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Convergence of the Modified Extragradient Method for Variational Inequalities with Non-Lipschitz Operators

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Cybernetics and Systems Analysis Aims and scope

Abstract

We propose a modified extragradient method with dynamic step size adjustment to solve variational inequalities with monotone operators acting in a Hilbert space. In addition, we consider a version of the method that finds a solution of a variational inequality that is also a fixed point of a quasi-nonexpansive operator. We establish the weak convergence of the methods without any Lipschitzian continuity assumption on operators.

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Authors and Affiliations

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

    S. V. Denisov & V. V. Semenov

  2. Hetman Konashevych-Sahaidachnyi Kyiv State Maritime Academy, Kyiv, Ukraine

    L. M. Chabak

Authors
  1. S. V. Denisov
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  2. V. V. Semenov
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  3. L. M. Chabak
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Corresponding authors

Correspondence to S. V. Denisov, V. V. Semenov or L. M. Chabak.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 5, September–October, 2015, pp. 102–110.

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Denisov, S.V., Semenov, V.V. & Chabak, L.M. Convergence of the Modified Extragradient Method for Variational Inequalities with Non-Lipschitz Operators. Cybern Syst Anal 51, 757–765 (2015). https://doi.org/10.1007/s10559-015-9768-z

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  • DOI: https://doi.org/10.1007/s10559-015-9768-z

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