Painlevé–Kuratowski Stability of Approximate Solution Sets for Perturbed Set Optimization Problems Under General Ordering Sets by Recession Cone

The aim of this paper is to study the stability of perturbed set optimization problems via general ordering sets. Firstly, for a set optimization problem (SOP) via general ordering sets, four kinds of concepts about the minimal solutions of (SOP) are given. Then, some properties of the four kinds of solution sets and the level set of objective mappings are investigated. Finally, by employing the recession cone technique, sufficient conditions of upper Painlevé–Kuratowski convergence of minimal approximate solution sets, Painlevé–Kuratowski convergence of weak minimal approximate solution sets of (SOP) are obtained, where the feasible set is perturbed. Some examples are given to illustrate the mainly results in the paper.