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Extension of Extragradient Techniques for Variational Inequalities

Author

Listed:
  • Yonghong Yao

    (School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China
    The Key Laboratory of Intelligent Information and Data Processing of NingXia Province, North Minzu University, Yinchuan 750021, China
    Health Big Data Research Institute of North Minzu University, Yinchuan 750021, China)

  • Ke Wang

    (School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China)

  • Xiaowei Qin

    (School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China)

  • Li-Jun Zhu

    (The Key Laboratory of Intelligent Information and Data Processing of NingXia Province, North Minzu University, Yinchuan 750021, China
    Health Big Data Research Institute of North Minzu University, Yinchuan 750021, China)

Abstract

An extragradient type method for finding the common solutions of two variational inequalities has been proposed. The convergence result of the algorithm is given under mild conditions on the algorithm parameters.

Suggested Citation

  • Yonghong Yao & Ke Wang & Xiaowei Qin & Li-Jun Zhu, 2019. "Extension of Extragradient Techniques for Variational Inequalities," Mathematics, MDPI, vol. 7(2), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:111-:d:199707
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    References listed on IDEAS

    as
    1. H. K. Xu & T. H. Kim, 2003. "Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 185-201, October.
    2. Q. L. Dong & Y. J. Cho & L. L. Zhong & Th. M. Rassias, 2018. "Inertial projection and contraction algorithms for variational inequalities," Journal of Global Optimization, Springer, vol. 70(3), pages 687-704, March.
    3. J. Bello Cruz & A. Iusem, 2010. "Convergence of direct methods for paramonotone variational inequalities," Computational Optimization and Applications, Springer, vol. 46(2), pages 247-263, June.
    4. 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.
    5. 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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