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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Vydáno v:Vietnam journal of mathematics Ročník 53; číslo 1; s. 109 - 130
Hlavní autoři: Halilu, Abubakar Sani, Majumder, Arunava, Waziri, Mohammed Yusuf, Ahmed, Kabiru, Murtala, Salisu
Médium: Journal Article
Jazyk:angličtina
Vydáno: Singapore Springer Nature Singapore 01.01.2025
Springer Nature B.V
Témata:
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
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Abstract 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.
AbstractList 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.
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.
Author Majumder, Arunava
Halilu, Abubakar Sani
Murtala, Salisu
Ahmed, Kabiru
Waziri, Mohammed Yusuf
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  organization: Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Department of Mathematics, Sule Lamido University, Numerical Optimization Research Group, Bayero University
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  givenname: Salisu
  surname: Murtala
  fullname: Murtala, Salisu
  organization: Numerical Optimization Research Group, Bayero University, Department of Mathematics, Federal University
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Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2023.
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Issue 1
Keywords Conjugate gradient method
Primary 65K05
90C53
Hager–Zhang parameter
Global convergence
Numerical experiment
Secondary 90C30
Monotone nonlinear equations
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Snippet In this paper, a conjugate gradient method combined with the projection technique of Solodov and Svaiter (Kluwer Academic Publishers, pp. 355–369, 1998 ) to...
In this paper, a conjugate gradient method combined with the projection technique of Solodov and Svaiter (Kluwer Academic Publishers, pp. 355–369, 1998) to...
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StartPage 109
SubjectTerms Algorithms
Conjugate gradient method
Mathematics
Mathematics and Statistics
Methods
Nonlinear equations
Optimization
Original Article
Value analysis
Title Three-Term Hager–Zhang Projection Method for Monotone Nonlinear Equations
URI https://link.springer.com/article/10.1007/s10013-023-00639-x
https://www.proquest.com/docview/3256782882
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