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Strong convergence of Bregman projection method for solving variational inequality problems in reflexive Banach spaces

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Abstract

This paper aims to introduce a new projection method for solving pseudomonotone variational inequality problems in real reflexive Banach spaces. The main algorithm is based on the self-adaptive method, subgradient extragradient method and Bregman projection method. Under some appropriate assumptions imposed on the parameters, we prove a strong convergence theorem of the proposed algorithm. Finally, several numerical examples are given to show that our method has better convergence performance than the known results in the literatures.

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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. cstc2020jcyj-msxmX0455, 2022NSCQ-JQX2745), Science and Technology Project of Chongqing Education Committee (Grant No. KJZD-K201900504), and the Program of Chongqing Innovation Research Group Project in University (Grant No. CXQT19018).

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Authors and Affiliations

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

    Zhongbing Xie & Gang Cai

  2. Tianjin Key Laboratory for Advanced Signal Processing and College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Qiao-Li Dong

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  1. Zhongbing Xie
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  2. Gang Cai
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Correspondence to Gang Cai.

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Xie and Cai wrote the main manuscript text and Dong finished the numerical examples. All authors reviewed the manuscript.

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Xie, Z., Cai, G. & Dong, QL. Strong convergence of Bregman projection method for solving variational inequality problems in reflexive Banach spaces. Numer Algor 93, 269–294 (2023). https://doi.org/10.1007/s11075-022-01414-8

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