# 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
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TYPE = "Technical Report",
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URL = "https://doi.org/10.1155/2013/304628",
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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."
}
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abstract="The DC programming and its DC algorithm (DCA) address the problem of minimizing a function f=gâˆ’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"
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International
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%CCCCCCC
@ARTICLE{2018arXiv180609222C,
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}
@book {MR2294029,
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SERIES = {Mathematics, Finance and Risk},
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YEAR = {2007},
PAGES = {xii+345},
ISBN = {978-0-521-86170-0},
MRCLASS = {91-01 (90C90 91B28)},
MRNUMBER = {2294029},
}
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institution = "Department of Computer Science, Cornell University",
year = "1982",
number = "TR 82-509",
address = "Ithaca, NY"}
@MISC {ColFen:85,
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institution = "Faculty of Mathematics, University of Waterloo",
year = "1987",
number = "CORR 87-89"}
@TECHREPORT {ColLi:87b,
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institution = "Department of Computer Science, Cornell University",
year = "1987",
number = "CS-87-812",
address = "Ithaca, NY"}
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YEAR = {1996},
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DOI = {10.1137/S1052623494240456},
URL = {http://dx.doi.org/10.1137/S1052623494240456},
}
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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},
}
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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
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institution = "Department of Computer Science, Cornell University",
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address = "Ithaca, NY"}
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TYPE = "Report",
INSTITUTION = "Dept.\ of Computer Science, Cornell University",
YEAR = "1998",
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@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)},
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VOLUME = {22},
YEAR = {2000},
NUMBER = {1},
PAGES = {243--262 (electronic)},
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MRCLASS = {90C25 (65K10)},
MRNUMBER = {MR1769494 (2001c:90053)},
MRREVIEWER = {Shu Zhong Zhang},
}
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author = "David A. Cox and John B. Little and Don O'Shea",
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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",
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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,
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FJOURNAL = {Mathematical Programming},
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URL = {http://dx.doi.org/10.1007/s10107-009-0286-5},
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@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},
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YEAR = {2010},
NUMBER = {1},
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ISSN = {0022-247X},
CODEN = {JMANAK},
MRCLASS = {15A09},
MRNUMBER = {2567299 (2010i:15007)},
MRREVIEWER = {Gustavo Corach},
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year = 2018,
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@ARTICLE{2016arXiv160201886F,
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title = "{Variational Perspective on Local Graph Clustering}",
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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}
}
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%GGGGGGGGGG
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author = "E.G. GOL{'}STEIN",
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journal = "Mathematical Programming Studies",
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pages = "67-81"
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MRCLASS = {65F15},
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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",
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least squares problems whose variables separate",
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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,
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YEAR = "1991",
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}
@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"
}
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year = "1981"}
@book {MR98g:90003,
TITLE = {Advances in sensitivity analysis and parametric
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EDITOR = {Gal, Tomas and Greenberg, Harvey J.},
PUBLISHER = {Kluwer Academic Publishers},
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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",
}
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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.},
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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
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TYPE = "TR/PA/00/56",
address = "Toulouse Cedex 1, France",
institution = "CERFACS",
YEAR = "2001",
}
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author = "W. GRAEUB",
title = "Die Grundelhren der Mathematischen Wissenschaften",
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year = "1947 - uncertain",
volume = "47 - uncertain",
pages = "158-163"}
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journal = "Math. Comp.",
year = "1970",
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@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)},
}
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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"}
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author = "A.O. Griewank and Ph.L. Toint",
title = "Partitioned variable metric updates for large sparse
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journal = "Numer. Math.",
year = "1982",
volume = "39",
pages = "37-119"}
@ARTICLE {GrTo:82b,
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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"}
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PUBLISHER = {Interscience Publishers John Wiley \& Sons, Inc., New York},
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MRNUMBER = {37 #2085},
MRREVR = {G. T. Sallee},
}
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title = "A divide-and-conquer algorithm for the symmetric
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institution = "Department of Computer Science, Yale University",
year = "1994",
number = "RR-932"}
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MRCLASS = {90.58},
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}
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}
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}
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AUTHOR = {GRAVER, J.E. and SERVATIUS, B. and SERVATIUS, H.},
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YEAR = {1994},
MRCLASS = {05B35 (05C10)},
MRNUMBER = {MR1310581 (95j:05064)},
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}
@book {MR1251062,
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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",
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Full Rank Linear Least Squares Residuals},
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address = "California",
note = {arXiv:1003.2737v3},
year = "2010"}
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@article{doi:10.1137/13090849X,
author = {He, B. and Liu, H. and Wang, Z. and Yuan, X.},
title = {A Strictly Contractive Peaceman--Rachford 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 Peaceman-Rachford 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
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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,
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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"}
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YEAR = {1993},
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MRCLASS = {90C05 (90-02)},
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}
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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},
}
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URL =
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%HHHHHHHH
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@book {MR14:474f,
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NUMBER = {},
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YEAR = {2005},
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ISBN = {0-89871-578-4},
MRCLASS = {65-00 (00A20)},
MRNUMBER = {2135945},
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@book {MR1927606,
AUTHOR = {Higham, N.J.},
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YEAR = {2002},
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ISBN = {0-89871-521-0},
MRCLASS = {65G50 (65-02)},
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AUTHOR = {Higham, Desmond J. and Higham, N.J.},
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YEAR = {2000},
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ISBN = {0-89871-469-9},
MRCLASS = {65-04 (00A20)},
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AUTHOR = {Higham, N.J.},
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PAGES = {xxviii+688},
ISBN = {0-89871-355-2},
MRCLASS = {65G05 (65-02 65F05)},
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author = "N.J. Higham",
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year = "2008",
pages = "xx+425",
isbn = "978-0-898716-46-7"
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@book {Higbook:93,
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@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"
}
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NUMBER = {2},
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MRCLASS = {65F15},
MRNUMBER = {2002i:65039},
MRREVIEWER = {David Scott Watkins},
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ISSN = {0272-4979},
CODEN = {IJNADN},
MRCLASS = {65F30},
MRNUMBER = {98e:65036},
}
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@techreport{BorweinJuly:16,
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title = "Generalizations, examples and counter-examples in analysis
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institution = "CARMA, University of Newcastle",
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number = "In honour of Michel Thera at 70"
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URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/BF02418571},
}
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JOURNAL = {Acta Math.},
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@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}
}
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title = {Alternative Theorems for Quadratic Inequality Systems and
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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}
}
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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}
}
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URL =
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}
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%KKKKKKKKKKKK
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BOOKTITLE = {The {G}ohberg anniversary collection, {V}ol.\ {I}
({C}algary,
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Structure
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pages = "185--211",
kwds = "nla, geig, Kronecker form, reducing subspace, matrix pencil"
}
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}
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AUTHOR = {KANTOROVICH, L.V. and AKILOV, G.P.},
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EDITION = {Second},
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PAGES = {xiv+589},
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MRCLASS = {46-01 (47-01 65-01)},
MRNUMBER = {83h:46002},
}
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year = "1986",
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}
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institution = "Department of Mathematics, North Carolina
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year = "1985"}
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MRCLASS = {65J15 (47H17)},
MRNUMBER = {1643348},
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author="Lewis, A.S.
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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"
}
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MRNUMBER = {3097282},
MRREVIEWER = {Russell Luke},
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URL = {https://doi-org.proxy.lib.uwaterloo.ca/10.1007/s10107-012-0514-2},
}
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Seeking
Global Optima and Their Applications in Science,
Management
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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}
}
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%MMMMMMMMMMMM
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%NNNNNNNNNNNNNNNNNNNNN
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title = {Nikkei 225 (\^N225)},
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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",
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institution = "Department of Electrical Engineering and
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AUTHOR = {Nocedal, Jorge},
TITLE = {Large scale unconstrained optimization},
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MRNUMBER = {MR1628351 (99b:90003)},
}
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%OOOOO
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}
@article {MR3911718,
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JOURNAL = {SIAM J. Matrix Anal. Appl.},
FJOURNAL = {SIAM Journal on Matrix Analysis and Applications},
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YEAR = {2019},
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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},
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ISSN = {0036-1445},
MRCLASS = {00A17},
MRNUMBER = {3806606},
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JOURNAL = {SIAM J. Optim.},
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AUTHOR = {Orban, Dominique and Arioli, Mario},
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SERIES = {SIAM Spotlights},
VOLUME = {3},
PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM),
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YEAR = {2017},
PAGES = {xiv+93},
ISBN = {978-1-611974-72-0},
MRCLASS = {65F10 (15A06)},
MRNUMBER = {3660695},
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}
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JOURNAL = {Optim. Eng.},
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Journal to Promote Optimization Theory \& Applications in
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@incollection {MR3446845,
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BOOKTITLE = {Numerical analysis and optimization},
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YEAR = {2015},
MRCLASS = {90C51 (65K05 90C26)},
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}
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JOURNAL = {Numer. Algorithms},
FJOURNAL = {Numerical Algorithms},
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YEAR = {2015},
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}
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Arnold and Orban, Dominique and Schichl, Hermann},
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YEAR = {2010},
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MRCLASS = {90-04 (90C30)},
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MRCLASS = {90C05},
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DOI = {10.1016/j.cor.2009.03.020},
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[download]
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}
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%PPPPPPPPPPPPP
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type = "DAMTP Report",
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%QQQQQQQQQQQQQQQ
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%TTTTTTTTTTTTTTTTTTTT
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address = "to appear"
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%%%%%%%%%%%%%colourful papers - colourful simplex e.g. by Deza et al
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%end colourful simplices
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%UUUUUUUUUUUUUU
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%VVVVVVVVV
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AUTHOR = {Vavasis, S.A. and Ye, Y.},
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VOLUME = {62},
YEAR = {1996},
PAGES = {565--572},
ISSN = {0254-5330},
MRCLASS = {90C05},
MRNUMBER = {96m:90036},
}
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AUTHOR = {Vavasis, S.A. and Ye, Y.},
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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
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institution = "Department of Computer Science,
Cornell University",
year = "1990",
address = "Ithaca, NY"}
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AUTHOR = "VENKATAKRISHNAN, V. and SIMON, H. and BARTH, T.",
TITLE = "A MIMD Implementation of A Parallel Euler
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@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"
}
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{$\frac{n}{2}$}-{DIRECTED}-{BISECTION} and {MAX}
{$\frac{n}{2}$}-{DENSE}-{SUBGRAPH}},
JOURNAL = {J. Global Optim.},
FJOURNAL = {Journal of Global Optimization. An International Journal
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Global Optima and Their Applications in Science,
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}
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(Aalborg, 1998)},
SERIES = {Lecture Notes in Comput. Sci.},
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MRCLASS = {68R10 (05C85 68Q25)},
MRNUMBER = {MR1465947 (98g:68120)},
}
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% WWWWWWWWWWWWWW
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month = jun,
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adsnote = {Provided by the SAO/NASA Astrophysics Data System}
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%XXXXXXXXXXXXXXXXXXXXXXXXXXX
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primaryClass = "math.OC",
keywords = {Mathematics - Optimization and Control},
year = 2015,
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%YYYYYYYYYYYYYYY
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institution = "Department of Applied Mathematics and Theoretical
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title = "Some properties of trust region algorithms for
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institution = "Department of Applied Mathematics and Theoretical
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year = "1983",
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institution = "Department of Applied Mathematics and Theoretical
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%ZZZZZZZZZZZZZ
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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"
}
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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{kn:hanson,
author = "C.L. Lawson and R.J. Hanson",
year = 1974,
title = { Solving Least Square Problems},
publisher = " Prentice-Hall"
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@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",
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title = { Minimax Solution of Nonlinear Equations Without Calculating
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}
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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"
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year = 1949,
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@article{kn:gm2,
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year = 1979,
title = { Steplength Algorithms for Minimizing a Class of Nondifferentiable
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@article{kn:water,
author = "W. MURRAY and M.H. Wright",
year = 1982,
title = {Computation of the Search Direction
in Constrained Optimization Algorithms},
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volume = 16,
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@article{kn:nocedal,
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year = 1985,
title = { Projected {H}essian Updating Algorithms
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@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.",
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pages = " 63-68 "
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author = "M. R. Osborne and G. A. Watson",
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title = {A Note on Singular Minimax Approximation Problem},
journal = "J. Math. Anal. and Appl.",
volume = 25,
pages = "692-709"
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@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},
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year = 1964,
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{Tchebyshev} Approximation},
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@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},
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organization= " math. research center",
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@book{kn:val,
author = "S. Vajda",
year = 1961,
title = mprog,
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@article{kn:bdmd,
author = "J. W. Bandler and P. A. McDobald",
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year = 1976,
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Equations},
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author = "R. S. Womersley and R. Fletcher",
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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},
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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",
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volume = 11,
year = 1963,
pages = "205-211"
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@article{ro,
author = "D. M. Ryan and M. R. Osborne",
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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},
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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",
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#%%% from F. Jarre - end
# some from Serge
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@incollection {MR1482247,
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MRCLASS = {90C25 (52A41)},
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}
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MRCLASS = {90C33},
MRNUMBER = {99i:90098},
MRREVR = {Siegfried Schaible},
}
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author = "Stephen K. Park and Keith W. Miller",
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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.",
}
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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).",
}
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pages = "850--864",
volume = "13",
note = "This paper introduces the notion of cryptographically
secure pseudo-random number generator.",
}
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pages = "105--110",
month = jul,
year = "1993",
keywords = "random number generator, RNG, pseudo PRNG",
abstract = "via enews",
}
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MRCLASS = {15A09},
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@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"}
@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},
}
@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, Heinz H. and Combettes, Patrick 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},
}
#################################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,
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volume = {117},
year = {1995}
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@phdthesis{Kingsford:2005:CAP:1123937,
author = {Kingsford, C.L.},
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title = {Computational approaches to problems in protein structure and function},
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school = {Princeton University},
address = {Princeton, NJ, USA},
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#####################added by Dima march/2014
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@article{MR3062007,
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%%%%%%%%%%%%%%%%%%%%%quantum references CK Li et al
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#######################added paper by Greg Reid 2014
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AUTHOR = {Bates, Daniel J. and Hauenstein, Jonathan D. and Sommese,
Andrew J. and Wampler, Charles W.},
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YEAR = {2013},
PAGES = {xx+352},
ISBN = {978-1-611972-69-6},
MRCLASS = {13-04 (13P15 65D99 68W30)},
MRNUMBER = {3155500},
MRREVIEWER = {Jan M. Verschelde},
}
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title={The Numerical solution of systems of polynomials arising in
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PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM),
Philadelphia, PA; Mathematical Optimization Society,
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YEAR = {2013},
PAGES = {xx+476},
ISBN = {978-1-611972-28-3},
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PUBLISHER = {American Mathematical Society, Providence, RI},
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NUMBER = {3},
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MRNUMBER = {2014037},
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@book {MR3059590,
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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},
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URL =
{http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1007/978-1-4614-5128-0},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Haesol entries
@article{MR3421846,
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VOLUME={489},
YEAR={2016},
PAGES={199--216},
ISSN={0024-3795},
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MRNUMBER={3421846},
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}
@article{MR2169053,
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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},
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}
@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},
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}
@book{MR2472514,
AUTHOR={Griva, I. and Nash, S.G. and Sofer, A.},
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EDITION={Second},
PUBLISHER={Society for Industrial and Applied Mathematics (SIAM), Philadelphia,
PA},
YEAR={2009},
PAGES={xxii+742},
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MRCLASS={90-01 (90Bxx 90Cxx)},
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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"}
}
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journal={ms},
volume={"9"},
year={"1963"}
}
@conference{copyBalMaz80,
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organization={"TIMS/ORSA"},
address={"{Washington D.c.}"},
month={"May"}
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@book{copyBrRy:91,
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@inproceedings{copyipps97.qap,
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Perregaard"},
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Parallel"},
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pages={"418--427"}
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@book{MR2546839,
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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},
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URL={http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1515/9781400831050}
}
@article{MR2853227,
AUTHOR={Desario, D. and Robins, S.},
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VOLUME={62},
YEAR={2011},
NUMBER={4},
PAGES={1003--1015},
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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 â‰?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
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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},
}
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AUTHOR = {Gauvin, Jacques},
TITLE = {Formulae for the sensitivity analysis of linear programming
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YEAR = {2001},
MRCLASS = {90C31 (90C05)},
MRNUMBER = {1842881},
}
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AUTHOR={Gray, A. and Abbena, E. and Salamon, S.},
TITLE={Modern differential geometry of curves and surfaces with {M}athematica{$^\circledR$}},
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EDITION={Third},
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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}
}
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YEAR={2004},
NUMBER={1},
PAGES={Article 14, 21},
ISSN={1443-5756},
MRCLASS={90C22 (15A39 90C53)},
MRNUMBER={2048490}
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and polyhedra},
NOTE={ACM Symposium on Computational Geometry (North Conway, NH, 1991)},
JOURNAL={Discrete Comput. Geom.},
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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},
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}
@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},
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ISSN = {1052-6234},
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}
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VOLUME = {18},
YEAR = {2009},
NUMBER = {2},
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}
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}
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PAGES = {371--408},
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VOLUME = {3},
YEAR = {2007},
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}
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AUTHOR = {Alizadeh, F. and Xia, Yu},
TITLE = {The {$Q$} method for the second-order cone programming},
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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, 7:153â€?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"
}
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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",
}
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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}
}
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YEAR = {2018},
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PAGES = {653--679},
ISSN = {2189-3756},
MRCLASS = {90C26 (90C56)},
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MRREVIEWER = {Fusheng Bai},
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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},
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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.}
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nonsmooth problems},
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volume={146},
number={1-2},
pages={459--494},
year={2014},
publisher={Springer}
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##############################extra from Haesol
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AUTHOR={Ribando, J.M.},
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Journal of
Mathematics and Computer Science},
VOLUME={36},
YEAR={2006},
NUMBER={3},
PAGES={479--487},
ISSN={0179-5376},
MRCLASS={51M25},
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MRREVIEWER={Beata Randrianantoanina},
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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},
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@book {MR3237726,
AUTHOR = {Conforti, M. and Cornu\'ejols, G. and Zambelli,
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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},
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#########################from Fei Wang for singlecell paper 2018
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