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Strict directional solutions in vectorial problems: necessary optimality conditions

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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.

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Acknowledgements

The authors thank the two anonymous reviewers for their constructive comments which improved the presentation of the paper.

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Authors and Affiliations

  1. Département de Physiques, LPFAS, Faculté Polydisciplinaire, Université Cadi Ayyad, Safi, Morocco

    Mohamed Ait Mansour

  2. Faculty of Mathematics, “Alexandru Ioan Cuza” University, Bd. Carol I, nr. 11, 700506, Iaşi, Romania

    Marius Durea

  3. “Octav Mayer” Institute of Mathematics of the Romanian Academy, Iaşi, Romania

    Marius Durea

  4. Département de Mathématiques, Faculté des Sciences Semlalia, Laboratoire Mathématiques et Dynamique des Populations, Université Cadi Ayyad, Marrakesh, Morocco

    Hassan Riahi

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  1. Mohamed Ait Mansour
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  2. Marius Durea
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  3. Hassan Riahi
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Correspondence to Marius Durea.

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Ait Mansour, M., Durea, M. & Riahi, H. Strict directional solutions in vectorial problems: necessary optimality conditions. J Glob Optim 82, 119–138 (2022). https://doi.org/10.1007/s10898-021-01067-2

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  • DOI: https://doi.org/10.1007/s10898-021-01067-2

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