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An Explicit Extragradient Algorithm for Solving Variational Inequalities

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Abstract

In this paper, we introduce an explicit iterative algorithm for solving a (pseudo) monotone variational inequality under Lipschitz condition in a Hilbert space. The algorithm is constructed around some projections incorporated by inertial terms. It uses variable stepsizes which are generated at each iteration by some simple computations. Furthermore, it can be easily implemented without the prior knowledge of the Lipschitz constant of the operator. Theorems of weak convergence are established under mild conditions, and some numerical results are reported for the purpose of comparison with other algorithms. The obtained results in this paper extend some related works in the literature.

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Acknowledgements

The authors would like to thank the Associate Editor and the anonymous referees for their valuable comments and suggestions which helped us very much in improving the original version of this paper. The paper is supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under the Project: 101.01-2020.06 and by Namur Institute for Complex Systems (naXys), University of Namur, Belgium.

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Authors and Affiliations

  1. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Dang Van Hieu

  2. Department of Mathematics, Namur Institute for Complex Systems, University of Namur, Namur, Belgium

    Jean Jacques Strodiot

  3. TIMAS, Thang Long University, Hanoi, Vietnam

    Le Dung Muu

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  1. Dang Van Hieu
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  2. Jean Jacques Strodiot
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Correspondence to Dang Van Hieu.

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Communicated by Igor Konnov.

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Hieu, D.V., Strodiot, J.J. & Muu, L.D. An Explicit Extragradient Algorithm for Solving Variational Inequalities. J Optim Theory Appl 185, 476–503 (2020). https://doi.org/10.1007/s10957-020-01661-6

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