Characterizations of generalized Levitin-Polyak well-posed set optimization problems
Set optimisation problems in normed spaces are considered. A notion of generalised Levitin-Polyak well-posedness for such problems is introduced, extending the known analogous concept of the scalar optimization setting. Generalized Levitin-Polyak well-posedness is then characterised by properties of the set of approximate solutions. Scalarizations are introduced and their well-posedness is related to that of the given problem. Further characterisations are obtained, making use of forcing functions and the Kuratowski measure of non-compactness of the approximate solutions. Sufficient conditions for well-posedness are derived.
scientific article; zbMATH DE number 7040055
scientific article