Levitin-Polyak well-posedness of constrained vector optimization problems

Abstract. In this paper, we consider Levitin–Polyak-type well-posedness for a general con-strained optimization problem. We introduce generalized Levitin–Polyak well-posedness and strongly generalized Levitin–Polyak well-posedness. Necessary and sufficient conditions for these types of well-posedness are given. Relations among these types of well-posedness are investigated. Finally, we consider convergence of a class of penalty methods and a class of augmented Lagrangian methods under the assumption of strongly generalized Levitin–Polyak well-posedness