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

摘要

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) arestable. Secondly, we obtain some sufficient conditions for the existence of one essentialweakly efficient solution or one essential component of the weakly efficient solution set .