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ID:40081682
大小:586.94 KB
页数:43页
时间:2019-07-20
《Introduction to Global Optimization》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、IntroductiontoGlobalOptimizationLeoLibertiLIX,EcolePolytechnique,PalaiseauF-91128,France´(liberti@lix.polytechnique.fr)February15,2008AbstractAccuratemodellingofreal-worldproblemsoftenrequiresnonconvextermstobeintroducedinthemodel,eitherintheobjectivefunctionorintheconstraints.Nonconvexpr
2、ogrammingisoneofthehardestfieldsofoptimization,presentingmanychallengesinbothpracticalandtheoreticalaspects.Thepresenceofmultiplelocalminimacallsfortheapplicationofglobaloptimizationtechniques.Thispaperisamini-courseaboutglobaloptimizationtechniquesinnonconvexprogramming;itdealswithsomethe
3、oreticalaspectsofnonlinearprogrammingaswellaswithsomeofthecurrentstate-of-the-artalgorithmsinglobaloptimization.Thesyllabusisasfollows.SomeexamplesofNonlinearProgrammingProblems(NLPs).Generaldescriptionoftwo-phasealgorithms.LocaloptimizationofNLPs:derivationofKKTconditions.Shortnotesabout
4、stochasticglobalmultistartalgorithmswithaconcreteexample(SobolOpt).In-depthstudyofadeterministicspatialBranch-and-Boundalgorithm,andconvexrelaxationofanNLP.Latestadvancesinbilinearprogramming:thetheoryofreductionconstraints.Contents1Introduction21.1Scopeofthispaper........................
5、................31.2ExampleswhichrequireGlobalOptimization.........................41.3Abriefhistoryofglobaloptimization..............................62ThestructureofGlobalOptimizationAlgorithms82.1Stochasticglobalphase......................................92.2Deterministicglobalphase....
6、................................112.2.1Fathoming........................................132.3ExampleofsolutionbyBranch-and-Select...........................133LocalOptimizationofNLPs163.1Fundamentalnotionsofconvexanalysis............................163.2Necessaryandsufficientconditionsforlo
7、caloptimality....................183.3Alocaloptimizationalgorithm:SQP..............................241INTRODUCTION24TheSobolOptalgorithm255ThespatialBranch-and-Boundalgorithm275.1Boundstightening........................................285.1.1Optimization-basedbounds
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