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An Adaptive Analog of Nesterov’s Method for Variational Inequalities with a Strongly Monotone Operator

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Abstract

An adaptive analog of Nesterov’s method for variational inequalities with a strongly monotone operator is proposed. The main idea of the method is an adaptive choice of constants in the maximized concave functionals at each iteration. In this case there is no need in specifying exact values of the constants, since this method makes it possible to find suitable constants at each iteration. Some estimates for the parameters determining the quality of the solution to the variational inequality are obtained as functions of the number of iterations.

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Acknowledgements

The author would like to thank A.V.Gasnikov, Yu.E.Nesterov, and the anonymous reviewers for their useful discussions and comments.

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Authors and Affiliations

  1. Vernadsky Crimean Federal University, pr. Vernadskogo 4, Simferopol, 295007, Russia

    F. S. Stonyakin

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  1. F. S. Stonyakin
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Correspondence to F. S. Stonyakin.

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Russian Text © The Author(s), 2019, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2019, Vol. 22, No. 2, pp. 201–221.

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Stonyakin, F.S. An Adaptive Analog of Nesterov’s Method for Variational Inequalities with a Strongly Monotone Operator. Numer. Analys. Appl. 12, 166–175 (2019). https://doi.org/10.1134/S199542391902006X

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  • DOI: https://doi.org/10.1134/S199542391902006X

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