一类非光滑优化问题的最优性与对偶new

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1、万方数据2010年6月June，2010运筹学学报0RTRANSACTIONSOptimalityandDualityforaClassofNonsmoothOptimizationProblems+ZhaoKequanl十TangLipin91YangXinminl第14卷第2期V61．14No．2AbstractInthispaper，aclassofnonsmoothmultiobjectiveoptimizationprob-lemsinwhichinvolvedequalityconstraintsandinequalityconstraintsisconsidered．Th

2、egeneralizedKarush-Kuhn-Tuckernecessaryandsufficientoptimalityconditionsaregiven．Furthermore，mixedtypedualmodelisdiscussed，andtheoremsofweakduality,strongduality,converseduality，strictconversedualityandrestrictedconversedualityarepre-sented．KeywordsOperationsresearch，B—p，r)·invexity,optimality,d

3、uality,nonsmoothmultiobjectiveoptimizationSubjectClassification(GB／T13745-92)110．74一类非光滑优化问题的最优性与对偶赵克全1t唐莉萍1杨新民，摘要本文研究了一类带等式和不等式约束的非光滑多目标优化问题，给出了该类问题的Karush．Kuhn—Tucker最优性必要条件和充分条件，建立了该类规划问题的一类混合对偶模型的弱对偶定理、强对偶定理、逆对偶定理、严格逆对偶定理和限制逆对偶定理．关键词运筹学，B—p，r)一不变凸性，最优性，对偶，非光滑多目标优化学科分类号(GB／T13745-92)110．741In

4、troductionandpreliminariesInrecentyears，Nonsmoothanalysishasbeenbecomeanimportantresearchaspectinmathematicalprogrammingandoptimizationtheory(see[1】)．Someconceptsofgeneral-izedconvexityweregeneralizedtothenonsmoothcaseandsomenonsmoothoptimizationproblemswerestudied(see[2—5】)．JabarootianandZafara

5、niintroducetheconceptofnon-differentiableinvexfunctionin【2]．Jeyakumardefinedgeneralizedinvexityfornonsmoothscalar-valuedfunctions，establishedanequivalenceofsaddlepointsandoptimaandstudied收稿日期：2009年12月21日．4ThisworkispartiallysupposedbytheNationalNaturalScienceFoundationofChina(10771228)，Researchg

6、rantofEducationCommitteeofChongqing(KJ090812)andResearchgrantofChongqingNormalUniversity(08XLQ01)．1．DepartmentofMathematicsandComputerSciences，ChongqingNormalUniversity,Chongqing400047，China；重庆师范大学数学与计算机科学学院，重庆，400047．tCorrespondingauthor通讯作者万方数据ZhaoKequan，TangLiping，YangXinmin14卷dualityresultsf

7、ornonsmoothoptimizationproblemin[3]．Kauleta1．establishedoptimal-ityanddualityresultsinnondifferentiablemathematicalprogrammingproblemsinvolvingLipschitzfunctionsundergeneralizedinvexityassumptionsin[4】．AntczakintroducedLip-s