Pointwise and global well-posedness in set optimization: a direct approach

The aim of this paper is to characterize some of the pointwise and global wellposedness notions available in literature for a set optimization problem completely by compactness or upper continuity of an appropriate minimal solution set maps. The characterizations of compactness of set-valued maps, lead directly to many characterizations for well-posedness. Sufficient conditions are also given for global well-posedness.