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Modified Extragradient Methods with Inertial Technique for Solving Pseudo-Monotone Variational Inequality Problems

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Abstract

In this paper, based on Mann-type and Halpern-type algorithms, we introduce two modified extragradient algorithms with novel stepsize rules and inertial technique for solving pseudo-monotone variational inequality problems in Hilbert and reflexive Banach spaces. Under some reasonable assumptions on the parameters, strong convergence and R-linear convergence results for our methods are established without prior knowledge of the Lipschitz constant of the bounded operator. Moreover, we provide some numerical experiments to demonstrate the efficiency of our proposed algorithm, and numerical results reveal that our algorithm outruns other algorithms in the literature.

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Acknowledgements

The authors wish to thank the anonymous referees for their valuable comments and suggestions which lead to an improvement of this paper.

Funding

This work was supported by the NSF of China (Grant No. 12171062), the Natural Science Foundation of Chongqing (Grant No.CSTB2022NSCQ-JQX0004), the Chongqing Talent Support program (Grant No. cstc2024ycjh-bgzxm0121) and Science and Technology Project of Chongqing Education Committee (Grant No. KJZD-M202300503) and Postgraduate Scientic Research Innovation Project of Chongqing (Grant No. CYS240367, CYS240354). Moreover, P. Cholamjiak was supported by University of Phayao and Thailand Science Research and Innovation Fund, Thailand (Fundamental Fund 2025, Grant No. 5012/2567).

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Authors and Affiliations

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    Qingqing Fu & Gang Cai

  2. School of Science, University of Phayao, Phayao, 56000, Thailand

    Prasit Cholamjiak & Papatsara Inkrong

Authors
  1. Qingqing Fu
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  2. Gang Cai
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  3. Prasit Cholamjiak
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  4. Papatsara Inkrong
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Contributions

Fu and Cai wrote the main manuscript text, Cholamjiak and Inkrong finished the numerical examples. All authors reviewed the manuscript.

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Correspondence to Gang Cai.

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Fu, Q., Cai, G., Cholamjiak, P. et al. Modified Extragradient Methods with Inertial Technique for Solving Pseudo-Monotone Variational Inequality Problems. J Sci Comput 102, 59 (2025). https://doi.org/10.1007/s10915-024-02784-y

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  • DOI: https://doi.org/10.1007/s10915-024-02784-y

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