Three-Term Hager–Zhang Projection Method for Monotone Nonlinear Equations

In this paper, a conjugate gradient method combined with the projection technique of Solodov and Svaiter (Kluwer Academic Publishers, pp. 355–369, 1998 ) to solve monotone nonlinear equations is presented. The proposed method improved the numerical performance of the Hager–Zhang (HZ) method proposed...

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Bibliographic Details
Published in:Vietnam journal of mathematics Vol. 53; no. 1; pp. 109 - 130
Main Authors: Halilu, Abubakar Sani, Majumder, Arunava, Waziri, Mohammed Yusuf, Ahmed, Kabiru, Murtala, Salisu
Format: Journal Article
Language:English
Published: Singapore Springer Nature Singapore 01.01.2025
Springer Nature B.V
Subjects:
Algorithms
Conjugate gradient method
Mathematics
Mathematics and Statistics
Methods
Nonlinear equations
Optimization
Original Article
Value analysis
Conjugate gradient method
Primary 65K05
90C53
Hager–Zhang parameter
Global convergence
Numerical experiment
Secondary 90C30
Monotone nonlinear equations
ISSN:2305-221X, 2305-2228
Online Access:Get full text
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Summary:In this paper, a conjugate gradient method combined with the projection technique of Solodov and Svaiter (Kluwer Academic Publishers, pp. 355–369, 1998 ) to solve monotone nonlinear equations is presented. The proposed method improved the numerical performance of the Hager–Zhang (HZ) method proposed by Waziri et al. (Appl. Math. Comput. 361 , 645–660, 2019 ), by extending its direction to three-term conjugate gradient direction. The proposed method has been shown to be globally convergent under some mild conditions. Numerical experiments show that the proposed method is effective and produces better results than some existing methods.
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ISSN:2305-221X
2305-2228
DOI:10.1007/s10013-023-00639-x