Approximate Solutions in Linear Fractional Vector Optimization

TL;DR

This paper develops new theoretical conditions for approximating solutions in linear fractional vector optimization problems without assuming bounded constraints, extending understanding of weakly efficient and efficient solutions.

Contribution

It introduces necessary and sufficient conditions for approximate solutions in unbounded linear fractional vector optimization, with applications to linear vector optimization.

Findings

Established conditions for weakly efficient points

Derived criteria for approximate efficient solutions

Applied results to linear vector optimization problems

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.