Stability and Scalarization for a Unified Vector Optimization Problem

Abstract

This paper aims at investigating the Painleve–Kuratowski convergence of solution sets of a sequence of perturbed vector problems, obtained by perturbing the feasible set and the objective function of a unified vector optimization problem, in real normed linear spaces. We establish convergence results, both in the image and given spaces, under the assumptions of domination and strict domination properties. Moreover, scalarization techniques are employed to establish the Painleve–Kuratowski convergence in terms of the solution sets of a sequence of scalarized problems.