beginfilecontentsseceqn.sty typeoutDocument Option `seceqn': 13 Apr 89 addtoresetequationsection par addtoresetfiguresection par addtoresettablesection endfilecontents par documentclass[12pt]article usepackageamssymb usepackagefloat par titleNumerical Methods for Optimization par author hrefhttp://orion.math.uwaterloo.ca/ hwolkowi/Henry WolkowiczthanksResearch supported by The Natural Sciences and Engineering Research Council of Canada. Email hwolkowicz@uwaterloo.ca datetoday par newedenvironmentnotebeginquotesmallsf NJH $diamondsuit$ endquote par newedenvironmentnoteMbeginquotesmallsf MFA $clubsuit$ endquote newedenvironmentnoteHbeginquotesmallsf HW $clubsuit$ endquote par newedtheoremnmbrsNumbering[section] newedtheoremdefi[nmbrs]Definition newedtheoremexample[nmbrs]Example newedtheoremprop[nmbrs]Proposition newedtheoremprob[nmbrs]Problem newedtheoremlem[nmbrs]Lemma newedtheoremthm[nmbrs]Theorem newedtheoremcor[nmbrs]Corollary newedtheoremrem[nmbrs]Remark newedtheoremremark[nmbrs]Remark newedtheoremconj[nmbrs]Conjecture newedtheoremalg[nmbrs]Algorithm newedtheoremex[nmbrs]Exercise newedcountercount newedcommandZSmathcal Z_S newedcommandXSmathcal X newedcommandXSumathcal X_u newedcommandXSdmathcal X_d newedcommandXXmathcal X newedcommandSOmathcal S newedcommandSOumathcal S newedcommandSsmathcal S newedcommandEmathcal E newedcommandKKmathcal K newedcommandEEmathcal E newedcommandFFmathcal F newedcommandDDmathcal D newedcommandBBmathcal B newedcommandGGmathcal G newedcommandPPmathcal P newedcommandTTmathcal T newedcommandScmathcal S_C newedcommandShmathcal S_H newedcommandsnnmathcal S_n-1 newedcommandMCbfrm MC newedcommandMCqbfrm MCQP newedcommandMCqqbfrm MCQQ newedcommandMCsdpbfrm MCSDP newedcommandhsH_sigma newedcommandSDPbfrm SDP newedcommandadjrm adj newedcommandtracerm trace newedcommandrankrm rank newedcommandspanlrm span newedcommandtrrm trace newedcommanddomrm dom newedcommanddiagrm diag newedcommandDiagrm Diag newedcommanddDiagrm dDiag newedcommandDdiagrm Ddiag newedcommandconvrm conv newedcommandgaprm gap newedcommandoptvalrm optval newedcommandNucal N newedcommandRnmathcal R^n newedcommandSnmathcal S^n newedcommandRtnmathcal R^scriptsizepmatrixncr 2 newedcommandRtnpmathcal R^scriptsizepmatrixn+1cr 2 newedcommandMnmathcal M^n newedcommandMSmathcal M_S newedcommandNSmathcal N_S newedcommandMSimathcal M_S^-1 newedcommandCpmathcal C newedcommandpmathcal P newedcommandppmathcal P_Sn newedcommandAmathcal A newedcommandFmathcal F newedcommandNmathcal N newedcommandFliftcal F_n newedcommandbeqbeginequation newedcommandbetbegintable newedcommandeeqendequation newedcommandbeqrbegineqnarray newedcommandfa  forall newedcommandreq[1](ref#1) newedcommandsncal S_n newedcommandhncal H_n newedcommandgcal G newedcommandkvecrm vec newedcommandbprnoindentbf Proof. hspace1 em newedcommandQEDhfill  rule[-1pt] 8pt8ptpar medskip    newedcommandeprQED newedcommandMatrm Mat newedcommandoffDiagrm offDiag newedcommandusMatrm us2Mat newedcommandusvecrm us2vec newedcommandsvecrm s2vec newedcommanddsvecrm dsvec newedcommandHmatrm Hmat newedcommandvSmatrm vSmat newedcommandSmatrm S2mat newedcommandsMatrm sMat newedcommandhMatrm hMat newedcommandvsMatrm vsMat newedcommandkmatrm Mat newedcommandsdiagrm sdiag newedcommandKprodotimes newedcommandKcalcal K newedcommandHcalcal H newedcommandtran^t newedcommandCmathbb C newedcommandgesemsucceq newedcommandlesempreceq newedcommandSbarbarS newedcommandQbarbarQ newedcommandTbarbarT newedcommandxbarbarx newedcommandXbarbarX newedcommandrelintrm relint newedcommandncnewcommand nc arrowrm arrow nc Arrowrm Arrow nc BoDiagrm B^0Diag nc bodiagrm b^0diag newedcommandoodiagrm o^0diag newedcommandOoDiagrm O^0Diag nc proofbf Proof. rm nr nc Mmncal M_m,n nc kwqqpQ$^2$P nc kwqqpsQ$^2$Ps par begindocument bibliographystyleplain maketitle begincenter hrefhttp://www.uwaterloo.ca/University of Waterloo
hrefhttp://www.math.uwaterloo.ca/CandO_Dept/homepage.htmlDepartment of Combinatorics & Optimization
Waterloo, Ontario N2L 3G1, Canada
Research Report CORR 2001-??
endcenter par bf Key words: par footnotetext URL for papers: hrefhttp://orion.math.uwaterloo.ca/ hwolkowi/henry/reports/ABSTRACTS.htmlhttp://orion.math.uwaterloo.ca/~ hwolkowi/henry/reports/ABSTRACTS.html par beginabstract endabstract par tableofcontents par sectionIntroduction The theory and methods of optimization are in constant use in branches of e.g. mathematics and engineering. The aim of this course is to assist the student, researcher, and teacher to obtain an understanding of the basic theory and the current state of the art in numerical methods for optimization. The modern era of Optimization (within Operations Research) can be said to have begun with Dantzig's simplex method in 1949. Since then the field has advanced tremendously. In particular, the introduction of interior point methods has dramatically increased the size of problems that can be solved. par This course will begin with an introduction of a general nonlinear program (NLP). We then develop the theory and methods for unconstrained optimization and for solving nonlinear equations. This leads to methods for solving general NLPs and also to special models such as semidefinite programming, SDPs. par No text will be used. However, an excellent reference is the book: Numerical Optimization, by Jorge Nocedal, and Stephen Wright, 1999, Springer Verlag. par sectionBackground beginenumerate item introduce the general NLP model and its properties item outline several applications endenumerate par sectionUncontrained Minimization beginenumerate item optimality conditions item Algorithms beginenumerate item line search methods: least change secant methods item trust region methods endenumerate endenumerate par sectionContrained Minimization Theory beginenumerate item optimality conditions item duality item algorithms beginenumerate item interior point methods item Sequential Quadratic Programming (SQP) methods endenumerate endenumerate par sectionSpecial Models beginenumerate item Semidefinite Programming and applications endenumerate par bibliography.master,.psd,.publs par enddocument