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Strong convergence of an extragradient-like algorithm involving pseudo-monotone mappings

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Abstract

The purpose of this paper is to introduce a new extragradient-like algorithm for solving a variational inequality problem with a pseudo-monotone and Lipschitz continuous mapping in a Hilbert space. The iterative algorithm combines inertial ideas and hybrid extragradient ideas with the Armijo-like step size rule. Strong convergence of the algorithm is obtained and numerical experiments are provided.

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Acknowledgments

The authors are grateful to the referees for their useful suggestions which improved the contents of this paper.

Funding

This paper was supported by the National Natural Science Foundation of China under Grant No.11401152.

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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

    Liya Liu & Xiaolong Qin

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  1. Liya Liu
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  2. Xiaolong Qin
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Correspondence to Xiaolong Qin.

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Liu, L., Qin, X. Strong convergence of an extragradient-like algorithm involving pseudo-monotone mappings. Numer Algor 83, 1577–1590 (2020). https://doi.org/10.1007/s11075-019-00737-3

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  • DOI: https://doi.org/10.1007/s11075-019-00737-3

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