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Metric Inequality Conditions on Sets and Consequences in Optimization

Author

Listed:
  • Marius Durea

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

  • Diana Maxim

    (“Alexandru Ioan Cuza” University)

  • Radu Strugariu

    (“Gheorghe Asachi” Technical University)

Abstract

We study the implications of a well-known metric inequality condition on sets to the applicability of standard necessary optimality conditions for constrained optimization problems when a new constraint is added. We compare this condition with several other constraint qualification conditions in the literature, and due to its metric nature, we apply it to nonsmooth optimization problems in order to perform first a penalization and then to give optimality conditions in terms of generalized differentiability.

Suggested Citation

  • Marius Durea & Diana Maxim & Radu Strugariu, 2021. "Metric Inequality Conditions on Sets and Consequences in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 189(3), pages 744-771, June.
    • Handle: RePEc:spr:joptap:v:189:y:2021:i:3:d:10.1007_s10957-021-01848-5
    DOI: 10.1007/s10957-021-01848-5
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    References listed on IDEAS

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    1. Alexander Y. Kruger & Nguyen H. Thao, 2015. "Quantitative Characterizations of Regularity Properties of Collections of Sets," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 41-67, January.
    2. Marius Durea & Radu Strugariu, 2017. "Vectorial penalization for generalized functional constrained problems," Journal of Global Optimization, Springer, vol. 68(4), pages 899-923, August.
    3. Teodor Chelmuş & Marius Durea & Elena-Andreea Florea, 2019. "Directional Pareto Efficiency: Concepts and Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 336-365, July.
    4. M. Durea & R. Strugariu, 2013. "Calculus of tangent sets and derivatives of set-valued maps under metric subregularity conditions," Journal of Global Optimization, Springer, vol. 56(2), pages 587-603, June.
    Full references (including those not matched with items on IDEAS)

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