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A hybrid three-term conjugate gradient projection method for constrained nonlinear monotone equations with applications

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Abstract

In this paper, based on the three-term conjugate gradient method and the hybrid technique, we propose a hybrid three-term conjugate gradient projection method by incorporating the adaptive line search for solving large-scale nonlinear monotone equations with convex constraints. The search direction generated by the proposed method is close to the one yielded by the memoryless BFGS method, and has the sufficient descent property and the trust region property independent of line search technique. Under some mild conditions, we establish the global convergence of the proposed method. Our numerical experiments show the effectiveness and robustness of the proposed method in comparison with two existing algorithms in the literature. Moreover, we show applicability and encouraging efficiency of the proposed method by extending it to solve sparse signal restoration and image de-blurring problems.

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Acknowledgments

The authors wish to thank the three anonymous referees for their very professional comments and quite useful suggestions, which greatly helped us to improve the original version of this paper.

Funding

This work was supported by the National Natural Science Foundation of China (11771383), the Natural Science Foundation of Guangxi Province (2018GXNSFAA281099), the Research Project of Guangxi University for Nationalities (2018KJQD02), and the Middle-aged and Young Teachers’ Basic Ability Promotion Project of Guangxi Province (2018KY0700) of China.

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Authors and Affiliations

  1. School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, China

    Jianghua Yin

  2. College of Mathematics and Physics, Guangxi University for Nationalities, Nanning, 530006, China

    Jinbao Jian & Xianzhen Jiang

  3. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Meixing Liu

  4. School of Mechanical and Electrical Engineering, Guangxi Science and Technology Normal University, Laibin, 546199, China

    Lingzhi Wang

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  1. Jianghua Yin
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Correspondence to Jinbao Jian.

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Yin, J., Jian, J., Jiang, X. et al. A hybrid three-term conjugate gradient projection method for constrained nonlinear monotone equations with applications. Numer Algor 88, 389–418 (2021). https://doi.org/10.1007/s11075-020-01043-z

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