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Directional Pareto Efficiency: Concepts and Optimality Conditions

  • Teodor Chelmuş
  • Marius DureaEmail author
  • Elena-Andreea Florea
Article
  • 73 Downloads

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; 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.

Keywords

Directional Pareto minimality Optimality conditions Directional tangent cones Directional regularity Set-valued optimization 

Mathematics Subject Classification

54C60 46G05 90C46 

Notes

Acknowledgements

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Mathematics“Al. I. Cuza” UniversityIasiRomania
  2. 2.“Octav Mayer” Institute of Mathematics of the Romanian AcademyIasiRomania

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