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On the Weak Convergence of the Extragradient Method for Solving Pseudo-Monotone Variational Inequalities

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  • Phan Tu Vuong

    (Vienna University of Technology)

Abstract

In infinite-dimensional Hilbert spaces, we prove that the iterative sequence generated by the extragradient method for solving pseudo-monotone variational inequalities converges weakly to a solution. A class of pseudo-monotone variational inequalities is considered to illustrate the convergent behavior. The result obtained in this note extends some recent results in the literature; especially, it gives a positive answer to a question raised in Khanh (Acta Math Vietnam 41:251–263, 2016).

Suggested Citation

  • Phan Tu Vuong, 2018. "On the Weak Convergence of the Extragradient Method for Solving Pseudo-Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 399-409, February.
    • Handle: RePEc:spr:joptap:v:176:y:2018:i:2:d:10.1007_s10957-017-1214-0
    DOI: 10.1007/s10957-017-1214-0
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    References listed on IDEAS

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    1. N. N. Tam & J. C. Yao & N. D. Yen, 2008. "Solution Methods for Pseudomonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 138(2), pages 253-273, August.
    2. 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.
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