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First-Order Optimality Conditions for Lipschitz Optimization Problems with Vanishing Constraints

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Abstract

This article deals with a class of non-smooth mathematical programming with vanishing constraints. We introduce several kinds of constraint qualifications for these problems, and we study the relations between them. Then, we apply these constraint qualifications to obtain several stationary conditions. Finally, a sufficient condition for optimality of the problem is presented.

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Acknowledgements

The authors are very grateful to the referees for their constructive comments.

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Authors and Affiliations

  1. Department of Mathematics, Payame Noor University (PNU), P. O. Box 19395-3697, Tehran, Iran

    Hadis Mokhtavayi, Aghileh Heydari & Nader Kanzi

Authors
  1. Hadis Mokhtavayi
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  2. Aghileh Heydari
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  3. Nader Kanzi
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Correspondence to Nader Kanzi.

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Mokhtavayi, H., Heydari, A. & Kanzi, N. First-Order Optimality Conditions for Lipschitz Optimization Problems with Vanishing Constraints. Iran J Sci Technol Trans Sci 44, 1853–1861 (2020). https://doi.org/10.1007/s40995-020-00988-z

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  • DOI: https://doi.org/10.1007/s40995-020-00988-z

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