集值优化问题的ε严有效解的最优性条件  

Optimality Conditions of ε-Strict Efficient Solutions for Set-Valued Optimization Problems

作　　者：王其林[1] 吴云[1] 

机构地区：[1]重庆交通大学理学院,重庆400074

出　　处：《西南师范大学学报（自然科学版）》2006年第4期40-43,共4页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：重庆交通大学青年科学基金资助项目(20040220).

摘　　要：在局部凸拓扑向量空间中引入了ε严有效点、ε严有效解的概念.在近似锥次类凸集值映射下,利用拓扑向量空间中的凸集分离定理,获得了带广义不等式约束的集值优化问题的ε严有效解的必要条件.同时,利用锥基的一个性质,获得了这类集值优化问题的ε严有效解的充分条件.In locally-convex topological vector spaces, ε-strict efficient points and ε-strict efficient solutions are introduced. Under the nearly cone-subconvexlike set-valued maps, by applying separation theorem of convex sets of topological vector spaces, the optimality necessary conditions of ε-strict efficient solutions for set-valued optimization problem with generalized inequality constraints are obtained. At the same time, by applying a property of base of a cone, the optimality sufficient conditions of ε-strict efficient solutions for the set-valued optimization problem are obtained.

关 键 词：集值优化问题 ε-严有效点 ε-严有效解 近似锥-次类凸 最优性条件 

分 类 号：O224[理学—运筹学与控制论]