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A modified generalized version of projected reflected gradient method in Hilbert spaces

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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 map** 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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Authors and Affiliations

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    **aolin Zhou & Gang Cai

  2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Bing Tan

  3. Tian** Key Laboratory for Advanced Signal Processing and College of Science, Civil Aviation University of China, Tian**, 300300, China

    Qiao-Li Dong

Authors
  1. **aolin Zhou
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  2. Gang Cai
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  3. Bing Tan
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  4. Qiao-Li Dong
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Contributions

Zhou and Cai wrote the main manuscript text, Tan and Dong finished the numerical examples. All authors reviewed the manuscript.

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Correspondence to Gang Cai.

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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

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