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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| Published in | Arabian Journal of Mathematics Vol. 7; no. 4; pp. 289 - 301 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.12.2018
Springer Springer Nature B.V |
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| Abstract | 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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| AbstractList | 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. 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. Mathematics Subject Classification 90C30 * 90C56 * 65K05 * 65K10 |
| Audience | Academic |
| Author | Koorapetse, Mompati S. Kaelo, P. |
| Author_xml | – sequence: 1 givenname: Mompati S. surname: Koorapetse fullname: Koorapetse, Mompati S. organization: Department of Mathematics, University of Botswana – sequence: 2 givenname: P. surname: Kaelo fullname: Kaelo, P. email: kaelop@mopipi.ub.bw organization: Department of Mathematics, University of Botswana |
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| SubjectTerms | Benchmarking Convergence Convergence (Mathematics) Mathematical analysis Mathematical research Mathematics Mathematics and Statistics Nonlinear differential equations Nonlinear equations Nonlinear programming Nonlinear systems |
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| Title | Globally convergent three-term conjugate gradient projection methods for solving nonlinear monotone equations |
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