Set optimization using improvement sets

Abstract

In this paper we introduce a notion of minimal solutions for set-valued optimization problem, unifying a set criterion notion introduced by Kuroiwa [15] for set-valued
problems and a notion introduced by Chicco et al. [4] using improvement sets for vector optimization problems. For these solutions, we establish the existence and lower convergence in the sense of Painleve-Kuratowski.
Keywords Set-valued optimization Improvement set Painleve-Kuratowski convergence.