Directional Pareto Efficiency: Concepts and Optimality Conditions
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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; 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.
KeywordsDirectional Pareto minimality Optimality conditions Directional tangent cones Directional regularity Set-valued optimization
Mathematics Subject Classification54C60 46G05 90C46
This research was supported by a Grant of Romanian Ministry of Research and Innovation, CNCS-UEFISCDI, Project No. PN-III-P4-ID-PCE-2016-0188, within PNCDI III. The authors thank two anonymous referees and the Editor-in-Chief for several suggestions that improved the presentation of the paper.
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