锥方向高阶广义邻近导数及高阶Mond-Weir对偶(英文)  

Cone-directed Higher Order Generalized Adjacent Derivative and Higher Order Mond-Weir Duality

作　　者：王其林[1,2] 

机构地区：[1]重庆交通大学理学院,重庆400074 [2]重庆大学数学与统计学院,重庆400044

出　　处：《数学进展》2011年第5期537-548,共12页Advances in Mathematics（China）

基　　金：supported by NSFC(No.10871216 and No.11071267);Natural Science Foundation Project of CQ CSTC;Science and Technology Research Project of Chongqing Municipal Education Commission(No.K J100419);the Excellent Young Teachers Program of Chongqing Jiaotong University,Chongqing,China

摘　　要：本文引入了集值映射的锥方向的高阶广义邻近导数.应用这种导数,构建了约束的集值优化问题的一种高阶Mond-Weir型对偶,并建立了相应的弱对偶,强对偶和逆对偶性,获得的结果推广了文献中的相应结论.In this paper, cone-directed higher order generalized adjacent derivative for a set-valued map is defined. By virtue of the cone-directed higher order generalized adjacent derivative, a higher order Mond-Weir type dual problem for a constrained set-valued optimiza- tion problem is introduced and its weak duality, strong duality and converse duality properties are established. The results obtained improve the corresponding results in the literatures.

关 键 词：集值优化 锥方向高阶广义邻近导数 弱极小解 高阶Mond—Weir对偶 

分 类 号：O224[理学—运筹学与控制论]