Convergence of solutions to set optimization problems

Abstract

The aim of this study is to establish convergence conditions in the Painlevé-Kuratowski sense for a sequence of solution sets of set optimization problems perturbed by the constraint set to the solution set of the original problem in the decision space. By relaxing the assumption of continuity by cone-continuity, we provide upper convergence conditions for the weakly efficient solutions and the efficient solutions. Furthermore, we introduce the dominance property of set optimization problems and the above-relaxed continuities to study the lower convergence of such problems with a new approach.