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The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space

Author

Listed:
  • Y. Censor

    (University of Haifa)

  • A. Gibali

    (The Technion—Israel Institute of Technology)

  • S. Reich

    (The Technion—Israel Institute of Technology)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:148:y:2011:i:2:d:10.1007_s10957-010-9757-3
    DOI: 10.1007/s10957-010-9757-3
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    References listed on IDEAS

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    1. W. Takahashi & M. Toyoda, 2003. "Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 417-428, August.
    2. N. Nadezhkina & W. Takahashi, 2006. "Weak Convergence Theorem by an Extragradient Method for Nonexpansive Mappings and Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 191-201, January.
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