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

2021 ◽  
Vol 41 (1) ◽  
Author(s):  
Habibu Abdullahi ◽  
A. K. Awasthi ◽  
Mohammed Yusuf Waziri ◽  
Abubakar Sani Halilu
Keyword(s):  
Conjugate Gradient ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Monotone Equations

scholarly journals Sufficient Descent Conjugate Gradient Methods for Solving Convex Constrained Nonlinear Monotone Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
San-Yang Liu ◽  
Yuan-Yuan Huang ◽  
Hong-Wei Jiao
Keyword(s):  
Global Convergence ◽  
Projection Method ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Monotone Equations ◽  
Mild Conditions ◽  
Sufficient Descent ◽  
Nonlinear Monotone Equations

Two unified frameworks of some sufficient descent conjugate gradient methods are considered. Combined with the hyperplane projection method of Solodov and Svaiter, they are extended to solve convex constrained nonlinear monotone equations. Their global convergence is proven under some mild conditions. Numerical results illustrate that these methods are efficient and can be applied to solve large-scale nonsmooth equations.

Modified Hager–Zhang conjugate gradient methods via singular value analysis for solving monotone nonlinear equations with convex constraint

2020 ◽  
pp. 2050043
Author(s):  
Jamilu Sabi’u ◽  
Abdullah Shah ◽  
Mohammed Yusuf Waziri ◽  
Kabiru Ahmed
Keyword(s):  
Conjugate Gradient ◽  
Gradient Methods ◽  
Singular Value ◽  
Recent Attempt ◽  
Conjugate Gradient Methods ◽  
Projection Technique ◽  
Value Analysis ◽  
Convex Constraint ◽  
Numerical Examples ◽  
Monotone Equations

Following a recent attempt by Waziri et al. [2019] to find an appropriate choice for the nonnegative parameter of the Hager–Zhang conjugate gradient method, we have proposed two adaptive options for the Hager–Zhang nonnegative parameter by analyzing the search direction matrix. We also used the proposed parameters with the projection technique to solve convex constraint monotone equations. Furthermore, the global convergence of the methods is proved using some proper assumptions. Finally, the efficacy of the proposed methods is demonstrated using a number of numerical examples.

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