用广义二阶组合切上图导数刻画集值优化的强有效解  

Strong efficient solutions of set-valued optimization based on the generalized second-order composed contingent epiderivates

作　　者：余丽[1] 

机构地区：[1]宜春学院数学与计算机科学学院,江西宜春336000

出　　处：《浙江大学学报（理学版）》2015年第5期542-545,共4页Journal of Zhejiang University（Science Edition）

基　　金：江西省自然科学基金资助项目(20122BAB211004);江西省教育厅科技项目(GJJ13696)

摘　　要：在实赋范线性空间中研究无约束集值优化问题的最优性条件.在集值映射是内部锥类凸假设下,基于广义二阶组合切上图导数的性质得到了集值优化强有效元的必要条件.在广义锥-预不变凸条件下,讨论了集值优化问题并得到了强有效元的充分条件.This paper deals with the optimality conditions of the set-valued unconstraint optimization problems in the real normed linear spaces.Assumpting the ic-cone-convex likeness of set-valued maps,an optimality necessary condition of strong efficient element is established for the set-valued optimization by using the properties of the generalized second-order composed contingent epiderivates.Based on the concept of generalized conepreinvexity for the set-valued maps,an optimality sufficient condition of strong efficient element for the set-valued optimization is also established.

关 键 词：广义二阶组合切上图导数 广义锥-预不变凸性 内部锥类凸性 强有效元 

分 类 号：O224[理学—运筹学与控制论]