Connectedness of the approximate solution sets for set optimization problems. (16th December 2022) - Han, Yu
ABSTRACT: In this paper, we deal with connectedness of the approximate solution sets for set optimization problems by using the scalarization method. We first obtain two scalarization results for the sets of l -minimal approximate solutions and weak l -minimal approximate solutions for set optimization problems without using the convexity of the objective mapping and the separation theorem of convex sets. Then, we establish connectedness of the sets of l -minimal approximate solutions and weak l -minimal approximate solutions for set optimization problems by utilizing the scalarization results. Finally, we derive arcwise connectedness of the set of weak l -minimal approximate solutions for set optimization problems.