Directional Pareto efficiency: concepts and optimality conditions

TL;DR

This paper introduces a new concept of directional Pareto minimality, extending classical Pareto efficiency, and provides necessary and sufficient optimality conditions using generalized differentiation techniques.

Contribution

It generalizes Pareto efficiency to directional Pareto minimality and develops new optimality conditions with connections to directional regularities.

Findings

Established necessary and sufficient conditions for directional Pareto minimality

Connected directional regularities with optimality conditions

Adapted generalized differentiation techniques for the new concept

Abstract

We introduce and study a notion of directional Pareto minimality with respect to a set that generalizes the classical concept of Pareto efficiency. Then we give separate necessary and sufficient conditions for the newly introduced efficiency and several situations concerning the objective mapping and the constraints are considered. In order to investigate different cases, we adapt some well-known constructions of generalized differentiation and the connections with some recent directional regularities come naturally into play. As a consequence, several techniques from the study of genuine Pareto minima are considered in our specific situation.