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Metric Inequality Conditions on Sets and Consequences in Optimization

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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.

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Acknowledgements

The research of D.-E. Maxim and R. Strugariu was supported by the grant PN-III-P1-1.1-TE-2016-0868 of Romanian Ministry of Education and Research, CNCS–UEFISCDI. The authors thank the two anonymous reviewers for their constructive comments which significantly improved the presentation of the paper.

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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 & Diana Maxim

  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

Authors
  1. Marius Durea
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  2. Diana Maxim
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  3. Radu Strugariu
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Correspondence to Marius Durea.

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Communicated by Asen L. Dontchev.

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Durea, M., Maxim, D. & Strugariu, R. Metric Inequality Conditions on Sets and Consequences in Optimization. J Optim Theory Appl 189, 744–771 (2021). https://doi.org/10.1007/s10957-021-01848-5

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