Levitin-Polyak well-posedness in set optimization concerning Pareto efficiency

This article aims to elaborate on various notions of Levitin-Polyak well-posedness for set optimization problems concerning Pareto efficient solutions. These notions are categorized into two classes including pointwise and global Levitin-Polyak well-posedness. We give various characterizations of both pointwise and global Levitin-Polyak well-posedness notions for set optimization problems. The hierarchical structure of their relationships is also established. Under suitable conditions on the input data of set optimization problems, we investigate the closedness of Pareto efficient solution sets in which they are different from the weakly efficient ones. Furthermore, we provide sufficient conditions for global Levitin-Polyak well-posedness properties of the reference problems without imposing the information on efficient solution sets.