Journal of Applied Mathematics and Stochastic Analysis
Volume 16 (2003), Issue 3, Pages 267-273
doi:10.1155/S1048953303000212
Abstract
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 .