, 2001)}, JOURNAL = {Acta Math. Sin. (Engl. Ser.)}, FJOURNAL = {Acta Mathematica Sinica (English Series)}, VOLUME = {19}, YEAR = {2003}, NUMBER = {3}, PAGES = {577--590}, ISSN = {1439-8516}, MRCLASS = {15A99 (05C50 47A20)}, MRNUMBER = {2014037}, DOI = {10.1007/s10114-003-0266-2}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s10114-003-0266-2}, } @article {MR2487961, AUTHOR = {Cravo, G.}, TITLE = {Recent progress on matrix completion problems}, JOURNAL = {J. Math. Sci. Adv. Appl.}, FJOURNAL = {Journal of Mathematical Sciences. Advances and Applications}, VOLUME = {1}, YEAR = {2008}, NUMBER = {1}, PAGES = {69--90}, ISSN = {0974-5750}, MRCLASS = {15A18 (15A83)}, MRNUMBER = {2487961}, MRREVIEWER = {Hugo Jan Woerdeman}, } @article {MR2508310, AUTHOR = {Cravo, G.}, TITLE = {Matrix completion problems}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {430}, YEAR = {2009}, NUMBER = {8-9}, PAGES = {2511--2540}, ISSN = {0024-3795}, CODEN = {LAAPAW}, MRCLASS = {15A83 (15A18)}, MRNUMBER = {2508310}, MRREVIEWER = {Hugo Jan Woerdeman}, DOI = {10.1016/j.laa.2008.12.029}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/j.laa.2008.12.029}, } @book {MR3059590, TITLE = {Distance geometry}, EDITOR = {Mucherino, A. and Lavor, C. and Liberti, L. and Maculan, N.}, NOTE = {Theory, methods, and applications}, PUBLISHER = {Springer, New York}, YEAR = {2013}, PAGES = {xvi+420}, ISBN = {978-1-4614-5127-3; 978-1-4614-5128-0}, MRCLASS = {92-06 (05-06)}, MRNUMBER = {3059590}, DOI = {10.1007/978-1-4614-5128-0}, URL = {http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/978-1-4614-5128-0}, } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Haesol entries @article{MR3421846, AUTHOR={Chuong, T. D. and Jeyakumar, V.}, TITLE={Characterizing robust local error bounds for linear inequality systems under data uncertainty}, JOURNAL={Linear Algebra Appl.}, FJOURNAL={Linear Algebra and its Applications}, VOLUME={489}, YEAR={2016}, PAGES={199--216}, ISSN={0024-3795}, MRCLASS={90C29 (65K05 90C46)}, MRNUMBER={3421846}, DOI={10.1016/j.laa.2015.10.011}, URL={http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/j.laa.2015.10.011} } @article{MR2169053, AUTHOR={Goldman, R.}, TITLE={Curvature formulas for implicit curves and surfaces}, JOURNAL={Comput. Aided Geom. Design}, FJOURNAL={Computer Aided Geometric Design}, VOLUME={22}, YEAR={2005}, NUMBER={7}, PAGES={632--658}, ISSN={0167-8396}, MRCLASS={65D17 (53A04 53A05)}, MRNUMBER={2169053}, MRREVIEWER={Bert J\~A${}^1\!/\!_4$ttler}, DOI={10.1016/j.cagd.2005.06.005}, URL={http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/j.cagd.2005.06.005} } @book{MR3522166, AUTHOR={Todd, M.J.}, TITLE={Minimum-volume ellipsoids}, SERIES={MOS-SIAM Series on Optimization}, VOLUME={23}, NOTE={Theory and algorithms}, PUBLISHER={Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA; Mathematical Optimization Society, Philadelphia, PA}, YEAR={2016}, PAGES={xiv+149}, ISBN={978-1-611974-37-9}, MRCLASS={90-02 (52A38 62K05 90C25 90C51)}, MRNUMBER={3522166}, DOI={10.1137/1.9781611974386.ch1}, URL={http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/1.9781611974386.ch1} } @book{MR2472514, AUTHOR={Griva, I. and Nash, S.G. and Sofer, A.}, TITLE={Linear and nonlinear optimization}, EDITION={Second}, PUBLISHER={Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA}, YEAR={2009}, PAGES={xxii+742}, ISBN={978-0-898716-61-0}, MRCLASS={90-01 (90Bxx 90Cxx)}, MRNUMBER={2472514}, DOI={10.1137/1.9780898717730}, URL={http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1137/1.9780898717730} } @article{doi:10.1137/040616851, author = {Beck, A. and Ben-Tal, A. and Teboulle, M.}, title = {Finding a Global Optimal Solution for a Quadratically Constrained Fractional Quadratic Problem with Applications to the Regularized Total Least Squares}, journal = {SIAM Journal on Matrix Analysis and Applications}, volume = {28}, number = {2}, pages = {425-445}, year = {2006}, doi = {10.1137/040616851}, URL = {https://doi.org/10.1137/040616851}, eprint = {https://doi.org/10.1137/040616851} } @book {MR3719240, AUTHOR = {Beck, A.}, TITLE = {First-order methods in optimization}, SERIES = {MOS-SIAM Series on Optimization}, VOLUME = {25}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA; Mathematical Optimization Society, Philadelphia, PA}, YEAR = {2017}, PAGES = {xii+475}, ISBN = {978-1-611974-98-0}, MRCLASS = {90-02 (49M20 65K05 90C06 90C25)}, MRNUMBER = {3719240}, MRREVIEWER = {Sven-\AA ke Gustafson}, DOI = {10.1137/1.9781611974997.ch1}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/1.9781611974997.ch1}, } @book{MR3410115, AUTHOR={Beck, M. and Robins, S.}, TITLE={Computing the continuous discretely}, SERIES={Undergraduate Texts in Mathematics}, EDITION={Second}, NOTE={Integer-point enumeration in polyhedra, With illustrations by David Austin}, PUBLISHER={Springer, New York}, YEAR={2015}, PAGES={xx+285}, ISBN={978-1-4939-2968-9; 978-1-4939-2969-6}, MRCLASS={11P21 (05A15 05B15 11-02 11H06 52B05 52B20)}, MRNUMBER={3410115}, DOI={10.1007/978-1-4939-2969-6}, URL={http://dx.doi.org/10.1007/978-1-4939-2969-6} } @techreport{copyAnsBri:00, author={K.M. Anstreicher and N.W. Brixius}, title={Solving quadratic assignment problems usingconvex quadratic programming relaxations}, institution={University of Iowa}, address={ Iowa City, IA"} } @article{copyArmBuf63, author={Armour, G.C. and Buffa, E.S.}, title={Heuristic algorithm and simulation approach to relative location of facilities}, journal={ms}, volume={9}, year={1963"} } @conference{copyBalMaz80, author={Balas, E. and Mazzola, J.B.}, title={Quadratic 0-1 programming by a new linearization}, booktitle={Proceedings of the TIMS/ORSA}, organization={TIMS/ORSA}, address={{Washington D.c.}}, month={May"} } @book{BrRy:91, author="Brualdi, R.A. and Ryser, H.J.", title="Combinatorial Matrix Theory", publisher="Cambridge University Press", year = "1991", address="New York" } @inproceedings{copyipps97.qap, author={Adrian Br{\"u}ngger and Ambros Marzetta and Jens Clausen and Michael Perregaard}, title={Joining Forces in Solving Large-Scale Quadratic AssignmentProblems in Parallel}, booktitle={Proceedings of the 11th International Parallel Processing Symposium (IPPS'97)}, year={1997}, pages={418--427"} } @book{MR2546839, AUTHOR={Ben-Tal, A. and El Ghaoui, L. and Nemirovski, A.}, TITLE={Robust optimization}, SERIES={Princeton Series in Applied Mathematics}, PUBLISHER={Princeton University Press, Princeton, NJ}, YEAR={2009}, PAGES={xxii+542}, ISBN={978-0-691-14368-2}, MRCLASS={90-02 (49K40 90C22 90C31 93C41)}, MRNUMBER={2546839}, MRREVIEWER={Alexander Shapiro}, DOI={10.1515/9781400831050}, URL={http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1515/9781400831050} } @article{MR2853227, AUTHOR={Desario, D. and Robins, S.}, TITLE={Generalized solid-angle theory for real polytopes}, JOURNAL={Q. J. Math.}, FJOURNAL={The Quarterly Journal of Mathematics}, VOLUME={62}, YEAR={2011}, NUMBER={4}, PAGES={1003--1015}, ISSN={0033-5606}, MRCLASS={52A38}, MRNUMBER={2853227}, MRREVIEWER={Dmitry Ryabogin}, DOI={10.1093/qmath/hap030}, URL={http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1093/qmath/hap030} } %%%%%%%%%%%%%%%from Daniela aug/17 @Article{Balas1975, author="Balas, E.", title="Facets of the knapsack polytope", journal="Mathematical Programming", year="1975", month="Dec", day="01", volume="8", number="1", pages="146--164", abstract="A necessary and sufficient condition is given for an inequality with coefficients 0 or 1 to define a facet of the knapsack polytope, i.e., of the convex hull of 0--1 points satisfying a given linear inequality. A sufficient condition is also established for a larger class of inequalities (with coefficients not restricted to 0 and 1) to define a facet for the same polytope, and a procedure is given for generating all facets in the above two classes. The procedure can be viewed as a way of generating cutting planes for 0--1 programs.", issn="1436-4646", doi="10.1007/BF01580440", url="https://doi.org/10.1007/BF01580440" } @Article{Wolsey1975, author="Wolsey, L.A.", title="Faces for a linear inequality in 0--1 variables", journal="Mathematical Programming", year="1975", month="Dec", day="01", volume="8", number="1", pages="165--178", abstract="Given a linear inequality in 0--1 variables we attempt to obtain the faces of the integer hull of 0--1 feasible solutions. For the given inequality we specify how faces of a variety of lower-dimensional inequalities can be raised to give full-dimensional faces. In terms of a set, called a ``strong cover'', we obtain necessary and sufficient conditions for any inequality with 0--1 coefficients to be a face, and characterize different forms that the integer hull must take.", issn="1436-4646", doi="10.1007/BF01580441", url="https://doi.org/10.1007/BF01580441" } @Article{Atamturk2005, author="Atamt{\"u}rk, A.", title="Cover and Pack Inequalities for (Mixed) Integer Programming", journal="Annals of Operations Research", year="2005", month="Oct", day="01", volume="139", number="1", pages="21--38", abstract="We review strong inequalities for fundamental knapsack relaxations of (mixed) integer programs. These relaxations are the 0-1 knapsack set, the mixed 0-1 knapsack set, the integer knapsack set, and the mixed integer knapsack set. Our aim is to give a unified presentation of the inequalities based on covers and packs and highlight the connections among them. The focus of the paper is on recent research on the use of superadditive functions for the analysis of knapsack polyhedra.", issn="1572-9338", doi="10.1007/s10479-005-3442-1", url="https://doi.org/10.1007/s10479-005-3442-1" } @article{Gu1998, author = {Z. Gu and G.L. Nemhauser and M.W.P. Savelsbergh}, title = {Lifted Cover Inequalities for 0-1 Integer Programs: Computation}, journal = {INFORMS Journal on Computing}, volume = {10}, number = {4}, pages = {427-437}, year = {1998}, doi = {10.1287/ijoc.10.4.427}, URL = { https://doi.org/10.1287/ijoc.10.4.427 }, eprint = { https://doi.org/10.1287/ijoc.10.4.427 } , abstract = { We investigate the algorithmic and implementation issues related to the effective and efficient use of lifted cover inequalities and lifted GUB cover inequalities in a branch and cut algorithm for 0-1 integer programming. We have tried various strategies on several test problems and we identify the best ones for use in practice. } } @Article{Hammer1975, author="Hammer, P.L. and Johnson, E.L. and Peled, U. N.", title="Facet of regular 0--1 polytopes", journal="Mathematical Programming", year="1975", month="Dec", day="01", volume="8", number="1", pages="179--206", abstract="The role of 0--1 programming problems having monotone or regular feasible sets was pointed out in [6]. The solution sets of covering and of knapsack problems are examples of monotone and of regular sets respectively. Some connections are established between prime implicants of a monotone or a regular Boolean function$\beta$ on the one hand, and facets of the convex hullH of the zeros of$\beta$ on the other. In particular (Corollary 2) a necessary and sufficient condition is given for a constraint of a covering problem to be a facet of the corresponding integer polyhedron. For any prime implicantP of$\beta$, a nonempty familyF(P) of facets ofH is constructed. Proposition 17 gives easy-to-determine sharp upper bounds for the coefficients of these facets when$\beta$ is regular. A special class of prime implicants is described for regular functions and it is shown that for anyP in this class,F(P) consists of one facet ofH, and this facet has 0--1 coefficients. Every nontrivial facet ofH with 0--1 coefficients is obtained from this class.", issn="1436-4646", doi="10.1007/BF01580442", url="https://doi.org/10.1007/BF01580442" } @article{BalasZemel1978, ISSN = {00361399}, URL = {http://www.jstor.org/stable/2100862}, abstract = {In this paper we give easily computable best upper and lower bounds on the coefficients of facets of the knapsack polytope associated with minimal covers. For some coefficients the upper bounds are equal to the lower bounds; for the others the two bounds differ by 1. We give a necessary and sufficient condition for all lower bounds to be equal to the corresponding upper bounds, i.e. for the facet associated with the given minimal cover to be unique. Also, we define a partial order on the set of minimal covers and show that all facets associated with minimal covers can be obtained from weak covers; but that each facet obtainable from several ordered minimal covers is easiest to compute from the strongest one. Further, we characterize the class of all facets associated with minimal covers, and show that the facets obtainable by Padberg's sequential lifting procedure are precisely those members of the class which have integer coefficients for a certain right-hand side. We then give a procedure for generating the other (simultaneously) lifted facets, which have fractional coefficients for the same right-hand side.}, author = {E. Balas and E. Zemel}, journal = {SIAM Journal on Applied Mathematics}, number = {1}, pages = {119-148}, publisher = {Society for Industrial and Applied Mathematics}, title = {Facets of the Knapsack Polytope from Minimal Covers}, volume = {34}, year = {1978} } @article{Zemel1989, author = {E. Zemel}, title = {Easily Computable Facets of the Knapsack Polytope}, journal = {Mathematics of Operations Research}, volume = {14}, number = {4}, pages = {760-764}, year = {1989}, doi = {10.1287/moor.14.4.760}, URL = { https://doi.org/10.1287/moor.14.4.760 }, eprint = { https://doi.org/10.1287/moor.14.4.760 } , abstract = { It is known that facets and valid inequalities for the knapsack polytope P can be obtained by lifting a simple inequality derived from each minimal cover. We study the computational complexity of such lifting. In particular, we show that the task of computing a lifted facet can be accomplished in O(ns) where s ��?n is the cardinality of the minimal cover. Also, for a lifted inequality with integer coefficients, we show that the dual tasks of recognizing whether the inequality is valid for P or is a facet of P can be done within the same time bound. } } #################from Haesol Sept 17/17 @article {MR2254419, AUTHOR = {M.J. C\'anovas and M.A. L\'opez and J. Parra and F.J. Toledo}, TITLE = {Lipschitz continuity of the optimal value via bounds on the optimal set in linear semi-infinite optimization}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {31}, YEAR = {2006}, NUMBER = {3}, PAGES = {478--489}, ISSN = {0364-765X}, MRCLASS = {90C31 (90C34)}, MRNUMBER = {2254419}, MRREVIEWER = {Virginia N. Vera de Serio}, DOI = {10.1287/moor.1060.0198}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1287/moor.1060.0198}, } @incollection {MR1842881, AUTHOR = {Gauvin, Jacques}, TITLE = {Formulae for the sensitivity analysis of linear programming problems}, BOOKTITLE = {Approximation, optimization and mathematical economics ({P}ointe-\`a-{P}itre, 1999)}, PAGES = {117--120}, PUBLISHER = {Physica, Heidelberg}, YEAR = {2001}, MRCLASS = {90C31 (90C05)}, MRNUMBER = {1842881}, } @book{MR2253203, AUTHOR={Gray, A. and Abbena, E. and Salamon, S.}, TITLE={Modern differential geometry of curves and surfaces with {M}athematica{$^\circledR$}}, SERIES={Studies in Advanced Mathematics}, EDITION={Third}, PUBLISHER={Chapman {\&} Hall/CRC, Boca Raton, FL}, YEAR={2006}, PAGES={xxiv+984}, ISBN={978-1-58488-448-4; 1-58488-448-7}, MRCLASS={53-01 (53-04 53A04 53A05 65D18)}, MRNUMBER={2253203} } @article{MR2048490, AUTHOR={Jibrin, S. and Swift, J.W.}, TITLE={The boundary of weighted analytic centers for linear matrix inequalities}, JOURNAL={JIPAM. J. Inequal. Pure Appl. Math.}, FJOURNAL={JIPAM. Journal of Inequalities in Pure and Applied Mathematics}, VOLUME={5}, YEAR={2004}, NUMBER={1}, PAGES={Article 14, 21}, ISSN={1443-5756}, MRCLASS={90C22 (15A39 90C53)}, MRNUMBER={2048490} } @article{MR1174359, AUTHOR={Avis, D. and Fukuda, K.}, TITLE={A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra}, NOTE={ACM Symposium on Computational Geometry (North Conway, NH, 1991)}, JOURNAL={Discrete Comput. Geom.}, FJOURNAL={Discrete \{\&} Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME={8}, YEAR={1992}, NUMBER={3}, PAGES={295--313}, ISSN={0179-5376}, MRCLASS={68U05 (52B55 65Y25)}, MRNUMBER={1174359}, MRREVIEWER={Henk J. A. M. Heijmans}, DOI={10.1007/BF02293050}, URL={http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/BF02293050} } @article{MR3453429, AUTHOR={Goberna, M.A. and Jeyakumar, V. and Li, G. and Linh, N.}, TITLE={Radius of robust feasibility formulas for classes of convex programs with uncertain polynomial constraints}, JOURNAL={Oper. Res. Lett.}, FJOURNAL={Operations Research Letters}, VOLUME={44}, YEAR={2016}, NUMBER={1}, PAGES={67--73}, ISSN={0167-6377}, MRCLASS={90C25 (90C15 90C31)}, MRNUMBER={3453429}, DOI={10.1016/j.orl.2015.11.011}, URL={http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1016/j.orl.2015.11.011} } @article{GORISSEN2015124, title={A practical guide to robust optimization}, journal="Omega", volume="53", number="", pages="124 - 137", year="2015", issn="0305-0483", doi="http://dx.doi.org/10.1016/j.omega.2014.12.006", url="http://www.sciencedirect.com/science/article/pii/S0305048314001698", author={Gorissen, B. L. and Yanikoglu, I. and D. den Hertog}, keywords={Robust optimization} } @article {MR3566918, AUTHOR = {Kocvara, Michal and Nesterov, Yurii and Xia, Yu}, TITLE = {A subgradient method for free material design}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {26}, YEAR = {2016}, NUMBER = {4}, PAGES = {2314--2354}, ISSN = {1052-6234}, MRCLASS = {90C90 (90-08 90C06 90C25 90C30)}, MRNUMBER = {3566918}, MRREVIEWER = {Kurt Marti}, URL = {https://doi.org/10.1137/15M1019660}, } @article {MR3375674, AUTHOR = {Xia, Yu}, TITLE = {Gradient methods and conic least-squares problems}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods \& Software}, VOLUME = {30}, YEAR = {2015}, NUMBER = {4}, PAGES = {769--803}, ISSN = {1055-6788}, MRCLASS = {90C25 (90C06 90C20 90C22 90C51)}, MRNUMBER = {3375674}, MRREVIEWER = {Baha M. Alzalg}, URL = {https://doi.org/10.1080/10556788.2014.990452}, } @article {MR3175497, AUTHOR = {Xia, Yu and McNicholas, Paul D.}, TITLE = {A gradient method for the monotone fused least absolute shrinkage and selection operator}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods \& Software}, VOLUME = {29}, YEAR = {2014}, NUMBER = {3}, PAGES = {463--483}, ISSN = {1055-6788}, MRCLASS = {62J07 (65C60 90C90)}, MRNUMBER = {3175497}, URL = {https://doi.org/10.1080/10556788.2013.801970}, } @article {MR3071865, AUTHOR = {Nesterov, Y.}, TITLE = {Gradient methods for minimizing composite functions}, JOURNAL = {Math. Program.}, FJOURNAL = {Mathematical Programming}, VOLUME = {140}, YEAR = {2013}, NUMBER = {1, Ser. B}, PAGES = {125--161}, ISSN = {0025-5610}, MRCLASS = {90C25 (68Q17 90C47)}, MRNUMBER = {3071865}, MRREVIEWER = {Dana Simian}, DOI = {10.1007/s10107-012-0629-5}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10107-012-0629-5}, } @article {MR3060948, AUTHOR = {Nesterov, Yurii and Xia, Yu}, TITLE = {Hessian distances and their applications in the complexity analysis of interior-point methods}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods \& Software}, VOLUME = {28}, YEAR = {2013}, NUMBER = {3}, PAGES = {543--563}, ISSN = {1055-6788}, MRCLASS = {90C51 (90C60)}, MRNUMBER = {3060948}, URL = {https://doi.org/10.1080/10556788.2012.737327}, } @article {MR2774149, AUTHOR = {Alizadeh, Farid and Xia, Yu}, TITLE = {The {$Q$} method for symmetric cone programming}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {149}, YEAR = {2011}, NUMBER = {1}, PAGES = {102--137}, ISSN = {0022-3239}, MRCLASS = {90C22 (17C99)}, MRNUMBER = {2774149}, URL = {https://doi.org/10.1007/s10957-010-9777-z}, } @article {MR2533250, AUTHOR = {Xia, Yu}, TITLE = {Two-dimensional second-order cone programming}, JOURNAL = {Int. J. Oper. Res.}, FJOURNAL = {International Journal of Operational Research}, VOLUME = {5}, YEAR = {2009}, NUMBER = {4}, PAGES = {468--484}, ISSN = {1745-7645}, MRCLASS = {90C49 (90C05 90C22)}, MRNUMBER = {2533250}, MRREVIEWER = {Dorel Duca}, URL = {https://doi.org/10.1504/IJOR.2009.025704}, } @article {MR2486220, AUTHOR = {Xia, Yu}, TITLE = {A global optimization method for semi-supervised clustering}, JOURNAL = {Data Min. Knowl. Discov.}, FJOURNAL = {Data Mining and Knowledge Discovery}, VOLUME = {18}, YEAR = {2009}, NUMBER = {2}, PAGES = {214--256}, ISSN = {1384-5810}, MRCLASS = {Expansion}, MRNUMBER = {2486220}, URL = {https://doi.org/10.1007/s10618-008-0104-3}, } @article {MR2578322, AUTHOR = {Xia, Yu and Alizadeh, Farid}, TITLE = {The {$Q$} method for second order cone programming}, JOURNAL = {Comput. Oper. Res.}, FJOURNAL = {Computers \& Operations Research}, VOLUME = {35}, YEAR = {2008}, NUMBER = {5}, PAGES = {1510--1538}, ISSN = {0305-0548}, MRCLASS = {90C22 (90C25)}, MRNUMBER = {2578322}, URL = {https://doi.org/10.1016/j.cor.2006.08.009}, } @article {MR2424169, AUTHOR = {Xia, Yu}, TITLE = {Complexity of the primal-dual path-following algorithms for the weighted determinant maximization problems with linear matrix inequalities in the narrow neighbourhood}, JOURNAL = {Optim. Methods Softw.}, FJOURNAL = {Optimization Methods \& Software}, VOLUME = {23}, YEAR = {2008}, NUMBER = {3}, PAGES = {421--440}, ISSN = {1055-6788}, MRCLASS = {90C51 (90C22)}, MRNUMBER = {2424169}, MRREVIEWER = {J\"org Fliege}, URL = {https://doi.org/10.1080/10556780701830048}, } @article {MR2335101, AUTHOR = {Xia, Yu}, TITLE = {A {N}ewton's method for perturbed second-order cone programs}, JOURNAL = {Comput. Optim. Appl.}, FJOURNAL = {Computational Optimization and Applications. An International Journal}, VOLUME = {37}, YEAR = {2007}, NUMBER = {3}, PAGES = {371--408}, ISSN = {0926-6003}, MRCLASS = {90C55 (90C46)}, MRNUMBER = {2335101}, MRREVIEWER = {Lyudmila N. Polyakova}, URL = {https://doi.org/10.1007/s10589-007-9023-2}, } @article {MR2294050, AUTHOR = {Tsuchiya, Takashi and Xia, Yu}, TITLE = {An extension of the standard polynomial-time primal-dual path-following algorithm to the weighted determinant maximization problem with semidefinite constraints}, JOURNAL = {Pac. J. Optim.}, FJOURNAL = {Pacific Journal of Optimization. An International Journal}, VOLUME = {3}, YEAR = {2007}, NUMBER = {1}, PAGES = {165--182}, ISSN = {1348-9151}, MRCLASS = {90C22 (65K05 90C51 90C60)}, MRNUMBER = {2294050}, MRREVIEWER = {Qingzhi Yang}, } @incollection {MR2029443, AUTHOR = {Alizadeh, F. and Xia, Yu}, TITLE = {The {$Q$} method for the second-order cone programming}, BOOKTITLE = {Topics in applied and theoretical mathematics and computer science}, SERIES = {Math. Comput. Sci. Eng.}, PAGES = {208--213}, PUBLISHER = {WSEAS, Athens}, YEAR = {2001}, MRCLASS = {90C22 (90C51)}, MRNUMBER = {2029443}, } ############################## ###extra for daniela/marcia/fei jan/18 @incollection {gallo, author="Gallo, G. and Hammer, P. L. and Simeone, B.", editor="Padberg, M. W.", title="Quadratic knapsack problems", bookTitle="Combinatorial Optimization", year="1980", publisher="Springer Berlin Heidelberg", address="Berlin, Heidelberg", pages="132--149", abstract="The quadratic knapsack (QK) model naturally arises in a variety of problems in operations research, statistics and combinatorics. Some ``upper planes'' for the QK problem are derived, and their different uses in a branch-and-bound scheme for solving such a problem are discussed. Some theoretical results concerning the class of all upper planes, as well as extensive computational experience, are reported.", isbn="978-3-642-00802-3", doi="10.1007/BFb0120892", url="https://doi.org/10.1007/BFb0120892" } @incollection{Chaillou89, author="Chaillou, P. and Hansen, P. and Mahieu, Y.", editor="Simeone, Bruno", title="Best network flow bounds for the quadratic knapsack problem", bookTitle="Combinatorial Optimization: Lectures given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held at Como, Italy, August 25--September 2, 1986", year="1989", publisher="Springer Berlin Heidelberg", address="Berlin, Heidelberg", pages="225--235", abstract="A Lagrangean relaxation of the quadratic knapsack problem is studied. It is shown, among other properties, that the best value of the Lagrangean multiplier, and hence the best bound for the original problem, can be determined in at most n?1 applications of a maximum flow algorithm to a network with n+2 vertices and n+m arcs, where n and m denote the numbers of variables and of quadratic terms. A branch-and-bound algorithm using this result is presented and computational experience is reported on.", isbn="978-3-540-46810-3", doi="10.1007/BFb0083467", url="https://doi.org/10.1007/BFb0083467" } @article{Billionnet14, title = "Linear programming for the 0-1 quadratic knapsack problem", journal = "European Journal of Operational Research ", volume = "92", number = "2", pages = "310-325", year = "1996", note = "", issn = "0377-2217", doi = "http://dx.doi.org/10.1016/0377-2217(94)00229-0", url = "http://www.sciencedirect.com/science/article/pii/0377221794002290", author = "A. Billionnet and F. Calmels", } @article{Caprara99, author = {A. Caprara and D. Pisinger and P. Toth}, title = {Exact Solution of the Quadratic Knapsack Problem}, journal = {INFORMS Journal on Computing}, volume = {11}, number = {2}, pages = {125-137}, year = {1999}, doi = {10.1287/ijoc.11.2.125}, URL = {http://dx.doi.org/10.1287/ijoc.11.2.125}, eprint = {http://dx.doi.org/10.1287/ijoc.11.2.125} } @article{doi:10.1002/wics.1344, author = {B.A. Turlach and S.J. Wright}, title = {Quadratic programming}, journal = {Wiley Interdisciplinary Reviews: Computational Statistics}, volume = {7}, number = {2}, pages = {153-159}, keywords = {optimization, quadratic programming, interior-point algorithms, conditional-gradient algorithms, active-set methods}, doi = {10.1002/wics.1344}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/wics.1344}, eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/wics.1344}, abstract = {Optimization problems in which a quadratic objective function is optimized subject to linear constraints on the parameters are known as quadratic programming problems (QPs). This focus article reviews algorithms for convex QPs (in which the objective is a convex function) and provides pointers to various online resources about QPs. WIREs Comput Stat 2015, 7:153��?59. doi: 10.1002/wics.1344 This article is categorized under: Algorithms and Computational Methods > Quadratic and Nonlinear Programming} } @article{BillionnetFS99, author = {A. Billionnet and A. Faye and {\'{E}}. Soutif}, title = {A new upper bound for the 0-1 quadratic knapsack problem}, journal = {European Journal of Operational Research}, volume = {112}, number = {3}, pages = {664--672}, year = {1999}, url = {http://dx.doi.org/10.1016/S0377-2217(97)00414-1}, doi = {10.1016/S0377-2217(97)00414-1}, timestamp = {Thu, 06 Jan 2011 10:08:41 +0100}, biburl = {http://dblp2.uni-trier.de/rec/bib/journals/eor/BillionnetFS99}, bibsource = {dblp computer science bibliography, http://dblp.org} } @article{L79, year={1979}, journal={{IEEE} Transactions on Information Theory}, volume={25}, number={1}, title={ On the shannon capacity of a graph}, author={Lov\'asz, L.}, pages={1-7} } @Article{SF02, author="Sherali, H.D. and Fraticelli, Barbara M. P.", title="Enhancing RLT relaxations via a new class of semidefinite cuts", journal="Journal of Global Optimization", year="2002", month="Jan", day="01", volume="22", number="1", pages="233--261", abstract="In this paper, we propose a mechanism to tighten Reformulation-Linearization Technique (RLT) based relaxations for solving nonconvex programming problems by importing concepts from semidefinite programming (SDP), leading to a new class of semidefinite cutting planes. Given an RLT relaxation, the usual nonnegativity restrictions on the matrix of RLT product variables is replaced by a suitable positive semidefinite constraint. Instead of relying on specific SDP solvers, the positive semidefinite stipulation is re-written to develop a semi-infinite linear programming representation of the problem, and an approach is developed that can be implemented using traditional optimization software. Specifically, the infinite set of constraints is relaxed, and members of this set are generated as needed via a separation routine in polynomial time. In essence, this process yields an RLT relaxation that is augmented with valid inequalities, which are themselves classes of RLT constraints that we call semidefinite cuts. These semidefinite cuts comprise a relaxation of the underlying semidefinite constraint. We illustrate this strategy by applying it to the case of optimizing a nonconvex quadratic objective function over a simplex. The algorithm has been implemented in C++, using CPLEX callable routines, and two types of semidefinite restrictions are explored along with several implementation strategies. Several of the most promising lower bounding strategies have been implemented within a branch-and-bound framework. Computational results indicate that the cutting plane algorithm provides a significant tightening of the lower bound obtained by using RLT alone. Moreover, when used within a branch-and-bound framework, the proposed lower bound significantly reduces the effort required to obtain globally optimal solutions.", issn="1573-2916", doi="10.1023/A:1013819515732", url="https://doi.org/10.1023/A:1013819515732" } @article{Pisinger2007, author = {D. Pisinger}, title = "The quadratic knapsack problem, a survey", journal = "Discrete Applied Mathematics", volume = "155", number = "5", pages = "623 - 648", year = "2007", issn = "0166-218X", doi = "https://doi.org/10.1016/j.dam.2006.08.007", url = "http://www.sciencedirect.com/science/article/pii/S0166218X06003878", author = "David Pisinger", keywords = "Quadratic knapsack problem, Upper bounds, Approximation algorithms, Semidefinite programming, Valid inequalities" } @ARTICLE{Witzgall, author = {{Witzgall}, C.}, title = "{Mathematical methods of site selection for Electronic Message Systems (EMS)}", journal = {Technical Report, NBS Internal Report}, keywords = {Messages, Network Synthesis, Systems Engineering, Telecommunication, Cost Analysis, Linear Programming, Radio Relay Systems}, year = 1975, adsurl = {http://adsabs.harvard.edu/abs/1975STIN...7618321W}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } @article{Michelon96, title = "Lagrangean methods for the 0-1 Quadratic Knapsack Problem ", journal = "European Journal of Operational Research ", volume = "92", number = "2", pages = "326 - 341", year = "1996", note = "", issn = "0377-2217", doi = "http://dx.doi.org/10.1016/0377-2217(94)00286-X", url = "http://www.sciencedirect.com/science/article/pii/037722179400286X", author = "P. Michelon and L. Veillieux", keywords = "Nonlinear integer programming", keywords = "Lagrangean methods", keywords = "Branch-and-bound algorithm " } @Article{Cunha2016, author="Cunha, J.O. and Simonetti, L. and Lucena, A.", title="Lagrangian heuristics for the Quadratic Knapsack Problem", journal="Computational Optimization and Applications", year="2016", month="Jan", day="01", volume="63", number="1", pages="97--120", abstract="This paper investigates two Lagrangian heuristics for the Quadratic Knapsack Problem. They originate from distinct linear reformulations of the problem and follow the traditional approach of generating Lagrangian dual bounds and then using their corresponding solutions as an input to a primal heuristic. One Lagrangian heuristic, in particular, is a Non-Delayed Relax-and-Cut algorithm. Accordingly, it differs from the other heuristic in that it dualizes valid inequalities on-the-fly, as they become necessary. The algorithms are computationally compared here with two additional heuristics, taken from the literature. Comparisons being carried out over problem instances up to twice as large as those previously used. Three out of the four algorithms, including the Lagrangian heuristics, are CPU time intensive and typically return very good quality feasible solutions. A certificate of that being given by the equally good Lagrangian dual bounds we generate. Finally, this paper is intended as a contribution towards the investigation of more elaborated heuristics to the problem, an area that has been barely investigated so far.", issn="1573-2894", doi="10.1007/s10589-015-9763-3", url="https://doi.org/10.1007/s10589-015-9763-3" } @Article{Scheiderer2006, author="Scheiderer, C.", title="Sums of squares on real algebraic surfaces", journal="manuscripta mathematica", year="2006", month="April", day="01", volume="119", number="4", pages="395--410", } @inproceedings{permenterparrilo2012, title={Selecting a monomial basis for sums of squares programming over a quotient ring}, author={Permenter, F. and Parrilo, P.A}, booktitle={Decision and Control (CDC), 2012 IEEE 51st Annual Conference on}, pages={1871--1876}, year={2012}, organization={IEEE} } @article {MR3904099, AUTHOR = {Sabach, S. and Teboulle, M. and Voldman, S.}, TITLE = {A smoothing alternating minimization-based algorithm for clustering with sum-min of {E}uclidean norms}, JOURNAL = {Pure Appl. Funct. Anal.}, FJOURNAL = {Pure and Applied Functional Analysis}, VOLUME = {3}, YEAR = {2018}, NUMBER = {4}, PAGES = {653--679}, ISSN = {2189-3756}, MRCLASS = {90C26 (90C56)}, MRNUMBER = {3904099}, MRREVIEWER = {Fusheng Bai}, } @misc{jiang2019recovery, title={Recovery of a mixture of Gaussians by sum-of-norms clustering}, author={J. Tao and S. Vavasis and C.W. Zhai}, year={2019}, eprint={1902.07137}, archivePrefix={arXiv}, primaryClass={cs.LG} } @unpublished {jiangvavasiszhai, title = {Recovery of a mixture of Gaussians by sum-of-norms clustering}, year = {2019}, note = {Arxiv link: http://arxiv.org/abs/1902.07137}, author = {Jiang, T. and Vavasis, S. and Zhai., C. W.} } @article{bolte2014, title={Proximal alternating linearized minimization for nonconvex and nonsmooth problems}, author={Bolte, J. and Sabach, S. and Teboulle, M.}, journal={Mathematical Programming}, volume={146}, number={1-2}, pages={459--494}, year={2014}, publisher={Springer} } ##############################extra from Haesol @article{MR2255515, AUTHOR={Ribando, J.M.}, TITLE={Measuring solid angles beyond dimension three}, JOURNAL={Discrete Comput. Geom.}, FJOURNAL={Discrete \{\&} Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME={36}, YEAR={2006}, NUMBER={3}, PAGES={479--487}, ISSN={0179-5376}, MRCLASS={51M25}, MRNUMBER={2255515}, MRREVIEWER={Beata Randrianantoanina}, DOI={10.1007/s00454-006-1253-4}, URL={http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/s00454-006-1253-4} } @book {MR2317344, AUTHOR = {Aliprantis, C.D. and Tourky, R.}, TITLE = {Cones and duality}, SERIES = {Graduate Studies in Mathematics}, VOLUME = {84}, PUBLISHER = {American Mathematical Society, Providence, RI}, YEAR = {2007}, PAGES = {xiv+279}, ISBN = {978-0-8218-4146-4}, MRCLASS = {46A40 (46B40 46N10 47B60)}, MRNUMBER = {2317344}, MRREVIEWER = {Nicolae Popovici}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1090/gsm/084}, } @book {MR3237726, AUTHOR = {Conforti, M. and Cornu\'ejols, G. and Zambelli, G.}, TITLE = {Integer programming}, SERIES = {Graduate Texts in Mathematics}, VOLUME = {271}, PUBLISHER = {Springer, Cham}, YEAR = {2014}, PAGES = {xii+456}, ISBN = {978-3-319-11007-3; 978-3-319-11008-0}, MRCLASS = {90-01 (90C10)}, MRNUMBER = {3237726}, MRREVIEWER = {Marcin Anholcer}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/978-3-319-11008-0}, } #########################from Fei Wang for singlecell paper 2018 @article{kaparis2010, author = {Kaparis, K. and Letchford, A.}, year = {2010}, month = {07}, pages = {69-91}, title = {Separation Algorithms for 0-1 Knapsack Polytopes}, volume = {124}, booktitle = {Mathematical Programming} } @article {MR4337986, AUTHOR = {Fampa, M. and Lee, J. and Ponte, G. and Xu, L.}, TITLE = {Experimental analysis of local searches for sparse reflexive generalized inverses}, JOURNAL = {J. Global Optim.}, FJOURNAL = {Journal of Global Optimization. An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering}, VOLUME = {81}, YEAR = {2021}, NUMBER = {4}, PAGES = {1057--1093}, ISSN = {0925-5001}, MRCLASS = {15A09 (65F20 65K10)}, MRNUMBER = {4337986}, DOI = {10.1007/s10898-021-01087-y}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10898-021-01087-y}, } @article {MR4284421, AUTHOR = {Xu, L. and Fampa, M. and Lee, J. and Ponte, G.}, TITLE = {Approximate 1-norm minimization and minimum-rank structured sparsity for various generalized inverses via local search}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {31}, YEAR = {2021}, NUMBER = {3}, PAGES = {1722--1747}, ISSN = {1052-6234}, MRCLASS = {90C26 (15A09 65K05 90C25)}, MRNUMBER = {4284421}, DOI = {10.1137/19M1281514}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/19M1281514}, } @article {MR3876787, AUTHOR = {Fampa, M. and Lee, J.}, TITLE = {On sparse reflexive generalized inverse}, JOURNAL = {Oper. Res. Lett.}, FJOURNAL = {Operations Research Letters}, VOLUME = {46}, YEAR = {2018}, NUMBER = {6}, PAGES = {605--610}, ISSN = {0167-6377}, MRCLASS = {15A09 (90C05 90C90)}, MRNUMBER = {3876787}, DOI = {10.1016/j.orl.2018.09.005}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1016/j.orl.2018.09.005}, } @article{Fampa2017, author = {Fampa, M. and Lee, J. and Melo, W.}, year = {2017}, month = {09}, pages = {309-337}, title = {On global optimization with indefinite quadratics}, volume = {5}, number = {3}, journal = {EURO Journal on Computational Optimization} } @article{Horst1999, author = {Horst, R. and Thoai, N.V.l}, year = {1999}, pages = {1-43}, title = {DC Programming: Overview}, volume = {103}, journal = {Journal of Optimization Theory and Applications} } @book{Jolliffe2010, title={Principal component analysis}, author={Jolliffe, I.}, series={2nd ed.}, year={2010}, publisher={Springer, Berlin} } @article{goldfarb2013, title={Fast alternating linearization methods for minimizing the sum of two convex functions}, author={Goldfarb, D. and Ma, S. and Scheinberg, K.}, journal={Mathematical Programming}, volume={141}, number={1-2}, pages={349--382}, year={2013}, publisher={Springer} } @article{xia2016s, title={S-lemma with equality and its applications}, author={Xia, Y. and Wang, S. and Sheu, R.-L.}, journal={Mathematical Programming}, volume={156}, number={1-2}, pages={513--547}, year={2016}, publisher={Springer} } @article {MR3143838, AUTHOR = {Han, D. and Yuan, X.}, TITLE = {Local linear convergence of the alternating direction method of multipliers for quadratic programs}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {51}, YEAR = {2013}, NUMBER = {6}, PAGES = {3446--3457}, ISSN = {0036-1429}, MRCLASS = {90C25 (65K05 90C20)}, MRNUMBER = {3143838}, MRREVIEWER = {D. Klatte}, DOI = {10.1137/120886753}, URL = {https://doi.org/10.1137/120886753}, } @article {MR3801109, AUTHOR = {Han, D. and Sun, D. and Zhang, L.}, TITLE = {Linear rate convergence of the alternating direction method of multipliers for convex composite programming}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {43}, YEAR = {2018}, NUMBER = {2}, PAGES = {622--637}, ISSN = {0364-765X}, MRCLASS = {90C25 (65K05 90C20)}, MRNUMBER = {3801109}, MRREVIEWER = {Gerardo Toraldo}, DOI = {10.1287/moor.2017.0875}, URL = {https://doi.org/10.1287/moor.2017.0875}, } @article {MR3813005, AUTHOR = {He, Y. and Li, H. and Liu, X.}, TITLE = {Relaxed inertial proximal {P}eaceman-{R}achford splitting method for separable convex programming}, JOURNAL = {Front. Math. China}, FJOURNAL = {Frontiers of Mathematics in China}, VOLUME = {13}, YEAR = {2018}, NUMBER = {3}, PAGES = {555--578}, ISSN = {1673-3452}, MRCLASS = {90C25 (90C30)}, MRNUMBER = {3813005}, MRREVIEWER = {Liusheng Hou}, DOI = {10.1007/s11464-018-0706-z}, URL = {https://doi.org/10.1007/s11464-018-0706-z}, } @article {MR3123832, AUTHOR = {Boley, D.}, TITLE = {Local linear convergence of the alternating direction method of multipliers on quadratic or linear programs}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {23}, YEAR = {2013}, NUMBER = {4}, PAGES = {2183--2207}, ISSN = {1052-6234}, MRCLASS = {90C20 (65K05 90C05)}, MRNUMBER = {3123832}, MRREVIEWER = {K. Zimmermann}, DOI = {10.1137/120878951}, URL = {https://doi.org/10.1137/120878951}, } @article {MR3456957, AUTHOR = {Deng, W. and Yin, W.}, TITLE = {On the global and linear convergence of the generalized alternating direction method of multipliers}, JOURNAL = {J. Sci. Comput.}, FJOURNAL = {Journal of Scientific Computing}, VOLUME = {66}, YEAR = {2016}, NUMBER = {3}, PAGES = {889--916}, ISSN = {0885-7474}, MRCLASS = {65K10 (90C30)}, MRNUMBER = {3456957}, MRREVIEWER = {Driss Mentagui}, DOI = {10.1007/s10915-015-0048-x}, URL = {https://doi.org/10.1007/s10915-015-0048-x}, } @article {MR3828857, AUTHOR = {Liu, Y. and Yuan, X. and Zeng, S. and Zhang, J.}, TITLE = {Partial error bound conditions and the linear convergence rate of the alternating direction method of multipliers}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {56}, YEAR = {2018}, NUMBER = {4}, PAGES = {2095--2123}, ISSN = {0036-1429}, MRCLASS = {90C25 (90C22 90C31)}, MRNUMBER = {3828857}, MRREVIEWER = {Xudong Li}, DOI = {10.1137/17M1144623}, URL = {https://doi.org/10.1137/17M1144623}, } @article {MR3472015, AUTHOR = {Yang, W.H. and Han, D.}, TITLE = {Linear convergence of the alternating direction method of multipliers for a class of convex optimization problems}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {54}, YEAR = {2016}, NUMBER = {2}, PAGES = {625--640}, ISSN = {0036-1429}, MRCLASS = {90C25 (65K10)}, MRNUMBER = {3472015}, MRREVIEWER = {Huibin Chang}, DOI = {10.1137/140974237}, URL = {https://doi.org/10.1137/140974237}, } @Article{Qi2014, author="Qi, H.-D. and Yuan, X.", title="Computing the nearest {E}uclidean distance matrix with low embedding dimensions", journal="Mathematical Programming", year="2014", month="Oct", day="01", volume="147", number="1", pages="351--389", } @article{qi2013semismooth, title={A semismooth {N}ewton method for the nearest {E}uclidean distance matrix problem}, author={Qi, H.-D.}, journal={SIAM Journal on Matrix Analysis and Applications}, volume={34}, number={1}, pages={67--93}, year={2013}, publisher={SIAM} } @article{kiraly2015algebraic, title={The algebraic combinatorial approach for low-rank matrix completion}, author={Kir{\'a}ly, F.J. and Theran, L. and Tomioka, R.}, journal={The Journal of Machine Learning Research}, volume={16}, number={1}, pages={1391--1436}, year={2015}, publisher={JMLR. org} } @article{CheungMaSo04, title={Least squares algorithms for time-of-arrival-based mobile location}, author={Cheung, K.W. and So, H.-C. and Ma, W-K and Chan, Y.-T.}, journal={IEEE Transactions on Signal Processing}, volume={52}, number={4}, pages={1121--1130}, year={2004}, publisher={IEEE} } @article{KoshimaHosen00, title={Personal locator services emerge}, author={Koshima, H. and Hoshen, J.}, journal={IEEE spectrum}, volume={37}, number={2}, pages={41--48}, year={2000}, publisher={IEEE} } @article{WarriorMcHenryMcGee03, title={They know where you are [location detection]}, author={Warrior, J. and McHenry, E. and McGee, K.}, journal={IEEE Spectrum}, volume={40}, number={7}, pages={20--25}, year={2003}, publisher={IEEE} } @article{Kundu14, title={Acoustic source localization}, author={Kundu, T.}, journal={Ultrasonics}, volume={54}, number={1}, pages={25--38}, year={2014}, publisher={Elsevier} } @article{borg2003, title={Modern multidimensional scaling: theory and applications}, author={Borg, I. and Groenen, P.}, journal={Journal of Educational Measurement}, volume={40}, number={3}, pages={277--280}, year={2003}, publisher={Wiley Online Library} } @book{cox2000, title={Multidimensional scaling}, author={Cox, T.F and Cox, M.A.}, year={2000}, publisher={Chapman and hall/CRC} } @book{crippen1988, title={Distance geometry and molecular conformation}, author={Crippen, G.M. and Havel, T.F.}, volume={74}, year={1988}, publisher={Research Studies Press Taunton} } @article{fangoleary2012, title={Euclidean distance matrix completion problems}, author={Fang, H. and O'Leary, D.P.}, journal={Optimization Methods and Software}, volume={27}, number={4-5}, pages={695--717}, year={2012}, publisher={Taylor \& Francis} } @book{dattorro2010, title={Convex optimization \& {E}uclidean distance geometry}, author={Dattorro, J.}, year={2010}, publisher={Lulu. com} } @incollection{krislockWolkowicz2012, title={Euclidean distance matrices and applications}, author={Krislock, N. and Wolkowicz, H.}, booktitle={Handbook on semidefinite, conic and polynomial optimization}, pages={879--914}, year={2012}, publisher={Springer} } ###########additions from .haesol.bib @article {MR0062968, AUTHOR = {T. Saaty and S. Gass}, TITLE = {Parametric objective function. {I}}, JOURNAL = {J. Operations Res. Soc. Amer.}, FJOURNAL = {Operational Research Society Journal}, VOLUME = {2}, YEAR = {1954}, PAGES = {316--319}, ISSN = {0160-5682}, MRCLASS = {49.0X}, MRNUMBER = {0062968}, MRREVIEWER = {R. Bellman}, } @article {MR1088985, AUTHOR = {J.E. Ward and R.E. Wendell}, TITLE = {Approaches to sensitivity analysis in linear programming}, JOURNAL = {Ann. Oper. Res.}, FJOURNAL = {Annals of Operations Research}, VOLUME = {27}, YEAR = {1990}, NUMBER = {1-4}, PAGES = {3--38}, ISSN = {0254-5330}, MRCLASS = {90C05 (49K40 90C31)}, MRNUMBER = {1088985}, MRREVIEWER = {Klaus Tammer}, DOI = {10.1007/BF02055188}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/BF02055188}, } @article {MR3836177, AUTHOR = {M.J. Gisbert and M.J. C\'{a}novas and J. Parra and F.J. Toledo}, TITLE = {Calmness of the optimal value in linear programming}, JOURNAL = {SIAM J. Optim.}, FJOURNAL = {SIAM Journal on Optimization}, VOLUME = {28}, YEAR = {2018}, NUMBER = {3}, PAGES = {2201--2221}, ISSN = {1052-6234}, MRCLASS = {90C31 (49J53 49K40 90C05)}, MRNUMBER = {3836177}, DOI = {10.1137/17M112333X}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/17M112333X}, } @book {MR701243, AUTHOR = {B. Bank and J. Guddat and D. Klatte and B. Kummer and K. Tammer}, TITLE = {Nonlinear parametric optimization}, PUBLISHER = {Birkh\"auser Verlag, Basel-Boston, Mass.}, YEAR = {1983}, PAGES = {228}, ISBN = {3-7643-1375-7}, MRCLASS = {90C31 (49-02 90-02 90C30)}, MRNUMBER = {701243}, MRREVIEWER = {Tomas Gal}, } @inproceedings{Jansen1993AnIP, title={An interior point approach to postoptimal and parametric analysis in linear programming Report 92-21}, author={B. Jansen and C. Roos and Tam{\'a}s Terlaky}, year={1993} } @article {MR848532, AUTHOR = {T. Gal}, TITLE = {Shadow prices and sensitivity analysis in linear programming under degeneracy: state-of-the-art survey}, JOURNAL = {OR Spektrum}, FJOURNAL = {OR Spektrum. Quantitative Approaches in Management}, VOLUME = {8}, YEAR = {1986}, NUMBER = {2}, PAGES = {59--71}, ISSN = {0171-6468}, MRCLASS = {90C05 (90A12)}, MRNUMBER = {848532}, DOI = {10.1007/BF01719736}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/BF01719736}, } @article{ARSHAM199079, title = "Perturbation analysis of general LP models: A unified approach to sensitivity, parametric, tolerance, and more-for-less analysis", journal = "Mathematical and Computer Modelling", volume = "13", number = "8", pages = "79 - 102", year = "1990", issn = "0895-7177", doi = "https://doi.org/10.1016/0895-7177(90)90073-V", url = "http://www.sciencedirect.com/science/article/pii/089571779090073V", author = "H. Arsham and M. Oblak" } @book {MR536349, AUTHOR = {G\'al, Tom\'a\v s}, TITLE = {Postoptimal analyses, parametric programming, and related topics}, NOTE = {Translated from the German by Geoffrey V. Davis, With a foreword by H.-J. Zimmermann}, PUBLISHER = {McGraw-Hill International Book Co., New York}, YEAR = {1979}, PAGES = {xx+380}, ISBN = {0-07-022679-2}, MRCLASS = {90C31}, MRNUMBER = {536349}, MRREVIEWER = {Uwe Zimmermann}, } @incollection {MR0081803, AUTHOR = {H.D. Mills}, TITLE = {Marginal values of matrix games and linear programs}, BOOKTITLE = {Linear inequalities and related systems}, SERIES = {Annals of Mathematics Studies, no. 38}, PAGES = {183--193}, PUBLISHER = {Princeton University Press, Princeton, N. J.}, YEAR = {1956}, MRCLASS = {90.0X}, MRNUMBER = {0081803}, MRREVIEWER = {J. Isbell}, } @book {MR2814377, AUTHOR = {B. Simon}, TITLE = {Convexity}, SERIES = {Cambridge Tracts in Mathematics}, VOLUME = {187}, NOTE = {An analytic viewpoint}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {2011}, PAGES = {x+345}, ISBN = {978-1-107-00731-4}, MRCLASS = {46-02 (46A55 46E30 52A01 52A07)}, MRNUMBER = {2814377}, MRREVIEWER = {S. Kutateladze}, DOI = {10.1017/CBO9780511910135}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1017/CBO9780511910135}, } @techreport{DeWolf, AUTHOR = {D. De Wolf and Y. Smeers}, TITLE = {Generalized derivatives of the optimal value of a linear program with respect to matrix coefficients}, institution = "Universite libre de Bruxelles, Belgium and Universite Catholique de Louvain, Belgium", address = "", type = "", number = "", pages = "", year = "2000" } @techreport{Still, AUTHOR = {G. Still}, TITLE = {Lectures on Parametric Optimization: An Introduction}, institution = "University of Twente, Netherlands", address = "", type = "", number = "", pages = "", year = "2018" } @article{10.2307/2490273, ISSN = {00218456, 1475679X}, URL = {http://www.jstor.org/stable/2490273}, author = {J.E. Strum}, journal = {Journal of Accounting Research}, number = {1}, pages = {160--162}, publisher = {[Accounting Research Center, Booth School of Business, University of Chicago, Wiley]}, title = {Note on "Two-Sided Shadow Prices}, volume = {7}, year = {1969} } ###########additions from haoh.bib @article{bhatt1984framework, title={A framework for solving VLSI graph layout problems}, author={Bhatt, S.N. and Leighton, F.T.}, journal={Journal of Computer and System Sciences}, volume={28}, number={2}, pages={300--343}, year={1984}, publisher={Elsevier} } @inproceedings{fu2005multi, title={Multi-directional width-bounded geometric separator and protein folding}, author={Fu, B. and Oprisan, S.A. and Xu, L.}, booktitle={International Symposium on Algorithms and Computation}, pages={995--1006}, year={2005}, organization={Springer} } @inproceedings{clusterpathBachetal:11, title={Clusterpath: An Algorithm for Clustering using Convex Fusion Penalties}, author={Hocking, T.D. and Vert, J-P and Bach, F. and Joulin, A.}, booktitle={28th International Conference on Machine Learning, ICML}, year={2011}, address = {Bellevue, Washington} } @article {MR3610421, AUTHOR = {Chiquet, J. and Gutierrez, P. and Rigaill, G.}, TITLE = {Fast tree inference with weighted fusion penalties}, JOURNAL = {J. Comput. Graph. Statist.}, FJOURNAL = {Journal of Computational and Graphical Statistics}, VOLUME = {26}, YEAR = {2017}, NUMBER = {1}, PAGES = {205--216}, ISSN = {1061-8600}, MRCLASS = {62J07 (62H30 62J10)}, MRNUMBER = {3610421}, DOI = {10.1080/10618600.2015.1096789}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1080/10618600.2015.1096789}, } @book{leighton1983complexity, title={Complexity Issues in VLSI: Optimal Layouts for the Shuffle-Exchange and Other Networks}, author={Leighton, F.T.}, year={1983}, publisher={MIT Press} } @article{miller1998geometric, title={Geometric separators for finite-element meshes}, author={Miller, G.L. and Teng, S.-H. and Thurston, W. and Vavasis, S.A.}, journal={SIAM Journal on Scientific Computing}, volume={19}, number={2}, pages={364--386}, year={1998}, publisher={SIAM} } @article{lipton1980applications, title={Applications of a planar separator theorem}, author={Lipton, R.J. and Tarjan, R.E.}, journal={SIAM journal on computing}, volume={9}, number={3}, pages={615--627}, year={1980}, publisher={SIAM} } @article{lipton1979generalized, title={Generalized nested dissection}, author={Lipton, R.J. and Rose, D.J. and Tarjan, R.E.}, journal={SIAM journal on numerical analysis}, volume={16}, number={2}, pages={346--358}, year={1979}, publisher={SIAM} } @article{helmberg1995spectral, title={A spectral approach to bandwidth and separator problems in graphs}, author={Helmberg, C. and Rendl, F. and Mohar, B. and Poljak, S.}, journal={Linear and Multilinear Algebra}, volume={39}, number={1-2}, pages={73--90}, year={1995}, publisher={Taylor \& Francis} } @article{rendl2018min, title={The min-cut and vertex separator problem}, author={Rendl, F. and Sotirov, R.}, journal={Computational Optimization and Applications}, volume={69}, number={1}, pages={159--187}, year={2018}, publisher={Springer} } @article{condat2016fast, title={Fast projection onto the simplex and the $l_{1}$ ball}, author={Condat, L.}, journal={Mathematical Programming}, volume={158}, number={1-2}, pages={575--585}, year={2016}, publisher={Springer} } @book{truetsch2014semidefinite, title={A semidefinite programming based branch-and-bound framework for the quadratic assignment problem}, author={Truetsch, U.}, year={2014}, publisher={Tilburg University} } @article{de2012improved, title={Improved semidefinite programming bounds for quadratic assignment problems with suitable symmetry}, author={de Klerk, E. and Sotirov, R.}, journal={Mathematical programming}, volume={133}, number={1-2}, pages={75--91}, year={2012}, publisher={Springer} } @article{mittelmann2010estimating, title={Estimating bounds for quadratic assignment problems associated with Hamming and Manhattan distance matrices based on semidefinite programming}, author={Mittelmann, H. and Peng, J.}, journal={SIAM Journal on Optimization}, volume={20}, number={6}, pages={3408--3426}, year={2010}, publisher={SIAM} } @article{sturm2001using, author={Sturm, J.F}, title = {Using {S}e{D}u{M}i 1.02, A {M}atlab toolbox for optimization over symmetric cones}, journal = {Optimization Methods and Software}, volume = {11}, number = {1-4}, pages = {625-653}, year = {1999}, publisher = {Taylor \& Francis}, doi = {10.1080/10556789908805766}, URL = { https://doi.org/10.1080/10556789908805766 }, eprint = { https://doi.org/10.1080/10556789908805766 } } @ARTICLE{Lofberg, author={J. {L\"{o}fberg}}, journal={IEEE Transactions on Automatic Control}, title={Pre- and Post-Processing Sum-of-Squares Programs in Practice}, year={2009}, volume={54}, number={5}, pages={1007-1011}} @inproceedings{lofberg2004yalmip, title={YALMIP: A toolbox for modeling and optimization in MATLAB}, author={L{\"o}fberg, J.}, booktitle={Proceedings of the CACSD Conference}, volume={3}, year={2004}, organization={Taipei, Taiwan} } @article{gatermann2004symmetry, title={Symmetry groups, semidefinite programs, and sums of squares}, author={Gatermann, K. and Parrilo, P.A.}, journal={Journal of Pure and Applied Algebra}, volume={192}, number={1-3}, pages={95--128}, year={2004}, publisher={Elsevier} } @article{gijswijt2010matrix, title={Matrix algebras and semidefinite programming techniques for codes}, author={Gijswijt, D.}, journal={PhD Thesis}, publisher={University of Amsterdam, The Netherlands}, year={2010} } @article{schrijver1979comparison, title={A comparison of the {D}elsarte and {L}ov{\'a}sz bounds}, author={{S}chrijver, A.}, journal={IEEE Transactions on Information Theory}, volume={25}, number={4}, pages={425--429}, year={1979}, publisher={IEEE} } # From Lanlan Mar/2020 @book {MR3242819, AUTHOR = {Mansini, R. and Ogryczak, W. and Speranza, M.G.}, TITLE = {Linear and mixed integer programming for portfolio optimization}, SERIES = {EURO Advanced Tutorials on Operational Research}, PUBLISHER = {Springer, Cham}, YEAR = {2015}, PAGES = {xii+119}, ISBN = {978-3-319-18481-4; 978-3-319-18482-1}, MRCLASS = {91-02 (90C05 90C11 90C90 91B30 91G10)}, MRNUMBER = {3242819}, DOI = {10.1007/978-3-319-18482-1}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/978-3-319-18482-1}, } @ARTICLE{2019PhyA..523.1371D, author = {{Dai}, Z. and {Wang}, F.}, title = "{Sparse and robust mean-variance portfolio optimization problems}", journal = {Physica A Statistical Mechanics and its Applications}, keywords = {Portfolio optimization, Mean-variance portfolio, Regularization, Robust optimization}, year = 2019, month = jun, volume = 523, pages = {1371-1378}, doi = {10.1016/j.physa.2019.04.151}, adsurl = {https://ui.adsabs.harvard.edu/abs/2019PhyA..523.1371D}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } @book {MR3837524, AUTHOR = {Cornu\'{e}jols, G. and Pe\~{n}a, J. and T\"{u}t\"{u}nc\"{u}, R.}, TITLE = {Optimization methods in finance}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {2018}, PAGES = {xii+337}, ISBN = {978-1-107-05674-9}, MRCLASS = {91-01 (90C90 91Gxx)}, MRNUMBER = {3837524}, DOI = {10.1017/9781107297340}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1017/9781107297340}, } @article {MR1702364, AUTHOR = {Ben-Tal, A. and Nemirovski, A.}, TITLE = {Robust solutions of uncertain linear programs}, JOURNAL = {Oper. Res. Lett.}, FJOURNAL = {Operations Research Letters}, VOLUME = {25}, YEAR = {1999}, NUMBER = {1}, PAGES = {1--13}, ISSN = {0167-6377}, MRCLASS = {90C05 (90C31)}, MRNUMBER = {1702364}, DOI = {10.1016/S0167-6377(99)00016-4}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1016/S0167-6377(99)00016-4}, } @article {MR1977752, AUTHOR = {Halld\'{o}rsson, B. V. and T\"{u}t\"{u}nc\"{u}, R. H.}, TITLE = {An interior-point method for a class of saddle-point problems}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {116}, YEAR = {2003}, NUMBER = {3}, PAGES = {559--590}, ISSN = {0022-3239}, MRCLASS = {90C22 (90C20 90C51)}, MRNUMBER = {1977752}, MRREVIEWER = {Shu Zhong Zhang}, DOI = {10.1023/A:1023065319772}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1023/A:1023065319772}, } @book {MR1297120, AUTHOR = {Mangasarian, O.}, TITLE = {Nonlinear programming}, SERIES = {Classics in Applied Mathematics}, VOLUME = {10}, NOTE = {Corrected reprint of the 1969 original}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA}, YEAR = {1994}, PAGES = {xvi+220}, ISBN = {0-89871-341-2}, MRCLASS = {90-02 (49-02 90Cxx)}, MRNUMBER = {1297120}, MRREVIEWER = {A. Ioffe}, DOI = {10.1137/1.9781611971255}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1137/1.9781611971255}, } @incollection {MR1835507, AUTHOR = {Uryasev, S. and Rockafellar, T.}, TITLE = {Conditional value-at-risk: optimization approach}, BOOKTITLE = {Stochastic optimization: algorithms and applications ({G}ainesville, {FL}, 2000)}, SERIES = {Appl. Optim.}, VOLUME = {54}, PAGES = {411--435}, PUBLISHER = {Kluwer Acad. Publ., Dordrecht}, YEAR = {2001}, MRCLASS = {90C15 (91B28)}, MRNUMBER = {1835507}, MRREVIEWER = {G. Pflug}, DOI = {10.1007/978-1-4757-6594-6_17}, URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/978-1-4757-6594-6_17}, } @techreport{crisismarkets:18, Author = {Mahalingam, A. and Coburn, A. and Jung, C.J. and Yeo, J.Z. and Cooper. G. and Evan, T.}, INSTITUTION = {Cambridge Centre for Risk Studies}, address = {University of Cambridge Judge Business School}, Title = {Impacts of Severe Natural Catastrophes on Financial Markets}, Year = {2018}} @article {MR2393721, AUTHOR = {Taleb, N.N.}, TITLE = {Black swans and the domains of statistics}, JOURNAL = {Amer. Statist.}, FJOURNAL = {The American Statistician}, VOLUME = {61}, YEAR = {2007}, NUMBER = {3}, PAGES = {198--200}, ISSN = {0003-1305}, MRCLASS = {Expansion}, MRNUMBER = {2393721}, DOI = {10.1198/000313007X219996}, URL = {https://doi.org/10.1198/000313007X219996}, } @book {MR1796805, AUTHOR = {Nielsen, M.A. and Chuang, I.L.}, TITLE = {Quantum computation and quantum information}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {2000}, PAGES = {xxvi+676}, ISBN = {0-521-63235-8; 0-521-63503-9}, MRCLASS = {81P68 (68-01 68-02 68Q05 81-02)}, MRNUMBER = {1796805}, } @misc{xu2017firstorder, title={First-order methods for constrained convex programming based on linea rized augmented Lagrangian function}, author={Y. Xu}, year={2017}, eprint={1711.08020}, archivePrefix={arXiv}, } @article{winick2017reliable, title={Reliable numerical key rates for quantum key distribution}, author={Winick, A. and L{\"u}tkenhaus, N. and Coles, P.J.}, volume={2}, ISSN={2521-327X}, url={http://dx.doi.org/10.22331/q-2018-07-26-77}, DOI={10.22331/q-2018-07-26-77}, journal={Quantum}, publisher={Verein zur Forderung des Open Access Publizierens in den Quantenwi ssenschaften}, year={2018}, month={Jul}, pages={77} } @article{anonymous:72, author = "Anonymous", title = "A new algorithm for optimization", journal = mprog, volume = 3, number = "", pages = "124--128", year = 1972 }