参数向量拟平衡问题解映射的Holder连续性陈纯荣重庆大学数学与统计学院，重庆401331摘要：本文利用非线性标量化方法研究参数向量拟平衡问题单值解映射（局部唯一解）的Holder连续性。著名的Gerstewitz非线性标量化函数在证明中发挥重要作用，特别是其全局Lipschitz性。文中得到的主要结果是新的，且非线性标量化的证明处理不同于相关文献所使用的方法。关键词：向量优化;参数向量拟平衡问题;Holder连续性;非线性标量化中图分类号：O221OnHolderContinuityofSolutionstoParametricVectorQuasiequilibriumProblemsCHENChun-RongCollegeofMathematicsandStatistics,ChongqingUniversity,Chongqing401331Abstract:Inthispaper,Holdercontinuityoftheuniquesolutiontoaparametricvectorquasiequilibriumproblemisstudiedbyusingnonlinearscalarizationapproach.Thewell-knownGerstewitznonlinearscalarizationfunctionasanefficienttoolplayskeyroles,especially,itsgloballyLipschitzpropertyisfullyemployed.Theresultobtainedisnewintheliterature,andtheapproachvianonlinearscalarizationisdifferentfromtheonesusedinrelatedworks.Keywords:Vectoroptimization;Parametricvectorquasiequilibriumproblems;Holdercontinuity;Nonlinearscalarization0IntroductionItiswellknownthatthevectorequilibriumproblemincludingthemoregeneralvectorquasiequilibriumproblemprovidesaunifiedmodelofseveralimportantproblems,suchasthevectoroptimizationproblem,thevectorvariationalinequalityandthevectorcomplementarityproblem(see[1]andthereferencestherein).Amongmanydesirablepropertiesofsolutionstovectorequilibriumandquasiequilibriumproblems,thestabilityanalysisisofconsiderableinterest,especially,H¨olderorLipschitzcontinuityofsolutionsplaysanimportantroleinthetheoryofstabilityanalysisforvectorequilibria.Recently,inthisfield,H¨oldercontinuityof基金项目：SpecializedResearchFundfortheDoctoralProgramofHigherEducation(20100191120043)作者简介：CHENChun-Rong（1981-），male，associateprofessor，majorresearchdirection：vectoroptimization.-2-solutionmappingstoparametricvectorequilibriumorquasiequilibriumproblemshasbeenintensivelystudiedintheliterature,suchas[2,3,4,5,6,7,8,9,10,11,12,13].Inrecentyears,scalarizingapproacheshavebeenusedasefficientmethodstostudyH¨oldercontinuityofparametricvectorequilibriumorquasiequilibriumproblems.Amongthem,scalar-izingapproacheswereappliedbyusinglinearfunctionals[7]ornonlinearscalarizationfunc-tions[5,11,12].Wenoticethatnonlinearscalarizationmethodstodealwithsolutionstabilitybyvirtueofdifferentnonlinearscalarizationfunctionshavereceivedsomeattention;forex-ample,SachandTuan[14,15]haveusedGerstewitz-likenonlinearscalarizationfunctionstostudyingbothupperandlowersemicontinuitiesofthesolutionmappingsforparametricvectorquasiequilibriumproblems.Formanynonlinearscalarizationfunctions,thenonlinearscalar-izationfunction𝜉𝑞(Definition1)commonlyknownastheGerstewitzfunctioninthefieldofvectoroptimization[1,16]isapowerfultool.Ithasmanygoodproperties,suchascontinu-ity,sublinearity,convexity,(strict)monotonicityandsoon.Thesepropertieshavebeenfullyexploitedintheliterature[1,16]todealwithvariousproblemswithvectorobjectives,suchasexistenceofsolutions,gapfunctions,duality,vectorvariationalprinciples,well-posedness,vectorminimaxinequalitiesandvectornetworkequilibriumproblems.However,thegloballyLipschitzpropertyof𝜉𝑞(Proposition3)hasnotreceivedattentionsofar.Untilrecently,Chen[11](seealso[12])hasappliedittodiscussingH¨oldercontinuityoftheuniquesolutiontoaparametricvectorquasiequilibriumpr...