一类广义凸多目标优化控制问题的改进的mond—weir型对偶

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1、维普资讯http://www.cqvip.com2006年3月内蒙古大学学报(自然科学版)Mar．2006第37卷第2期ActaScientlarumNaturaliumUniversitatiaNeiMongolVoI_37No．2ArticleID：1OOO一1638(2006)02—0129一O7AnImprovedMond—WierTypeDualforaGlassofMultiobjectiveControlProblemswithGeneralizedInvexityLIUHai—jun～．CHENGuo—qing(1．DepartmentofMathematics，C

2、ollegeofSciencesandTechnology，InnerMongoliaUniversity，Hohhot010021，China；2．DepartmentofBasicCurriculum，InnerMongoliaAgriculturalUniversity，Hohhot010018，China)Abstract：AnimprovedMond—Weirtypedualforaclassofmultiobjeetiveopti—malcontrolproblemsisconstructed．Undervectorfunctionalinvexityassumptio

3、n．anumberofweakandstrongdualitytheoremsaregivenandproved．Keywords：muhiobjectivecontrolproblems；dual；vectorIunetionalinvexityCLCnumber：0224Documentcode：AintroductionMondandSmartdefinedakindofinvexitywhentheydiscussedthedualityandefficiencyforaclassofscalarcontrolproblems．Recentlyquiteafewauthor

4、sextendedtheconceptofinvexitytoothergeneralizedinvexityandusedthemtodiscussdualityformultiobjeetivevariationalproblemsormuhiobjectiveoptimalcontrolproblems．suchasC2~93．BhatiaandKumardefinedp-invexity，anddiscusseddualityformultiobjectivecontrolproblemswithsuchgeneralizedinvexity；NahakandNandadi

5、scussedthedualityandefficiencyforaclassofmuhiobjectivevariationalproblemswith(F—JD)一convexity；IiangconstructedatypeofmixeddualanddiscussedefficiencyforaclassofmultiobjeetivecontrolproblemswithinvexitydefinedinC13．inthispaper，animprovedMond—Weirtypedualforaclassofmultiobjeetiveoptimalcontrolpro

6、blemsisgiven．Undervectorfunctionalin—vexityassumption，weproveanumberofweakandstrongdualitytheoremsforthedua1．Thedualmodelandresultsinthispapergeneralizethecorrespondingworks～‘·。～establishedearlierinthisfield．NotationsandPreliminariesConsidermultiobjectivecontrolproblems(VCP)bf(tminf(t,x,u)dt一(

7、fI6厂1(t,x,u)df，⋯．．，’rI／(f，z，“)出)■uJd口sobjectto(口)一口，(6)=(1)g(t。z，“)=：(gl(f，z，“)，⋯，gL(f，z，“))≤0，t∈(2)·Receiveddate：2005一O3一O3Foundationitem：SupportedbyNaturalScienceFoundationofInnerMongolia；SupportedbytheTeachingandResearchAwardProgramf