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On the sensitivity of Pareto efficiency in set-valued optimization problems

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Abstract

In this paper we present two main situations when the limit of Pareto minima of a sequence of perturbations of a set-valued map F is a critical point of F. The concept of criticality is understood in the Fermat generalized sense by means of limiting (Mordukhovich) coderivative. Firstly, we consider perturbations of enlargement type which, in particular, cover the case of perturbation with dilating cones. Secondly, we present the case of Aubin type perturbations, and for this we introduce and study a new concept of openness with respect to a cone.

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Acknowledgements

This research of Marius Durea was supported by the Grant PN-III-P4-ID-PCE-2016-0188 of Romanian Ministry of Research and Innovation, CNCS-UEFISCDI. The research of Radu Strugariu was supported by the Grant PN-III-P1-1.1-TE-2016-0868 of Romanian Ministry of Research and Innovation, CNCS-UEFISCDI. The authors would like to thank the referees and the Associate Editor for their costructive comments.

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Authors and Affiliations

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

    Marius Durea

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

    Marius Durea

  3. Department of Mathematics, “Gheorghe 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. Radu Strugariu
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Correspondence to Radu Strugariu.

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Durea, M., Strugariu, R. On the sensitivity of Pareto efficiency in set-valued optimization problems. J Glob Optim 78, 581–596 (2020). https://doi.org/10.1007/s10898-020-00925-9

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