Existence of solutions and well-posedness for set optimization problems with an application in the robust optimization

Abstract

In this paper, first a generalization of the Weierstrass theorem for set-valued mappings in the absence of usual continuity and compactness assumptions is derived. Then, new notions of well-posedness for set-valued optimization problems are presented and some necessary and sufficient conditions for well-posedness of these problems are obtained. Finally, as an application, we provide some results for a robust set-valued optimization problem