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A convergence analysis of hybrid gradient projection algorithm for constrained nonlinear equations with applications in compressed sensing

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Abstract

In this paper, we propose a projection-based hybrid spectral gradient algorithm for nonlinear equations with convex constraints, which is based on a certain line search strategy. Convex combination technique is used to design a novel spectral parameter that is inspired by some classical spectral gradient methods. The search direction also meets the sufficient descent condition and trust region feature. The global convergence of the proposed algorithm has been established under reasonable assumptions. The results of the experiment demonstrate the proposed algorithm is both more promising and robust than some similar methods, and it is also capable of handling large-scale optimization problems. Furthermore, we apply it to problems involving sparse signal recovery and blurred image restoration.

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

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Acknowledgements

The authors are very much indebted and grateful to the editors and anonymous referees for their valuable comments and suggestions which improved the quality of this paper.

Funding

This work is supported by the Guangdong Provincial Department of Education as a scientific research project (2022KQNCX136), the National Natural Science Foundation of China (11661001, 11661009), and the Natural Science Foundation of Guangxi Province of China (2020GXNSFAA159069).

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou, Guangdong, 511399, China

    Dandan Li

  2. School of Mathematics and Statistics, Baise University, Baise, Guangxi, 533099, China

    Songhua Wang & Yong Li

  3. School of Electronics and Information Engineering, Harbin Institute of Technology (Shenzhen), Shenzhen, Guangdong, 518071, China

    Jiaqi Wu

Authors
  1. Dandan Li
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  2. Songhua Wang
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  3. Yong Li
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  4. Jiaqi Wu
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Contributions

Study conception and design: Dandan Li, Jiaqi Wu. Convergence analysis: Dandan Li, Songhua Wang. Performing numerical experiment: Dandan Li, Yong Li, Jiaqi Wu. Draft manuscript preparation: Dandan Li, Jiaqi Wu. All authors reviewed the results and approved the final version of the manuscript.

Corresponding author

Correspondence to Jiaqi Wu.

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Li, D., Wang, S., Li, Y. et al. A convergence analysis of hybrid gradient projection algorithm for constrained nonlinear equations with applications in compressed sensing. Numer Algor 95, 1325–1345 (2024). https://doi.org/10.1007/s11075-023-01610-0

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  • DOI: https://doi.org/10.1007/s11075-023-01610-0

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