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Revisiting the extragradient method for finding the minimum-norm solution of non-Lipschitzian pseudo-monotone variational inequalities

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Abstract

In this paper, we propose a new version of the extragradient method for solving non-Lipschitzian and pseudo-monotone variational inequalities in real Hilbert spaces. First, we show that the proposed method converges strongly to the minimum-norm solution of a variational inequality under mild assumptions. Second, we obtain a linear convergence rate of this algorithm under strong pseudo-monotonicity and Lipschitz continuity assumptions. Our results improve some recent contributions in the literature on the extragradient method. Finally, we illustrate the performance of proposed algorithm by some numerical results.

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Acknowledgements

The authors would like to thank Associate Editor and anonymous reviewers for their comments on the manuscript which helped us very much in improving and presenting the original version of this paper.

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Correspondence to Duong Viet Thong.

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Communicated by Orizon Pereira Ferreira.

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Thong, D.V., Li, X., Dong, QL. et al. Revisiting the extragradient method for finding the minimum-norm solution of non-Lipschitzian pseudo-monotone variational inequalities. Comp. Appl. Math. 41, 186 (2022). https://doi.org/10.1007/s40314-022-01887-2

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  • DOI: https://doi.org/10.1007/s40314-022-01887-2

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