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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**e and Cai wrote the main manuscript text and Dong finished the numerical examples. All authors reviewed the manuscript.
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**e, 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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DOI: https://doi.org/10.1007/s11075-022-01414-8