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Metric regularity of epigraphical multivalued mappings and applications to vector optimization

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Abstract

In this work we combine in a meaningful way two techniques of variational analysis and nonsmooth optimization. On one hand, we use the error bound approach to study the metric regularity of some special types of multifunctions and, on the other hand, we exploit the incompatibility between the metric regularity and the Pareto minimality. This method allows us to present some \(\varepsilon \)-Fermat rules for set-valued optimization problem in the setting of general Banach spaces. Our results are comparable to several recent results in literature.

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Acknowledgments

The second author thanks Professor Constantin Zălinescu for meaningful help and interesting discussions while he visited “Al. I. Cuza” University of Iaşi with a research grant offered by Romanian Government within Eugen Ionescu programme coordinated by Agence Universitaire de la Francophonie (AUF). Research of the second author was partially supported by a doctoral grant from Région Limousin and by the ECOS-SUD C\(10\)E\(08\) project. The first and the third authors were supported by a grant of the Romanian National Authority for Scientific Research, CNCS–UEFISCDI, project number PN-II-ID-PCE-2011-3-0084. All the authors are indebted to Professors Michel Théra and Huynh van Ngai for their interest and for many valuable discussions on this work.

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Authors and Affiliations

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

    Marius Durea

  2. University of Quy Nhon, Qui Nhon, Vietnam

    Huu Tron Nguyen

  3. Laboratoire XLIM, UMR-CNRS 6172, Université de Limoges, Limoges, France

    Huu Tron Nguyen

  4. Department of Mathematics and Informatics, “Gh. Asachi” Technical University, Bd. Carol I, nr. 11, 700506 , Iaşi, Romania

    Radu Strugariu

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  1. Marius Durea
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  2. Huu Tron Nguyen
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  3. Radu Strugariu
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Correspondence to Marius Durea.

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Dedicated to Professor J. M. Borwein on the occasion of his sixtieth anniversary.

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Durea, M., Nguyen, H.T. & Strugariu, R. Metric regularity of epigraphical multivalued mappings and applications to vector optimization. Math. Program. 139, 139–159 (2013). https://doi.org/10.1007/s10107-013-0665-9

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  • DOI: https://doi.org/10.1007/s10107-013-0665-9

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