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Directional Pareto Efficiency: Concepts and Optimality Conditions

Author

Listed:
  • Teodor Chelmuş

    (“Al. I. Cuza” University)

  • Marius Durea

    (“Al. I. Cuza” University
    “Octav Mayer” Institute of Mathematics of the Romanian Academy)

  • Elena-Andreea Florea

    (“Al. I. Cuza” University)

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.

Suggested Citation

  • Teodor Chelmuş & Marius Durea & Elena-Andreea Florea, 2019. "Directional Pareto Efficiency: Concepts and Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 336-365, July.
    • Handle: RePEc:spr:joptap:v:182:y:2019:i:1:d:10.1007_s10957-019-01503-0
    DOI: 10.1007/s10957-019-01503-0
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    References listed on IDEAS

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    1. Alexander J. Zaslavski, 2016. "Numerical Optimization with Computational Errors," Springer Optimization and Its Applications, Springer, number 978-3-319-30921-7, September.
    2. Jean-Paul Penot, 1998. "Cooperative behavior of functions, relations and sets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 229-246, November.
    3. Alzorba, Shaghaf & Günther, Christian & Popovici, Nicolae & Tammer, Christiane, 2017. "A new algorithm for solving planar multiobjective location problems involving the Manhattan norm," European Journal of Operational Research, Elsevier, vol. 258(1), pages 35-46.
    4. M. Durea & R. Strugariu, 2013. "Calculus of tangent sets and derivatives of set-valued maps under metric subregularity conditions," Journal of Global Optimization, Springer, vol. 56(2), pages 587-603, June.
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    Cited by:

    1. Marius Durea & Diana Maxim & Radu Strugariu, 2021. "Metric Inequality Conditions on Sets and Consequences in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 189(3), pages 744-771, June.
    2. Mohamed Ait Mansour & Marius Durea & Hassan Riahi, 2022. "Strict directional solutions in vectorial problems: necessary optimality conditions," Journal of Global Optimization, Springer, vol. 82(1), pages 119-138, January.
    3. Vo Si Trong Long, 2022. "An Invariant-Point Theorem in Banach Space with Applications to Nonconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 440-464, August.

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