集值优化问题超有效解的高阶Mond-Weir对偶  

Higher Order Mond-Weir Duality for Super Efficient Solutions of Set-Valued Optimization

作　　者：徐义红[1] 韩倩倩[1] 涂相求[1] 

机构地区：[1]南昌大学数学系,南昌330031

出　　处：《应用泛函分析学报》2013年第3期234-238,共5页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(61175127);江西省自然科学基金(20122BAB201003);江西省教育厅科技项目(GJJ12010)

摘　　要：在实赋范线性空间中利用锥方向高阶广义邻接导数研究带约束的集值优化在超有效解意义下的高阶Mond-Weir对偶问题.在广义锥-凸假设下,利用锥方向高阶广义邻接导数的性质借助凸集分离定理得到了强对偶定理.利用超有效点的标量化定理得到逆对偶定理.In real normed linear spaces,by virtue of the cone-directed higher order generalized adjacent derivatives,a higher order Mond-Weir dual problem for a constrained set-valued optimization is considered in the sense of super efficient solutions.Under the assumption of generalized cone-convexity,with the help of the properties of cone-directed higher order generalized adjacent derivatives by applying separate theorem for convex sets,a strong duality theorem is established.By taking advantage of the scalarization theorem for a super efficient point,a converse duality theorem is obtained.

关 键 词：超有效解 锥方向高阶广义邻接导数 高阶Mond-Weir对偶 

分 类 号：O224[理学—运筹学与控制论]