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Self-adaptive inertial extragradient algorithms for solving variational inequality problems

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Abstract

In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems for the suggested algorithms are proved without the prior knowledge of the Lipschitz constant of the operator. Finally, we provide some numerical experiments to illustrate the performance of the proposed algorithms and provide a comparison with related ones.

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Acknowledgements

The authors are very grateful to the editor and the anonymous referee for their constructive comments, which significantly improved the original manuscript. We would also like to thank Professor Xiaolong Qin for reading the initial manuscript and giving us many useful suggestions.

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Authors and Affiliations

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

    Bing Tan, Jingjing Fan & Songxiao Li

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  1. Bing Tan
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  2. Jingjing Fan
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  3. Songxiao Li
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Correspondence to Songxiao Li.

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Communicated by Baisheng Yan.

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Tan, B., Fan, J. & Li, S. Self-adaptive inertial extragradient algorithms for solving variational inequality problems. Comp. Appl. Math. 40, 19 (2021). https://doi.org/10.1007/s40314-020-01393-3

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