Descent three-term DY-type conjugate gradient methods for constrained monotone equations with application

As it is known that, not all conjugate gradient (CG) methods satisfy descent property, a necessary condition for attaining global convergence result. In this article, we propose three different sufficient-descent conjugate gradient projection algorithms for constrained monotone equations. Using Dai–...

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Bibliographic Details
Published in:Computational & applied mathematics Vol. 41; no. 1
Main Authors: Abdullahi, Habibu, Awasthi, A. K., Waziri, Mohammed Yusuf, Halilu, Abubakar Sani
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.02.2022
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Conjugate gradient method
Convergence
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Nonlinear equations
Performance assessment
Projection method
Constrained-monotone nonlinear equations
Compressive sensing
65K05
34G20H18
65D32
Descent conjugate gradient
90C05
ISSN:2238-3603, 1807-0302
Online Access:Get full text
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Summary:As it is known that, not all conjugate gradient (CG) methods satisfy descent property, a necessary condition for attaining global convergence result. In this article, we propose three different sufficient-descent conjugate gradient projection algorithms for constrained monotone equations. Using Dai–Yuan (DY) conjugate gradient parameter, we generate three satisfied sufficient-descent directions. Under suitable conditions, global convergence of the algorithms is established. Numerical examples using benchmark test functions indicate that the algorithms are effective for solving constrained monotone nonlinear equations. Moreover, we also extend the method to solve ℓ 1 -norm regularized problems to decode a sparse signal in compressive sensing. Performance comparisons show that the proposed methods are practical, efficient and competitive with the compared methods.
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ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-021-01724-y