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Strong convergence theorem for a new Bregman extragradient method with a different line-search process for solving variational inequality problems in reflexive Banach spaces

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Abstract

In this paper, we introduce a new Bregman extragradient method with a different line-search process for solving variational inequality problems in reflexive Banach spaces. Precisely, we prove that the sequence generated by our proposed iterative algorithm converges strongly to an element of the solution sets of variational inequality problems. Moreover, some numerical examples are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature.

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Acknowledgements

This work was supported by the NSF of China (Grant No 12171435).

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Authors and Affiliations

  1. School of Marxism, Chongqing Normal University, Chongqing, 401331, China

    Shaotao Hu

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Shaotao Hu & Yuanheng Wang

  3. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

    Ping Jing

  4. College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Qiao-Li Dong

Authors
  1. Shaotao Hu
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  2. Yuanheng Wang
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  3. Ping Jing
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  4. Qiao-Li Dong
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Correspondence to Shaotao Hu or Yuanheng Wang.

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Hu, S., Wang, Y., Jing, P. et al. Strong convergence theorem for a new Bregman extragradient method with a different line-search process for solving variational inequality problems in reflexive Banach spaces. Optim Lett 18, 783–801 (2024). https://doi.org/10.1007/s11590-023-02019-3

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  • DOI: https://doi.org/10.1007/s11590-023-02019-3

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