集值优化问题严有效解的高阶最优性条件  

Higher-Order Optimality Conditions of Strictly Efficient Solutions for Set-Valued Optimization Problem

作　　者：杨扬[1] 徐义红[1] 汪涛[1] 

机构地区：[1]南昌大学数学系,南昌330031

出　　处：《吉林大学学报（理学版）》2010年第5期737-742,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10461007);江西省自然科学基金(批准号:2009GZS0021);江西省教育厅科技项目(批准号:GJJ09069)

摘　　要：在实赋范线性空间中考虑集值优化问题的严有效性.当目标函数和约束函数均为锥凹集值映射时,利用凸集分离定理并借助集值映射高阶导数给出了带约束集值优化问题取得严最大有效解的Fritz John最优性必要条件,并用构造性方法证明了集值优化问题取得严最大有效解的充分条件。The strict efficiency of set-valued optimization was considered in real normed spaces.When both objective function and constraint function were concave,Fritz John type necessary optimality condition was established for set-valued optimization problem with constraint to attain its strict maximal solution with higherorder derivatives and separation theorem for convex sets.With the properties of base functional and the constructive method,sufficient optimality condition was also derived.

关 键 词：严有效解 m-阶相依导数 集值优化 

分 类 号：O224[理学—运筹学与控制论]