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An effective inertial-relaxed CGPM for nonlinear monotone equations

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Abstract

In this paper, we propose an effective inertial-relaxed CGPM by considering the Armijo line search technique proposed by Amini and Kamandi (Numer Algorithms 70:559–570, 2015). The search direction designed possesses good properties. Furthermore, the global convergence is proved in the absence of the Lipschitz continuity. The numerical results on large-scale equations verify that our proposed method is efficient with the lower computational cost. In particular, applying it to sparse signal restoration indicates that the proposed algorithm is promising and competitive.

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Acknowledgements

This work was supported by the Natural Science Foundation of Guangxi Province (2023GXNSFBA026029), Guangxi Science and Technology Program (AD23023001), the Middle-aged and Young Teachers’ Basic Ability Promotion Project of Guangxi Province (2023KY0168), and Research Project of Guangxi Minzu University (2022KJQD03).

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Authors and Affiliations

  1. School of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning, 530006, China

    Jinbao Jian, Zhiwen Ren, Jianghua Yin, Daolan Han & Xiaodi Wu

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  1. Jinbao Jian
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  2. Zhiwen Ren
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  3. Jianghua Yin
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  4. Daolan Han
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  5. Xiaodi Wu
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Correspondence to Jianghua Yin.

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Jian, J., Ren, Z., Yin, J. et al. An effective inertial-relaxed CGPM for nonlinear monotone equations. J. Appl. Math. Comput. 70, 689–710 (2024). https://doi.org/10.1007/s12190-024-01991-y

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