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The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space

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Abstract

We present a subgradient extragradient method for solving variational inequalities in Hilbert space. In addition, we propose a modified version of our algorithm that finds a solution of a variational inequality which is also a fixed point of a given nonexpansive mapping. We establish weak convergence theorems for both algorithms.

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Authors and Affiliations

  1. Department of Mathematics, University of Haifa, Mt. Carmel, 31905, Haifa, Israel

    Y. Censor

  2. Department of Mathematics, The Technion—Israel Institute of Technology, 32000, Haifa, Israel

    A. Gibali & S. Reich

Authors
  1. Y. Censor
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  2. A. Gibali
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  3. S. Reich
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Corresponding author

Correspondence to Y. Censor.

Additional information

Communicated by B.T. Polyak.

This work was partially supported by Award Number R01HL070472 from the National Heart, Lung and Blood Institute. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Heart, Lung and Blood Institute or the National Institutes of Health. The third author was partially supported by the Israel Science Foundation (Grant 647/07), by the Fund for the Promotion of Research at the Technion and by the Technion President’s Research Fund.

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Censor, Y., Gibali, A. & Reich, S. The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space. J Optim Theory Appl 148, 318–335 (2011). https://doi.org/10.1007/s10957-010-9757-3

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  • DOI: https://doi.org/10.1007/s10957-010-9757-3

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