18692.帶約束的向量均衡問題解的最優(yōu)性條件

1、帶約束的向量均衡問題解的最優(yōu)性條件Optimalityconditionsforvectorequilibriumproblemswithconstraints作者：葉琳Author：始Lin指導(dǎo)教師：仇秋生專業(yè)：應(yīng)用數(shù)學(xué)學(xué)位：理學(xué)碩士授予單位：浙江師范大學(xué)Supervisor：Qi墜Qi望璺塾旦里gMajor：壘巳P!i旦墮墜堡壘!墮旦望!壘!i竺璺Degree：MasterofScienceInstitute：——ZhejiangN

2、ormalUniversity——June，2015AbstractVectorequilibriumproblemsisakindofgeneralmodel，whichcontainsvectoropti—mizationproblems，variationalinequalityproblemsasspecialcasesVectorequilibriummodelcannotcompletelyinsteadofspecialp

3、urposeofthesemodelsBut，thecommonpropertiesofthemcanbeunifiedhandledratherthanstudyeachmodelOntheotherhand，themethodsandideasofvectoroptimizationproblemsandvariationalinequalityproblemscanalsopromotethedevelopmentofvector

4、equilibriumproblemsTherefore，vectorequilibriumproblemsbecomesthehotissuesofoptimizationproblemsTheS—tudyofoptimalityconditionscanprovidetheoreticalbasisforthealgorithmofvectorequilibriumproblems，moreover，italsowillpromot

5、etheinvestigationofdualtheoryandStabilitytheoryofvectorequilibriumproblemsThus，itisnecessarytoinvestigatetheoptimalityconditionsofvectorequilibriumproblemsInthispaper，wemainlydiscusstheoptimalityconditionsforweaklyeffici

6、entsolutions，efficientsolutionsandapproximateweaklyefficientsolutionsofvectorequilibriumproblemswithconstraintsinthelinearspacesandthetopologicalspacesThecontentsareasfollow：Inchapterone，webrieflyintroducethebackgroundan

7、dstatus，somedefinitionsandlemmasarealsointroducedinthischapterInchaptertwo，wefirstlydiscussthenecessaryandsufficientconditionsforweaklyefficientsolutionsofvectorequilibriumproblemswithconstraintsundertheassumptionofthema

8、ppingisnear—subconvexlikenessinthelinearspacesAsweknow，itisnosignificantforweakefficientsolutionwhenthealgebraicinte—rioroftheconeisemptyTherefore，westudythenecessaryandsufficientconditionsforefficientsolutionsofvectoreq

9、uilibriumproblemswithconstraintsundertheassumptionofthemappingisic—cone—convexlikeness，moreover，wediscusstheoptimalityconditionforefficientsolutionofthevectorequilibriumproblemsinlocallyconvexspacesFinally，wegivetheneces

10、saryandsufficientconditionsforweaklyefficientsolutionstovariationalinequalityproblemsasapplicationsAsweknow，thereisonlyalgebraicstructureinthelinearspaceThus，manypropertiesofthefunctions(suchas，continuityanddifferentiabi

11、lity)wecannotuseHence，inchapterthree，wefirstlydiscusstheoptimalityconditionsforweaklyefficientsolutionsofvectorequilibriumproblemswithconstraintsinthetopologicalspacesbyusingthedifferentiabilityofmappingSecondly，wedefine