A family of three-term conjugate gradient projection methods with a restart procedure and their relaxed-inertial extensions for the constrained nonlinear pseudo-monotone equations with applications

Al-Baali et al. ( Comput. Optim. Appl. 60:89–110, 2015) have proposed a three-term conjugate gradient method which satisfies a sufficient descent condition and global convergence. In this paper, we extend this method to a family of three-term conjugate gradient projection methods with a restart proc...

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Bibliographic Details
Published in:Numerical algorithms Vol. 94; no. 3; pp. 1055 - 1083
Main Authors: Liu, Pengjie, Shao, Hu, Yuan, Zihang, Wu, Xiaoyu, Zheng, Tianlei
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2023
Springer Nature B.V
Subjects:
Algebra
Algorithms
Computer Science
Conjugate gradient method
Continuity (mathematics)
Convergence
Iterative methods
Mathematical analysis
Methods
Nonlinear equations
Numeric Computing
Numerical Analysis
Optimization
Original Paper
Regression analysis
Theory of Computation
Logistic regression
Global convergence
65K05
90C30
90C56
Nonlinear pseudo-monotone equations
Relaxed-inertial strategy
Conjugate gradient projection method
Compressed sensing
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:Al-Baali et al. ( Comput. Optim. Appl. 60:89–110, 2015) have proposed a three-term conjugate gradient method which satisfies a sufficient descent condition and global convergence. In this paper, we extend this method to a family of three-term conjugate gradient projection methods with a restart procedure and their relaxed-inertial versions for constrained nonlinear pseudo-monotone equations. The accelerated gradient-descent method MSM and the relaxed-inertial strategy are incorporated into the proposed methods to obtain better computational performance. The global convergence of the extended methods are established theoretically without the Lipschitz continuity of the underlying mapping. Numerical results on constrained nonlinear equations show that the extended methods with different settings are efficient. The applicability and efficiency of the extended methods in the regularized decentralized logistic regression and sparse signal restoration problems are also presented and verified.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-023-01527-8