集值优化问题全局真有效解集的连通性

Connectedness of Globally Proper Efficient Solution Set for set-valued optimization problems

在局部凸空间中给出了集值向量优化问题全局真有效解的连通性定理,该定理是在可行域为弧连通紧的,目标函数为C-弧连通的集值映射的条件下得到的.

In this paper,we present the Theorem of the Connectedness of Globally Proper Efficient Solu- tion Set for set-valued optimization problems in locally convex spaces. The theorem is proved under the condition that the domain is an arcwise connected and compact subset, and the objective function is a cone-arcwise connected set-valued mapping.