SIGNAL RECOVERY WITH CONSTRAINED MONOTONE NONLINEAR EQUATIONS THROUGH AN EFFECTIVE THREE-TERM CONJUGATE GRADIENT METHOD

Peiting Gao; Wen Zheng; Tao Wang; Yifei Li; Futong Li

doi:10.11948/20220335

2023 Volume 13 Issue 4

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Article navigation > Journal of Applied Analysis & Computation > 2023 > 13(4): 2006-2025

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Peiting Gao, Wen Zheng, Tao Wang, Yifei Li, Futong Li. SIGNAL RECOVERY WITH CONSTRAINED MONOTONE NONLINEAR EQUATIONS THROUGH AN EFFECTIVE THREE-TERM CONJUGATE GRADIENT METHOD[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 2006-2025. doi: 10.11948/20220335

Citation:

Peiting Gao, Wen Zheng, Tao Wang, Yifei Li, Futong Li. SIGNAL RECOVERY WITH CONSTRAINED MONOTONE NONLINEAR EQUATIONS THROUGH AN EFFECTIVE THREE-TERM CONJUGATE GRADIENT METHOD[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 2006-2025. doi: 10.11948/20220335

SIGNAL RECOVERY WITH CONSTRAINED MONOTONE NONLINEAR EQUATIONS THROUGH AN EFFECTIVE THREE-TERM CONJUGATE GRADIENT METHOD

1.
College of Computer Science and Technology(College of Data Science), Taiyuan University of Technology, No. 79 West Street Yingze, Taiyuan 030024, China

Corresponding authors: Email: gaopeiting3680@163.com (P. Gao); Email: zhengwen@tyut.edu.cn (W. Zheng)
Fund Project: This research was partially supported by the Natural Science Foundation of Shanxi Province, China(No. 202203021212255)

Abstract

Abstract

In this paper, we introduce a three-term conjugate gradient-type projection method for solving constrained monotone nonlinear equations. In this method, we firstly undertake the transformation of the relative matrices proposed by Yao and Ning. Secondly, we obtain the new relative matrices involving two parameters. Subsequently, we construct a relationship for the two parameters via the quasi-Newton equation and obtain the parameters by simplifying maximum eigenvalue of the new relative matrices. Finally, combining the three-term conjugate gradient method with projection technique, we establish an efficient three-term conjugate gradient-type projection algorithm. Meanwhile, we also give some theoretical analysis about the global convergence and R-linear convergence of the proposed algorithm under quite reasonable technical assumptions. Performance comparisons show that our proposed method is competitive and efficient for solving large-scale nonlinear monotone equations with convex constraints. Furthermore, the presented algorithm is also applied to recovery of a sparse signal in compressive sensing, and obtain practical, efficient and competitive performance in comparing with state-of-the-art algorithms.
- Quasi-Newton equation /
- conjugate gradient method /
- global convergence /
- signal recovery
MSC: 65F10, 90C52, 65K05

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References

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