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1、RobustOptimizationbyMelvynSimB.Eng,ElectricalEngineering,NationalUniverityofSingapore(1995)M.Eng,ElectricalEngineering,NationalUniverityofSingapore(1996)S.M,HPCES,Singapore-MIT-Alliance(2000)SubmittedtotheSloanSchoolofManagementinpartialful¯llmentoftherequirementsforthedegreeofD
2、octorofPhilosophyinOperationsResearchattheMASSACHUSETTSINSTITUTEOFTECHNOLOGYJune2004°cMassachusettsInstituteofTechnology2004.Allrightsreserved.Author..............................................................SloanSchoolofManagementMay14,2004Certi¯edby.........................
3、.................................DimitrisJ.BertsimasBoeingProfessorofOperationsResearchSloanSchoolofManagementThesisSupervisorAcceptedby.........................................................JamesB.OrlinEdwardPennellBrooksProfessorofOperationsResearchCo-Director,OperationsRese
4、archCenter2RobustOptimizationbyMelvynSimSubmittedtotheSloanSchoolofManagementonMay14,2004,inpartialful¯llmentoftherequirementsforthedegreeofDoctorofPhilosophyinOperationsResearchAbstractWeproposenewmethodologiesinrobustoptimizationthatpromisegreatertractabil-ity,boththeoreticall
5、yandpracticallythantheclassicalrobustframework.Wecoverabroadrangeofmathematicaloptimizationproblems,includinglinearoptimization(LP),quadraticconstrainedquadraticoptimization(QCQP),generalconicoptimiza-tionincludingsecondorderconeprogramming(SOCP)andsemide¯niteoptimization(SDP),m
6、ixedintegeroptimization(MIP),network°owsand0¡1discreteoptimiza-tion.Ourapproachallowsthemodelertovarythelevelofconservatismoftherobustsolutionsintermsofprobabilisticboundsofconstraintviolations,whilekeepingtheproblemtractable.Speci¯cally,forLP,MIP,SOCP,SDP,ourapproachesretainthe
7、samecomplexityclassastheoriginalmodel.TherobustQCQPbecomesaSOCP,whichiscomputationallyasattractiveasthenominalproblem.Innetwork°ows,weproposeanalgorithmforsolvingtherobustminimumcost°owprobleminpolynomialnumberofnominalminimumcost°owproblemsinamodi¯ednetwork.For0¡1discreteoptimi
8、zationproblemwithcostuncertainty,therobustcount
