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Vectorial penalization for generalized functional constrained problems

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Abstract

In this paper we use a double penalization procedure in order to reduce a set-valued optimization problem with functional constraints to an unconstrained one. The penalization results are given in several cases: for weak and strong solutions, in global and local settings, and considering two kinds of epigraphical mappings of the set-valued map that defines the constraints. Then necessary and sufficient conditions are obtained separately in terms of Bouligand derivatives of the objective and constraint mappings.

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Acknowledgements

This research was supported by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-RU-TE-2014-4-0019.

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Authors and Affiliations

  1. Faculty of Mathematics, “Al. I. Cuza” University, Bd. Carol I, nr. 11, 700506, Iasi, Romania

    Marius Durea

  2. Department of Mathematics, “Gh. Asachi” Technical University, Bd. Carol I, nr. 11, 700506, Iasi, Romania

    Radu Strugariu

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  1. Marius Durea
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  2. Radu Strugariu
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Correspondence to Radu Strugariu.

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Durea, M., Strugariu, R. Vectorial penalization for generalized functional constrained problems. J Glob Optim 68, 899–923 (2017). https://doi.org/10.1007/s10898-017-0505-1

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  • DOI: https://doi.org/10.1007/s10898-017-0505-1

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