Abstract
In this paper, we propose a method for efficiently obtaining an approximate solution for constrained nonlinear monotone operator equations. The search direction of the proposed method closely aligns with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) direction, known for its low storage requirement. Notably, the search direction is shown to be sufficiently descent and bounded without using the line search condition. Furthermore, under some standard assumptions, the proposed method converges globally. As an application, the proposed method is applied to solve image restoration problems. The efficiency and robustness of the method in comparison to other methods are tested by numerical experiments using some test problems.
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Acknowledgements
The authors would like to express their sincere thanks to the editor and referees for the valuable comments and helpful suggestions, which help to improve the paper. The first author also acknowledges with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University. Also, the second author is grateful to King Fahd University of Petroleum and Minerals for providing excellent research facilities.
Funding
The corresponding author is partially supported by the Natural Science Foundation of China (12071379), the Natural Science Foundation of Chongqing (cstc2021jcyj-msxmX0925, cstc2022ycjh-bgzxm0097), the Youth Project of Science and Technology Research Program of Chongqing Education Commission of China (KJQN202201802).
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A.B. Abubakar: Investigation, Software, Writing-original draft. A.H. Ibrahim: Methodology. M. Abdullahi: Methodology. M. Aphane: Methodology. J.W. Chen: Conceptualization, Methodology, Revising, Writing-review & editing. All authors contributed equally to this article.
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Abubakar, A.B., Ibrahim, A.H., Abdullahi, M. et al. A sufficient descent LS-PRP-BFGS-like method for solving nonlinear monotone equations with application to image restoration. Numer Algor 96, 1423–1464 (2024). https://doi.org/10.1007/s11075-023-01673-z
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DOI: https://doi.org/10.1007/s11075-023-01673-z