向量优化中Arrow-Barankin-Blackwell稠密性定理的评注

Arrow-Barankin-Blackwell theorem in vector optimization

真有效点集在Pareto有效点集中的Arrow-Barankin-Blackwell稠密性理论是向量优化理论的组成部分,已被广泛研究并获得了一系列深刻的结果.该文就弱紧凸集和紧凸集概述了正真有效点集在Pareto点集中的稠密性,并就弱紧非凸集介绍了超有效点集在Pareto点集中的稠密性.

In this note,we give a survey on the Arrow-Barrankin-Blackwell theorem for both weakly compact convex sets and compact convex sets in topological linear spaces and/or normed spaces.This note also concerns the denseness of the super-efficient point set in the Pareto efficient point set for a weakly compact(not necessarily convex) set.