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Two strong convergence subgradient extragradient methods for solving variational inequalities in Hilbert spaces

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Abstract

In this paper we are focused on solving monotone and Lipschitz continuous variational inequalities in real Hilbert spaces. Motivated by several recent results related to the subgradient extragradient method (SEM), we propose two SEM extensions which do not require the knowledge of the Lipschitz constant associated with the variational inequality operator. Under mild and standard conditions, we establish the strong convergence of our schemes. Primary numerical examples demonstrate the potential of our algorithms as well as compare their performances to several related results.

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Acknowledgements

The authors would like to thank the referees for their comments on the manuscript which helped in improving earlier version of this paper.

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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

    Duong Viet Thong

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

    Aviv Gibali

  3. The Center for Mathematics and Scientific Computation, University of Haifa, Mt. Carmel, 3498838, Haifa, Israel

    Aviv Gibali

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  1. Duong Viet Thong
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  2. Aviv Gibali
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Correspondence to Duong Viet Thong.

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Thong, D.V., Gibali, A. Two strong convergence subgradient extragradient methods for solving variational inequalities in Hilbert spaces. Japan J. Indust. Appl. Math. 36, 299–321 (2019). https://doi.org/10.1007/s13160-018-00341-3

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