LEVITIN-POLYAK WELL-POSEDNESS FOR SET OPTIMIZATION PROBLEMS

In this paper, we study different kinds of Levitin-Polyak well-posedness for set optimization problems and their relationships with respect to the set order relations defined by Minkowski difference on the family of bounded sets. Furthermore, by using the Kuratowski measure of noncompactness, we give some characterizations of Levitin-Polyak well-posedness for set optimization problems. Moreover, we establish the relationship between stability and LP well-posedness of set optimization problem by defining approximating solution maps. Several examples are given in support of concepts and results of this paper.