Journal of Applied Mathematics and Stochastic Analysis
Volume 16 (2003), Issue 3, Pages 267-273

A note of stability of weakly efficient solution set for optimization with set-valued maps

Luo Qun

Zhaoqing University, Department of Mathematics, Guangdong, Zhaoqing 526061, China

Received 1 December 2002; Revised 1 July 2003

Copyright © 2003 Luo Qun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, we study the stability of weakly efficient solution sets for optimization problems with set-valued maps. We introduce the concept of essential weakly efficient solutions and essential components of weakly efficient solution sets. We first show that most optimization problems with set-valued maps (in the sense of Baire category) are stable. Secondly, we obtain some sufficient conditions for the existence of one essential weakly efficient solution or one essential component of the weakly efficient solution set .