Abstract
This article is concerned with a universal version of projected reflected gradient method with new step size for solving variational inequality problem in Hilbert spaces. Under appropriate assumptions controlled by the operators and parameters, we acquire the weak convergence of the proposed algorithm. Moreover, we establish an R-linear convergence rate of our method on the condition that the relevant mapping is strongly monotone. We rework our first algorithm so that it can be simplified to several generalized methods in the literature. The efficacy and availability of our proposed iterative scheme are demonstrated in numerical experiments.
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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) and the Natural Science Foundation of Chongqing (Grant No. CSTB2022NSCQ-JQX0004).
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Zhou and Cai wrote the main manuscript text, Tan and Dong finished the numerical examples. All authors reviewed the manuscript.
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Zhou, X., Cai, G., Tan, B. et al. A modified generalized version of projected reflected gradient method in Hilbert spaces. Numer Algor 95, 117–147 (2024). https://doi.org/10.1007/s11075-023-01566-1
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DOI: https://doi.org/10.1007/s11075-023-01566-1