Scaled Three-Term Conjugate Gradient Methods for Solving Monotone Equations with Application

In this paper, we derived a modified conjugate gradient (CG) parameter by adopting the Birgin and Marti´nez strategy using the descent three-term CG direction and the Newton direction. The proposed CG parameter is applied and suggests a robust algorithm for solving constrained monotone equations wit...

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Bibliographic Details
Published in:Symmetry (Basel) Vol. 14; no. 5; p. 936
Main Authors: Sabi’u, Jamilu, Aremu, Kazeem Olalekan, Althobaiti, Ali, Shah, Abdullah
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.05.2022
Subjects:
Algorithms
Conjugate gradient method
Image restoration
Methods
Nonlinear equations
Parameter modification
Robustness (mathematics)
ISSN:2073-8994, 2073-8994
Online Access:Get full text
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Summary:In this paper, we derived a modified conjugate gradient (CG) parameter by adopting the Birgin and Marti´nez strategy using the descent three-term CG direction and the Newton direction. The proposed CG parameter is applied and suggests a robust algorithm for solving constrained monotone equations with an application to image restoration problems. The global convergence of this algorithm is established using some proper assumptions. Lastly, the numerical comparison with some existing algorithms shows that the proposed algorithm is a robust approach for solving large-scale systems of monotone equations. Additionally, the proposed CG parameter can be used to solve the symmetric system of nonlinear equations as well as other relevant classes of nonlinear equations.
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content type line 14
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14050936