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

Author

Listed:
  • Marius Durea

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

  • Radu Strugariu

    (“Gheorghe Asachi” Technical University)

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.

Suggested Citation

  • Marius Durea & Radu Strugariu, 2020. "On the sensitivity of Pareto efficiency in set-valued optimization problems," Journal of Global Optimization, Springer, vol. 78(3), pages 581-596, November.
    • Handle: RePEc:spr:jglopt:v:78:y:2020:i:3:d:10.1007_s10898-020-00925-9
    DOI: 10.1007/s10898-020-00925-9
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    References listed on IDEAS

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    1. Marius Durea & Radu Strugariu, 2017. "Vectorial penalization for generalized functional constrained problems," Journal of Global Optimization, Springer, vol. 68(4), pages 899-923, August.
    2. Giorgio Giorgi & Bienvenido Jiménez & Vicente Novo, 2016. "Approximate Karush–Kuhn–Tucker Condition in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 70-89, October.
    3. X. Huang, 2013. "Convergence of a class of penalty methods for constrained scalar set-valued optimization," Journal of Global Optimization, Springer, vol. 56(4), pages 1501-1513, August.
    4. Shiva Kapoor & C. S. Lalitha, 2019. "Stability in unified semi-infinite vector optimization," Journal of Global Optimization, Springer, vol. 74(2), pages 383-399, June.
    Full references (including those not matched with items on IDEAS)

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