R-linear convergence analysis of inertial extragradient algorithms for strongly pseudo-monotone variational inequalities

Vuong, Phan Tu and Duong, Thong (2022) R-linear convergence analysis of inertial extragradient algorithms for strongly pseudo-monotone variational inequalities. Journal of Computational and Applied Mathematics, 406, [114003]. (doi:10.1016/j.cam.2021.114003).

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Abstract

Some extragradient-type algorithms with inertial effect for solving strongly pseudo-monotone variational inequalities have been proposed and investigated recently. While the convergence of these algorithms was established, it is unclear if the linear rate is guaranteed. In this paper, we provide R-linear convergence analysis for two extragradient-type algorithms for solving strongly pseudo-monotone, Lipschitz continuous variational inequality in Hilbert spaces. The linear convergence rate is obtained without the prior knowledge of the Lipschitz constants of the variational inequality mapping and the stepsize is bounded from below by a positive number. Some numerical results are provided to show the computational effectiveness of the algorithms.

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e-pub ahead of print date: 21 December 2021

Published date: 1 May 2022

Additional Information: Funding Information: The authors are very thankful to both anonymous referees and the Principal Editor, Prof. Andre A. Keller, for their careful reading and constructive comments, which helped improving the presentation of the paper. This work was supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) project 101.01-2019.320 . Publisher Copyright: © 2021 Elsevier B.V.

Keywords: Forward–backward–forward method, Inertial subgradient extragradient method, Lipschitz continuity, R-linear rate, Strongly pseudo-monotone mapping