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Inertial subgradient extragradient algorithms with line-search process for solving variational inequality problems and fixed point problems

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Abstract

In this paper, basing on the subgradient extragradient method and inertial method with line-search process, we introduce two new algorithms for finding a common element of the solution set of a variational inequality and the fixed point set of a quasi-nonexpansive map** with a demiclosedness property. The weak convergence of the algorithms are established under standard assumptions imposed on cost operators. The proposed algorithms can be considered as an improvement of the previously known inertial extragradient method over each computational step. Finally, for supporting the convergence of the proposed algorithms, we also consider several preliminary numerical experiments on a test problem.

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Acknowledgments

The authors are grateful to the anonymous referees for valuable suggestions which helped to improve the manuscript.

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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, College of Air Force, Nha Trang, Vietnam

    Dang Van Hieu

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  1. Duong Viet Thong
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  2. Dang Van Hieu
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Correspondence to Duong Viet Thong.

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Thong, D.V., Hieu, D.V. Inertial subgradient extragradient algorithms with line-search process for solving variational inequality problems and fixed point problems. Numer Algor 80, 1283–1307 (2019). https://doi.org/10.1007/s11075-018-0527-x

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