Painlevé–Kuratowski convergences of the solution sets for set optimization problems with cone-quasiconnectedness

Abstract

This paper aims at investigating the Painlevé–Kuratowski convergence of the solution sets for set optimization problems with respect to the perturbations of the feasible set and the objective mapping. We introduce the concepts of cone-quasiconnectedness and strictly cone-quasiconnectedness for set-valued mappings and a new convergence for the sequence of set-valued mappings, and then we obtain the Painlevé–Kuratowski convergence of the sets of l-minimal solutions and weak l-minimal solutions for perturbed set optimization problems by using cone-quasiconnectedness and strictly cone-quasiconnectedness. As an application of the main results, we derive Painlevé–Kuratowski convergence of the solution sets for vector optimization problems.

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