集值映射最优化问题超有效解集的连通性

THE CONNECTEDNESS OF THE SUPER EFFICIENT SOLUTION SETS OF THE OPTIMIZATION PROBLEM FOR A SET-VALUED MAPPING

本文在局部凸空间中对集值映射最优化问题引入超有效解的概念．首先研究了超 有效点的一些重要特性．其后证明了当目标函数为锥类凸的集值映射时，其目标空间里 的超有效点集是连通的；若目标函数为锥凸的集值映射时，其超有效解集也是连通的．

In this paper, we introduce a concept of super efficient solution of the opti-mization problem for a set-valued mapping. Firstly, we discuss some characterizations of super efficient point of the vector optimization. Secondly, we prove that the super efficient point set of the objective space is connected when the objective function is cone convex-like, and obtain that if the objective function is a cone convex set-valued mapping, then the super efficient solution set is also connected.