Set Optimization Using Improvement Sets

M. Dhingra, C.S. Lalitha

In this paper we introduce a notion of minimal solutions for set-valued optimization problem in terms of improvement sets by unifying a solution notion, introduced by Kuroiwa [15] for set-valued problems, and a notion of optimal solutions in terms of improvement sets, introduced by Chicco et al. [4] for vector optimization problems. We provide existence theorems for these solutions, and establish lower convergence of the minimal solution sets in the sense of Painlevé-Kuratowski.