广义凸集值向量优化问题的弱有效解

Weak Efficient Solutions of Generalized Convex Set-Valued Vector Optimization Problems

在序线性拓扑空间中定义了广义凸集值映射. 引进了相对内部, 应用凸集分离定理建立了一个广义凸集值映射的择一性定理. 运用此定理获得了弱有效解意义下的集值向量优化问题的最优性条件.

In this paper, firstly the concept of generalized convex set-valued map is defined in ordered linear topological spaces. Then relative interior is introduced and an alternative theorem of generalized convex set-valued maps is established by using the separation theorem. And finally, the optimality conditions are obtained for set-valued vector optimization problems in a sense of weak efficient solutions by applying the theorem.