Convergence Analysis of a New Bregman Extragradient Method for Solving Fixed Point Problems and Variational Inequality Problems in Reflexive Banach Spaces

We mainly introduce a new self-adaptive extragradient method by using the inertial technique for solving variational inequality problems of pseudomonotone operators and fixed point problems of Bregman relatively nonexpansive mappings in real reflexive Banach spaces. Precisely, we show that the seque...

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Bibliographic Details
Published in:Journal of scientific computing 2023-07, Vol.96 (1), p.19, Article 19
Main Authors: Hu, Shaotao, Wang, Yuanheng, Dong, Qiao-Li
Format: Article
Language:English
Subjects:
Algorithms
Banach spaces
Computational Mathematics and Numerical Analysis
Convergence
Iterative methods
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Partial differential equations
Theoretical
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Summary:We mainly introduce a new self-adaptive extragradient method by using the inertial technique for solving variational inequality problems of pseudomonotone operators and fixed point problems of Bregman relatively nonexpansive mappings in real reflexive Banach spaces. Precisely, we show that the sequence generated by our iterative process converges strongly to a common element for the solution set of variational inequality problems and the set of fixed points of Bregman relatively nonexpansive mappings. Additionally, some numerical examples are given to show the effectiveness of our algorithm. The results obtained in this paper are the improvement and supplement of many recent ones in the field.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-023-02243-0