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Strict directional solutions in vectorial problems: necessary optimality conditions

Author

Listed:
  • Mohamed Ait Mansour

    (Université Cadi Ayyad)

  • Marius Durea

    (“Alexandru Ioan Cuza” University
    “Octav Mayer” Institute of Mathematics of the Romanian Academy)

  • Hassan Riahi

    (Université Cadi Ayyad)

Abstract

We study directional strict efficiency in vector optimization and equilibrium problems with set-valued map objectives. We devise several possibilities to define a meaningful concept of strict efficiency in a directional sense for these kinds of problems and then we present necessary optimality conditions from several perspectives by means of generalized differentiation calculus. A concept of generalized convexity for multimappings is employed as well and its role in getting equivalence between some classes of solutions is emphasized.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:82:y:2022:i:1:d:10.1007_s10898-021-01067-2
    DOI: 10.1007/s10898-021-01067-2
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    References listed on IDEAS

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    1. 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.
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