一致不变凸多目标规划的有效性条件和对偶性

《一致不变凸多目标规划的有效性条件和对偶性》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、2009年3月运筹学学报第13卷第1期March，20090RTRANSACTIONSVlo1．13No．1TheEficiencyConditionsandDualityforUniformInvexMultiobjectiveProgramLiangZhi’anZhangZhenhuaAbstractInthispaper．theauthorintroducesauniforminvexityconceptformulti—objectiveprogramwhichsynthesizestheinv

2、exityoffunctionsinvolvedinprogram，insteadofusingtheinvexityofeverysinglefunction．Themultiobjectiveprogramwithsuchfunc·tionsiSconsideredandemciencyconditionsandMond．Weirdualmode1areinvestigated．KeywordsOperationsresearch，multiobjectiveprogram，generalizedc

3、onvexity，Mond-Weirtypedualmode1．SubiectClassification(GB／W13745．92)I10．74一致不变凸多目标规划的有效性条件和对偶性梁治安-张振华2摘要作者对多目标规划引进一致不变凸的概念，用来综合规划所涉及函数的不变凸性，而不是用单个函数的不变凸性．考虑了涉及这样函数的多目标规划解的有效性和Mond．Weir对偶性．关键词运筹学，多目标规划，广义凸性，Mond—Weir型对偶模型学科分类号(GB／T13745—92)110．741Introduct

4、ionHansonintroducedtheconceptofinvexityinhispaper[1]．Hepointedoutthatforadiferentiableconvexfunction()definedonanopensetXinR，the~llowinginequalityholds(1)一(2)≥(2)T5l—2)foranyXl，52∈XItinvolvesalinearmap(X，X2)_÷—X2atpointX2fromX×XtoR．Hefoundthatinallproofs

5、oftheresultsrelatedthismapseemsnotplaythekeyrole．Therefore，hereplaceditbyapossiblenonlinearmap叼(，X2)from×XtoR．Thenhegavethe~llowing收稿日期：2007年l2月21日．TheresearchissupportedbytheCultivationFundoftheKeyScientificandTechnicalInnovationProject，MinistrvofEducat

6、ionofChina(NO708040)，NationalNaturalScienceFoundationofChinaunderProject10601030andLeadingAcademicDisciplineProgram，the10thfiveyearplanof211ProjectforShanghaiUniversityofFinanceandEconomics．1．DepartmentofAppliedMathematics，ShanghaiUniversityofFinanceandE

7、conomics，Shanghai200433，China；上海财经大学应用数学系，上海，2004332．SchoolofFinance．ShanghaiUniversityofFinanceandEconomics；上海财经大学金融学院，上海，2004331期TheEficiencyConditionsandDualityforUniformInvexMultiobjectiveProgram45concept：(1)一(2)≥V(2)T叼(1，2)forall1，2∈Xwhere卵：X×_Risam

8、ap．Healsogavetheconceptsofpseudo-invexityandquasi．invexity．Hereafter．HansonandMond[2JintroducedtheconceptsofI-typeandII—typeinvexity．RuedaandHanson[。Jgeneralizedtheseconceptstobepseudo—I—typeandquasi—I—typeinvexity，Kaulet．