Approximate Solutions in Linear Fractional Vector Optimization

Abstract

This paper studies approximate solutions of a linear fractional vector optimization problem without requiring boundedness of the constraint set. We establish necessary and sufficient conditions for approximating weakly efficient points of such a problem via some properties of the objective function and a technical lemma related to the intersection of the topological closure of the cone generated by a subset of the Euclidean space and the interior of the negative orthant. As a consequence, we obtain necessary conditions and sufficient conditions for approximate efficient solutions to the considered problem. Applications of these results to linear vector optimization are considered.