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Adaptive Two-Stage Bregman Method for Variational Inequalities

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Cybernetics and Systems Analysis Aims and scope

Abstract

The authors analyze the two-stage Popov method with Bregman divergence and a new adaptive rule for choosing the step size, which does not require the Lipschitz constants to be known and operator values at additional points to be calculated. For variational inequalities with pseudo-monotone and Lipschitz continuous operators acting in a finite-dimensional normed linear space, the convergence theorem for the method is proved.

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Authors and Affiliations

  1. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    V. V. Semenov, S. V. Denisov & A. V. Kravets

Authors
  1. V. V. Semenov
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  2. S. V. Denisov
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  3. A. V. Kravets
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Corresponding author

Correspondence to V. V. Semenov.

Additional information

The study was financially supported by the Ministry of Education and Science of Ukraine (project “Mathematical modeling and optimization of dynamic systems for defense, medicine, and ecology,” State Registration # 0119U100337).

Translated from Kibernetyka ta Systemnyi Analiz, No. 6, November–December, 2021, pp. 128–137.

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Semenov, V.V., Denisov, S.V. & Kravets, A.V. Adaptive Two-Stage Bregman Method for Variational Inequalities. Cybern Syst Anal 57, 959–967 (2021). https://doi.org/10.1007/s10559-021-00421-2

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