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A new hybrid CGPM-based algorithm for constrained nonlinear monotone equations with applications

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Abstract

The conjugate gradient projection method (CGPM) has good theoretical properties and numerical performance for solving large-scale nonlinear monotone equations with convex constraints. In this paper, by designing a modified adaptive line search, a new hybrid CGPM-based algorithm is proposed. The search direction satisfies the sufficient descent and trust region properties which are independent of the choices of the line search. The global convergence of the algorithm is analyzed without the Lipschitz continuity. The linear convergence rate is established under some appropriate assumptions. Some preliminary numerical experiment results are reported, which show that our proposed algorithm is promising. Finally, the proposed algorithm is extended to solve the sparse signal and image restoration problems in compressed sensing.

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Funding

This work was supported by the National Natural Science Foundation of China (12261008), the Natural Science Foundation of Guangxi Province (2023GXNSFAA026158), the Xiangsihu Young Scholars Innovative Research Team of Guangxi Minzu University(2022GXUNXSHQN04) and the Guangxi Scholarship Fund of Guangxi Education Department (GED)

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Authors and Affiliations

  1. School of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning, 530006, Guangxi, China

    Guodong Ma, Liqi Liu & Jinbao Jian

  2. School of Mathematics and Statistics, Taiyuan Normal University, Jinzhong, 030619, Shanxi, China

    Xihong Yan

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  1. Guodong Ma
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  2. Liqi Liu
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  3. Jinbao Jian
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  4. Xihong Yan
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Correspondence to Jinbao Jian.

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Ma, G., Liu, L., Jian, J. et al. A new hybrid CGPM-based algorithm for constrained nonlinear monotone equations with applications. J. Appl. Math. Comput. 70, 103–147 (2024). https://doi.org/10.1007/s12190-023-01960-x

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