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A conjugate gradient projection method with restart procedure for solving constraint equations and image restorations

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Abstract

The conjugate gradient projection method is one of the most effective methods for solving large-scale nonlinear monotone convex constrained equations. In this paper, a new search direction with restart procedure is proposed, and a self-adjusting line search criterion is improved, then a three-term conjugate gradient projection method is designed to solve the large-scale nonlinear monotone convex constrained equations and image restorations. Without using the Lipschitz continuity of these equations, the presented method is proved to be globally convergent. Moreover, its R-linear convergence rate is attained under Lipschitz continuity and the usual assumptions. Finally, large-scale numerical experiments for the convex constraint equations and image restorations have been performed, which show that the new method is effective.

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Authors and Affiliations

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

    Xianzhen Jiang, Zefeng Huang & Huihui Yang

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  2. Zefeng Huang
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Correspondence to Xianzhen Jiang.

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Project supported by the National Natural Science Foundation of China (Grant Nos.12361063, 12171106), Guangxi Science and Technology Program (Grant No. AD23023001), the Natural Science Foundation of Guangxi Province (Grant No.2016GXNSFAA380028), and the Research Project of Guangxi Minzu University (Grant No. 2018KJQD02).

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Jiang, X., Huang, Z. & Yang, H. A conjugate gradient projection method with restart procedure for solving constraint equations and image restorations. J. Appl. Math. Comput. 70, 2255–2284 (2024). https://doi.org/10.1007/s12190-024-02044-0

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