Well-posedness and stability in set optimization with applications (Q2045917)

The authors give some characterization concerned with several types of well-posedness with their relationships in set optimization. They obtain some necessary conditions for such types of well-posedness as well as some sufficient conditions for ensuring these types of well-posedness in set optimization by employing the locally C-Lipschitz continuity. Also, they obtain the upper semi-continuity, lower semi-continuity and compactness of minimal solution mappings for parametric set optimization involving the locally C-Lipschitz continuous set-valued mappings. As applications, the authors give some sufficient conditions for ensuring several kinds of well-posedness for vector-valued games with uncertainty.