Extended Well-posedness of Vector Optimization Problems: The Convex Case

Abstract

In this paper we investigate a notion of extended well-posedness in vector optimization. Appropriate asymptotically minimizing sequences, when both the objective function and the feasible region are subject to perturbation are introduced. We show that convex problems, i.e. problems in which both the objective function and the perturbations are $C$−convex, are extended wellposed. Further, we characterize the proposed well-posedness notion both in terms of linear and nonlinear scalarization.