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on the convergence of mixed integer pattern search algorithmsnew

on the convergence of mixed integer pattern search algorithmsnew

ID：34664196

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页数：18页

时间：2019-03-08

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1、OntheConvergenceofMixedIntegerPatternSearchAlgorithmsCharlesAudetandJ.E.DennisJr.CRPC-TR99785February1999CenterforResearchonParallelComputationRiceUniversity6100SouthMainStreetCRPC-MS41Houston,TX77005SubmittedFebruary1999OntheConvergenceofMixedIntegerPatternSearchAlgorithmsCharlesAud

2、etJ.E.DennisJr.fcharlesa,dennisg@caam.rice.eduRiceUniversityDepartmentofComputationalandAppliedMathematics6100SouthMainStreet-MS134Houston,Texas77005-1892USAFebruary11,1999Abstract:Thede nitionofpatternsearchmethodsforsolvingnonlinearuncon-strainedoptimizationproblemsisgeneralizedher

3、etoincludeintegervariables.Wepresentageneralizedpatternsearchalgorithmthatprovidesanaccumulationpointhavinganullgradientwithrespecttothecontinuousvariableandbeingalocalminimizerwithrespecttothediscretevariables.Thispointisthelimitofasubsequenceofunsuccessfuliterateswhosecorresponding

4、meshsizeparametersconvergetozero.Furthermore,additionalassumptionsensuringthattheseop-timalityconditionsholdforanyaccumulationpoint,notonlyunsuccessfulones,arepresented.KeywordsPatternsearchalgorithm,convergenceanalysis,unconstrainedop-timization,mixedintegerprogramming.Acknowledgmen

5、ts:Workofthe rstauthorwassupportedbyNSERC(NaturalSciencesandEngineeringResearchCouncil)fellowshipPDF-207432-1998andbyCRPC(CenterforResearchonParallelComputing).WorkofthesecondauthorwassupportedbyDOEDE-FG03-95ER25257,AFOSRF49620-98-1-0267,TheBoeingCompany,SandiaLG-4253andCRPCCCR-91200

6、08.11IntroductionTorczon[11]presentedageneralde nitionofanabstractpatternsearchmethod.Theobjec-ntiveofthemethodistominimizeacontinuouslydi erentiablefunctionf:R!Rwithoutanyknowledgeofitsderivative.Torczon[11]showsthatthemethodincludesalgorithmssuchascoordinatesearchwith xedstepsizes,

7、evolutionaryoperationusingfactorialdesign[2],theoriginalpatternsearchalgorithm[7],andthemultidirectionalsearchalgorithm[6].Anachievementof[11]istodevelopgeneralconvergenceresultsforthemethodthatsubsumesalltheothers.Asurveyofderivativefreemethodsforunconstrainedoptimizationcanbefoundi

8、nConn,Schein

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