Levitin–Polyak well-posedness of constrained vector optimization problems

Abstract

In this paper, we consider Levitin---Polyak type well-posedness for a general constrained vector optimization problem. We introduce several types of (generalized) Levitin---Polyak well-posednesses. Criteria and characterizations for these types of well-posednesses are given. Relations among these types of well-posedness are investigated. Finally, we consider convergence of a class of penalty methods under the assumption of a type of generalized Levitin---Polyak well-posedness.