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Metric Regularity of Quasidifferentiable Mappings and Optimality Conditions for Nonsmooth Mathematical Programming Problems

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Abstract

This article is devoted to the analysis of necessary and/or sufficient conditions for metric regularity in terms of Demyanov-Rubinov-Polyakova quasidifferentials. We obtain new necessary and sufficient conditions for the local metric regularity of a multifunction in terms of quasidifferentials of the distance function to this multifunction. We also propose a new MFCQ-type constraint qualification for a parametric system of quasidifferentiable equality and inequality constraints and prove that it ensures the metric regularity of a multifunction associated with this system. As an application, we utilize our constraint qualification to strengthen existing optimality conditions for quasidifferentiable programming problems with equality and inequality constraints. We also prove the independence of the optimality conditions of the choice of quasidifferentials and present a simple example in which the optimality conditions in terms of quasidifferentials detect the non-optimality of a given point, while optimality conditions in terms of various subdifferentials fail to disqualify this point as non-optimal.

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Acknowledgements

The author wishes to express his gratitude to the anonymous reviewers for thoughtful comments and for suggesting to include several additional examples illustrating theoretical results.

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  1. Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, Saint Petersburg, Russia

    M. V. Dolgopolik

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  1. M. V. Dolgopolik
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Correspondence to M. V. Dolgopolik.

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The results presented in this article were supported by the President of Russian Federation grant for the support of young Russian scientist (grant number MK-3621.2019.1).

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Dolgopolik, M.V. Metric Regularity of Quasidifferentiable Mappings and Optimality Conditions for Nonsmooth Mathematical Programming Problems. Set-Valued Var. Anal 28, 427–449 (2020). https://doi.org/10.1007/s11228-019-00521-4

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