On the stability of set optimization problems via upper set less order relations

Abstract

This paper aims to establish stability conditions, in the Painlevé–Kuratowski sense, for solution sets of set optimization problems under perturbations in both the constraint set and the objective mapping. By relaxing the assumptions of continuity and compactness of the objective mapping, we investigated external stability for weakly efficient and efficient solutions. Moreover, we employed the dominance property of set optimization problems under these conditions to analyze internal stability for efficient solutions. Our results represent a new contribution to the field.