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 .
Highlights
Introduction and PreliminariesIn this paper, our principle aim is to study the stability of the set of weakly efficient solutions for optimization problems with set-valued maps
Our principle aim is to study the stability of the set of weakly efficient solutions for optimization problems with set-valued maps
We give an example that shows that the weakly efficient solution set for the optimization problem with set-valued maps is not stable
Summary
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. We obtain some sufficient conditions for the existence of one essential weakly efficient solution or one essential component of the weakly efficient solution set.
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