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A modified subgradient extragradient method for solving the variational inequality problem

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Abstract

The subgradient extragradient method for solving the variational inequality (VI) problem, which is introduced by Censor et al. (J. Optim. Theory Appl. 148, 318–335, 2011), replaces the second projection onto the feasible set of the VI, in the extragradient method, with a subgradient projection onto some constructible half-space. Since the method has been introduced, many authors proposed extensions and modifications with applications to various problems. In this paper, we introduce a modified subgradient extragradient method by improving the stepsize of its second step. Convergence of the proposed method is proved under standard and mild conditions and primary numerical experiments illustrate the performance and advantage of this new subgradient extragradient variant.

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Acknowledgements

The authors express their thanks to the two anonymous referees, whose careful readings and suggestions led to improvements in the presentation of the results.

Funding

The first author is supported by National Natural Science Foundation of China (No. 71602144) and Open Fund of Tianjin Key Lab for Advanced Signal Processing (No. 2017ASP-TJ03). The third author is supported by the EU FP7 IRSES program STREVCOMS, grant no. PIRSES-GA-2013-612669.

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Authors and Affiliations

  1. Tianjin Key Laboratory for Advanced Signal Processing and College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Qiao-Li Dong & Dan Jiang

  2. Department of Mathematics, ORT Braude College, 2161002, Karmiel, Israel

    Aviv Gibali

Authors
  1. Qiao-Li Dong
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  2. Dan Jiang
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  3. Aviv Gibali
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Correspondence to Qiao-Li Dong.

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Dong, QL., Jiang, D. & Gibali, A. A modified subgradient extragradient method for solving the variational inequality problem. Numer Algor 79, 927–940 (2018). https://doi.org/10.1007/s11075-017-0467-x

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