scholarly journals A Three-Term Conjugate Gradient Method with Sufficient Descent Property for Unconstrained Optimization

2011 ◽  
Vol 21 (1) ◽  
pp. 212-230 ◽  
Author(s):  
Yasushi Narushima ◽  
Hiroshi Yabe ◽  
John A. Ford
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Sufficient Descent Property ◽  
Descent Property ◽  
Sufficient Descent

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.

A conjugate gradient method with sufficient descent property

2014 ◽  
Vol 70 (2) ◽  
pp. 269-286
Author(s):  
Hao Liu ◽  
Haijun Wang ◽  
Xiaoyan Qian ◽  
Feng Rao
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Sufficient Descent Property ◽  
Descent Property ◽  
Sufficient Descent

A Hybrid Nonlinear Conjugate Gradient Method with Sufficient Descent Property

2011 ◽  
Vol 58-60 ◽  
pp. 943-949
Author(s):  
Wan You Cheng ◽  
Xue Jie Liu
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Numerical Experiments ◽  
Test Problems ◽  
Sufficient Descent Property ◽  
Nonlinear Conjugate Gradient Method ◽  
Descent Property ◽  
Nonlinear Conjugate Gradient ◽  
Sufficient Descent

In this paper, on the basis of the recently developed HZ (Hager-Zhang) method [SIAM J. Optim., 16 (2005), pp. 170-192], we propose a hybrid descent conjugate gradient method which reserves the sufficient descent property of the HZ method. Under suitable conditions, we prove the global convergence of the proposed method. Extensive numerical experiments show that the method is promising for the test problems from the CUTE library.

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