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Revisiting subgradient extragradient methods for solving variational inequalities

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Abstract

In this paper, several extragradient algorithms with inertial effects and adaptive non-monotonic step sizes are proposed to solve pseudomonotone variational inequalities in real Hilbert spaces. The strong convergence of the proposed methods is established without the prior knowledge of the Lipschitz constant of the mapping. Some numerical experiments are given to illustrate the advantages and efficiency of the proposed schemes over previously known ones.

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Acknowledgements

The authors are would like to thank the anonymous referees for their valuable suggestions, which helped us to present this paper in a better way.

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Authors and Affiliations

  1. Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Bing Tan

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Xiaolong Qin

  3. Department of Human Health Care, Gyeongsang National University, Jinju, Korea

    Sun Young Cho

Authors
  1. Bing Tan
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  2. Xiaolong Qin
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  3. Sun Young Cho
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Correspondence to Xiaolong Qin.

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Tan, B., Qin, X. & Cho, S.Y. Revisiting subgradient extragradient methods for solving variational inequalities. Numer Algor 90, 1593–1615 (2022). https://doi.org/10.1007/s11075-021-01243-1

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  • DOI: https://doi.org/10.1007/s11075-021-01243-1

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