Global convergence result for conjugate gradient methods

1991 ◽  
Vol 71 (2) ◽  
pp. 399-405 ◽  
Author(s):  
Y. F. Hu ◽  
C. Storey
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient ◽  
Gradient Methods ◽  
Convergence Result ◽  
Conjugate Gradient Methods

scholarly journals A New Modified Three-Term Hestenes–Stiefel Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Bakhtawar Baluch ◽  
Zabidin Salleh ◽  
Ahmad Alhawarat
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Sufficient Descent Property ◽  
Descent Property ◽  
Sufficient Descent

This paper describes a modified three-term Hestenes–Stiefel (HS) method. The original HS method is the earliest conjugate gradient method. Although the HS method achieves global convergence using an exact line search, this is not guaranteed in the case of an inexact line search. In addition, the HS method does not usually satisfy the descent property. Our modified three-term conjugate gradient method possesses a sufficient descent property regardless of the type of line search and guarantees global convergence using the inexact Wolfe–Powell line search. The numerical efficiency of the modified three-term HS method is checked using 75 standard test functions. It is known that three-term conjugate gradient methods are numerically more efficient than two-term conjugate gradient methods. Importantly, this paper quantifies how much better the three-term performance is compared with two-term methods. Thus, in the numerical results, we compare our new modification with an efficient two-term conjugate gradient method. We also compare our modification with a state-of-the-art three-term HS method. Finally, we conclude that our proposed modification is globally convergent and numerically efficient.

scholarly journals Global Convergence Properties of Conjugate Gradient Methods for Optimization

1992 ◽  
Vol 2 (1) ◽  
pp. 21-42 ◽  
Author(s):  
Jean Charles Gilbert ◽  
Jorge Nocedal
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Convergence Properties

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.

Some descent three-term conjugate gradient methods and their global convergence

2007 ◽  
Vol 22 (4) ◽  
pp. 697-711 ◽  
Author(s):  
Li Zhang ◽  
Weijun Zhou ◽  
Donghui Li
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient ◽  
Gradient Methods ◽  
Conjugate Gradient Methods
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