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A New Halpern-Type Bregman Projection Method for Solving Variational Inequality Problems in Reflexive Banach Space

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Abstract

This paper proposes a new Halpern-type inertial subgradient extragradient method with Bregman distance for solving variational inequality problems in a real reflexive Banach space. The proposed algorithm is determined by a self-adaptive technology, which avoids the difficulty of adequately estimating the Lipschitz constant of monotone operators in practical applications. Weak and strong convergence theorems for our algorithm are established, and several numerical experiments are discussed to verify the validity and adaptability.

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Data Availability Statement

The datasets generated during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors thank the reviewers and editors for their constructive comments and valuable suggestions.

Funding

This article was funded by the Natural Science Foundation of Chongqing (cstc2021jcyj-msxmX0177), Science and Technology Research Project of Chongqing Municipal Education Commission (KJQN201900804), and the Graduate Research Innovation Project of Chongqing Technology and Business University  (yjscxx2023-211-71).

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  1. Chongqing Key Laboratory of Social Economy and Applied Statistics College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

    Yan Tang & Yeyu Zhang

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  1. Yan Tang
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  2. Yeyu Zhang
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All authors contributed equally to this work. All authors read and approved final manuscript.

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Correspondence to Yeyu Zhang.

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Tang, Y., Zhang, Y. A New Halpern-Type Bregman Projection Method for Solving Variational Inequality Problems in Reflexive Banach Space. Results Math 78, 168 (2023). https://doi.org/10.1007/s00025-023-01936-0

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