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The Extragradient Method for Solving Variational Inequalities in the Presence of Computational Errors

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  • A. J. Zaslavski

    (Technion)

Abstract

In a Hilbert space, we study the convergence of the subgradient method to a solution of a variational inequality, under the presence of computational errors. Most results known in the literature establish convergence of optimization algorithms, when computational errors are summable. In the present paper, the convergence of the subgradient method for solving variational inequalities is established for nonsummable computational errors. We show that the subgradient method generates a good approximate solution, if the sequence of computational errors is bounded from above by a constant.

Suggested Citation

  • A. J. Zaslavski, 2012. "The Extragradient Method for Solving Variational Inequalities in the Presence of Computational Errors," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 602-618, June.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:3:d:10.1007_s10957-011-9975-3
    DOI: 10.1007/s10957-011-9975-3
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    References listed on IDEAS

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    1. Y. Censor & A. Gibali & S. Reich, 2011. "The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 318-335, February.
    2. Kengy Barty & Jean-Sébastien Roy & Cyrille Strugarek, 2007. "Hilbert-Valued Perturbed Subgradient Algorithms," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 551-562, August.
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