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A modified inertial three-term conjugate gradient projection method for constrained nonlinear equations with applications in compressed sensing

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Abstract

In this paper, based on the three-term conjugate gradient projection method and the inertial technique, we propose a modified inertial three-term conjugate gradient projection method for solving nonlinear monotone equations with convex constraints. Embedding the inertial extrapolation step in the design for the search direction, the resulting direction satisfies the sufficient descent property which is independent of any line search rules. The global convergence and Q-linear convergence rate of the proposed algorithm are established under standard conditions. Numerical comparisons with three existing methods demonstrate that the proposed algorithm possesses superior numerical performance and good robustness for solving large-scale equations. Finally, the proposed method is applied to solve the sparse signal problems and image restoration in compressed sensing.

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Funding

This work is supported by the National Natural Science Foundation of China (12171106), the Natural Science Foundation of Guangxi Province (2020GXNSFDA238017) and the Research Foundation of Guangxi Minzu University (2021KJQD04).

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Authors and Affiliations

  1. College of Mathematics and Physics, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Center for Applied Mathematics and Artificial Intelligence, Guangxi Minzu University, Nanning, 530006, People’s Republic of China

    Guodong Ma, Jiachen Jin, Jinbao Jian, Jianghua Yin & Daolan Han

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  1. Guodong Ma
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Correspondence to Jinbao Jian.

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Ma, G., Jin, J., Jian, J. et al. A modified inertial three-term conjugate gradient projection method for constrained nonlinear equations with applications in compressed sensing. Numer Algor 92, 1621–1653 (2023). https://doi.org/10.1007/s11075-022-01356-1

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