集值向量均衡问题近似有效解的最优条件  

Optimality conditions of approximate efficient solutions to set-valued vector equilibrium problems

作　　者：孟旭东[1] MENG Xudong(Science and Technology College,Nanchang Hangkong University,Gongqingcheng 332020,Jiangxi Province,China)

机构地区：[1]南昌航空大学科技学院,江西共青城332020

出　　处：《浙江大学学报（理学版）》2021年第4期440-449,共10页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(11201216);江西省教育厅科学技术重点研究项目(GJJ181565,GJJ191614)。

摘　　要：分析实局部凸Hausdorff拓扑向量空间一类具约束集值向量均衡问题的近似有效解,讨论其有效解和近似有效解的关系。在近似锥-次类凸集值映射概念的基础上,运用凸集分离定理,建立了有效解和近似有效解的最优条件。在广义凸性假设条件下,借助相应的分析方法,得到集值向量均衡问题近似有效解的Kuhn-Tucker型和Lagrange型的最优充要条件。In this paper,a kind of approximate efficient solutions to set-valued vector equilibrium problems with constraints is analyzed in real locally convex Hausdorff topological vector spaces,and the relationship between the efficient solutions and the approximate efficient solutions is discussed.Based on the concept of nearly conesubconvexlike set-valued mapping,the optimality conditions of efficient solutions and approximate efficient solutions are established by applying the separation theorem for convex sets.Using analytic method,under the assumption of generalized convexity,the optimality necessary and sufficient conditions for both the Kuhn-Tucker-type and Lagrangetype approximate efficient solutions to the set-valued vector equilibrium problems are obtained.

关 键 词：集值向量均衡问题 近似锥-次类凸集值映射 近似有效解 最优条件 

分 类 号：O224[理学—运筹学与控制论]