Globally convergent three-term conjugate gradient projection methods for solving nonlinear monotone equations

In this paper, we propose two derivative-free conjugate gradient projection methods for systems of large-scale nonlinear monotone equations. The proposed methods are shown to satisfy the sufficient descent condition. Furthermore, the global convergence of the proposed methods is established. The pro...

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Bibliographic Details
Published inArabian Journal of Mathematics Vol. 7; no. 4; pp. 289 - 301
Main Authors Koorapetse, Mompati S., Kaelo, P.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2018
Springer
Springer Nature B.V
Subjects
Benchmarking
Convergence
Convergence (Mathematics)
Mathematical analysis
Mathematical research
Mathematics
Mathematics and Statistics
Nonlinear differential equations
Nonlinear equations
Nonlinear programming
Nonlinear systems
65K10
90C30
65K05
90C56
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Summary:In this paper, we propose two derivative-free conjugate gradient projection methods for systems of large-scale nonlinear monotone equations. The proposed methods are shown to satisfy the sufficient descent condition. Furthermore, the global convergence of the proposed methods is established. The proposed methods are then tested on a number of benchmark problems from the literature and preliminary numerical results indicate that the proposed methods can be efficient for solving large scale problems and therefore are promising.
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ISSN:2193-5343
2193-5351
2193-5351
DOI:10.1007/s40065-018-0206-8