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Modified Extragradient Method for Pseudomonotone Variational Inequalities in Infinite Dimensional Hilbert Spaces

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Abstract

In this paper, we prove the weak convergence of a modified extragradient algorithm for solving a variational inequality problem involving a pseudomonotone operator in an infinite dimensional Hilbert space. Moreover, we establish further the R-linear rate of the convergence of the proposed algorithm with the assumption of error bound. Several numerical experiments are performed to illustrate the convergence behaviour of the new algorithm in comparisons with others. The results obtained in the paper have extended some recent results 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 research of the first author was supported by the National Foundation for Science and Technology Development (NAFOSTED) of Vietnam under grant number 101.01-2020.06. The third author was supported by the National Natural Science Foundation of China under grant number 11771067 and the Applied Basic Project of Sichuan Province with grant number 2019YJ0204.

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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. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, People’s Republic of China

    Yeol Je Cho & Yi-Bin Xiao

  3. Department of Mathematics Education, Gyeongsang National University, Jinju, 52828, Korea

    Yeol Je Cho

  4. Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thrung Khru, Bangkok, 10140, Thailand

    Poom Kumam

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  1. Dang Van Hieu
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  2. Yeol Je Cho
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  3. Yi-Bin Xiao
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  4. Poom Kumam
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Correspondence to Dang Van Hieu.

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Van Hieu, D., Cho, Y.J., Xiao, YB. et al. Modified Extragradient Method for Pseudomonotone Variational Inequalities in Infinite Dimensional Hilbert Spaces. Vietnam J. Math. 49, 1165–1183 (2021). https://doi.org/10.1007/s10013-020-00447-7

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