Two Descent Dai-Yuan Conjugate Gradient Methods for Systems of Monotone Nonlinear Equations

In this paper, we present two Dai-Yuan type iterative methods for solving large-scale systems of nonlinear monotone equations. The methods can be considered as extensions of the classical Dai-Yuan conjugate gradient method for unconstrained optimization. By employing two different approaches, the Da...

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Bibliographic Details
Published in:Journal of scientific computing Vol. 90; no. 1; p. 36
Main Authors: Waziri, Mohammed Yusuf, Ahmed, Kabiru
Format: Journal Article
Language:English
Published: New York Springer US 01.01.2022
Springer Nature B.V
Subjects:
Algorithms
Approximation
Computational Mathematics and Numerical Analysis
Conjugate gradient method
Eigenvalues
Hyperplanes
Iterative methods
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Nonlinear equations
Nonlinear systems
Optimization
Searching
Theoretical
Line search
90C53
Projection operator
90C30
65K05
49M37
Inexact line search
Nonlinear monotone systems
15A18
ISSN:0885-7474, 1573-7691
Online Access:Get full text
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Summary:In this paper, we present two Dai-Yuan type iterative methods for solving large-scale systems of nonlinear monotone equations. The methods can be considered as extensions of the classical Dai-Yuan conjugate gradient method for unconstrained optimization. By employing two different approaches, the Dai-Yuan method is modified to develop two different search directions, which are combined with the hyperplane projection technique of Solodov and Svaiter. The first search direction was obtained by carrying out eigenvalue study of the search direction matrix of an adaptive DY scheme, while the second is obtained by minimizing the distance between two adaptive versions of the DY method. Global convergence of the methods are established under mild conditions and preliminary numerical results show that the proposed methods are promising and more effective compared to some existing methods in the literature.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-021-01713-7