Further study on the Levitin–Polyak well-posedness of constrained convex vector optimization problems

Abstract

In this paper, we first establish characterizations of the nonemptiness and compactness of the set of weakly efficient solutions of a convex vector optimization problem with a general ordering cone (with or without a cone constraint) defined in a finite dimensional space. Using one of the characterizations, we further establish for a convex vector optimization problem with a general ordering cone and a cone constraint defined in a finite dimensional space the equivalence between the nonemptiness and compactness of its weakly efficient solution set and the generalized type I Levitin–Polyak well-posednesses. Finally, for a cone-constrained convex vector optimization problem defined in a Banach space, we derive sufficient conditions for guaranteeing the generalized type I Levitin–Polyak well-posedness of the problem.