向量平衡问题强有效解集的连通性  

Connectedness of the Strong Efficient Solution Set for Vector Equilibrium Problems

作　　者：杨秀凤 范江华 YANG Xiufeng;FAN Jianghua(School of Mathematics and Statistics,Guangxi Normal University,Guilin Guangxi 541006,China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541006

出　　处：《广西师范大学学报（自然科学版）》2023年第2期98-105,共8页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11801102)。

摘　　要：本文主要在自反Banach空间中研究向量平衡问题强有效解集的连通性。利用新定义的非线性函数,将1个非凸非闭集合和1个紧致集分离;证明强向量平衡问题的强有效解集可以表示为非线性标量问题解集的并集,从而得到向量平衡问题强有效解集的连通性。The connectedness of the strong efficient solution set for vector equilibrium problems in reflexive Banach spaces is studied in this paper.A new nonlinear function is established,and a non-convex non-closed set and a compact set can be separated by the new nonlinear function.It is shown that the solution set of the strong vector equilibrium problems equals to the union of the solution set of a series of non-linear scalar problems.The connectedness of the strong efficient solution set for vector equilibrium problems is obtained.

关 键 词：向量平衡问题 连通性 非凸分离定理 强有效解集 

分 类 号：O224.1[理学—运筹学与控制论]