多目标半定规划的不可行内点算法

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1、上海交通大学硕士学位论文多目标半定规划的不可行内点算法姓名：王文庆申请学位级别：硕士专业：基础数学指导教师：王晓敏20070124k)w3k1(>oq[b["uf7U{Æ,v2
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5、t10'=npb)B?IAbstractTheinfeasibleinteriorpointalgorithmformultiobjectivesemidefiniteprogrammingAbstractSemidefiniteprogrammingisanextensionoflinearprogramming.Inrecentyears,theresearchforsemidefiniteprogramminghasarapiddevelopmentforalotofpractica

6、lrequirements.However,inourdailylife,multiobjectiveprogrammingproblemisveryfa-miliar.Itmainlyfocusesontheproblemswithcertainconditionsunderwhichmultiplenumericobjectivefunctionsarriveatoptimizationresultssynchronously.Multiobjec-tivesemidefiniteprogram

7、mingcombinemultiobjectiveprogrammingwithsemidefiniteprogramming.Ithasawideapplicationinmanyfieldssuchascombinatorialoptimiza-tion,financeandelectricalengineering.SoitisverysignificativetogiveanefficientalgorithmtosolveMultiobjectivesemidefiniteprogrammingpro

8、blem.Therearefourchaptersinthispaper.Thefirstchapteristheintroductionofthispaperwhichincludethehistoryandcontentsofmultiobjectiveprogrammingandsemidefiniteprogramming.Inthesecondone,weintroducesomeconceptionsandtrans-formationsaboutthematrix,andanalyzet

9、hetheoryfoundationofinterior-pointal-gorithmforsemidefiniteprogramming.Inthethirdchapter,wepresentaninfeasibleinteriorpointalgorithmforsemidefiniteprogramming,andprovethatthealgorithmisconvergent.Inthelastchapter,basedontheinfeasibleinteriorpointalgorit

10、hmforsemidefiniteprogramming,Weestablishaninfeasibleinteriorpointalgorithmformul-tiobjectivesemidefiniteprogramming,andgetaneffcientsolutioncorrespondingtoagivenweightingvector.Basedonthisoriginaleffcientsolution,wecangetnewefficientsolutionscorresp