Levitin-Polyak well-posedness for set-valued optimization problems with constraints

Abstract

In this paper, Levitin-Polyak well-posedness for set-valued optimization problems with constraints are also introduced and then, some sufficient and necessary conditions for the Levitin-Polyak well-posedness of these problems are established under some suitable conditions. The equivalence between the well-posedness of optimization problems with constraints and the existence and uniqueness of their solutions are proved. Finally, we give some examples to illustrate the presented results.