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A new Bregman projection method with a self-adaptive process for solving variational inequality problem in reflexive Banach spaces

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Abstract

In this paper, we mainly propose a new Bregman projection method with a different self-adaptive process for solving variational inequalities in a real reflexive Banach space. Exactly, we obtain that the iterative sequence generated by our new algorithm converges strongly to an element of solution set for the variational inequality problem. Our algorithm is interesting and easy to implement in numerical experiments because it has only one projection and does not need to know the Lipschitz constant of the considered operator in advance. The results obtained in this paper can be considered as an improvement and supplement of many recent ones in the field.

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

    Shaotao Hu & Yuanheng Wang

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

    Ping Jing

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

    Qiao-Li Dong

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  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 Yuanheng Wang.

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Hu, S., Wang, Y., Jing, P. et al. A new Bregman projection method with a self-adaptive process for solving variational inequality problem in reflexive Banach spaces. Optim Lett 17, 935–954 (2023). https://doi.org/10.1007/s11590-022-01909-2

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