Some nonlinear conjugate gradient methods with sufficient descent condition and global convergence

2014 ◽  
Vol 9 (7) ◽  
pp. 1421-1432 ◽  
Author(s):  
Xiao Liang Dong ◽  
Hongwei Liu ◽  
Yin Ling Xu ◽  
Xi Mei Yang
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Sufficient Descent Condition ◽  
Nonlinear Conjugate Gradient ◽  
Sufficient Descent ◽  
Descent Condition ◽  
Nonlinear Conjugate Gradient Methods

scholarly journals The Sufficient Descent Condition of Nonlinear Conjugate Gradient Method

2018 ◽  
Vol 7 (4.30) ◽  
pp. 458
Author(s):  
Srimazzura Basri ◽  
Mustafa Mamat ◽  
Puspa Liza Ghazali
Keyword(s):  
Conjugate Gradient ◽  
Large Scale ◽  
Gradient Methods ◽  
Sufficient Descent Condition ◽  
Nonlinear Conjugate Gradient Method ◽  
Non Linear ◽  
Nonlinear Conjugate Gradient ◽  
Sufficient Descent ◽  
Descent Condition ◽  
Scale Optimization

Non-linear conjugate gradient methods has been widely used instrumental in solving large scale optimization. These methods has been proved that only required very low memory other than its numerical efficiency. Thus, many studies have been conducted to improve these methods to find the most efficient method. In this paper, we proposed a new non-linear conjugate gradient coefficient that guarantees sufficient descent condition. Numerical tests indicate that the proposed coefficient is better than the three classical conjugate gradient coefficients.

scholarly journals A Hybrid of DL and WYL Nonlinear Conjugate Gradient Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Shengwei Yao ◽  
Bin Qin
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Test Problems ◽  
Conjugate Gradient Methods ◽  
Sufficient Descent Condition ◽  
Nonlinear Conjugate Gradient ◽  
Nonlinear Conjugate Gradient Methods

The conjugate gradient method is an efficient method for solving large-scale nonlinear optimization problems. In this paper, we propose a nonlinear conjugate gradient method which can be considered as a hybrid of DL and WYL conjugate gradient methods. The given method possesses the sufficient descent condition under the Wolfe-Powell line search and is globally convergent for general functions. Our numerical results show that the proposed method is very robust and efficient for the test problems.

GLOBAL CONVERGENCE OF A SPECIAL CASE OF THE DAI–YUAN FAMILY WITHOUT LINE SEARCH

2008 ◽  
Vol 25 (03) ◽  
pp. 411-420 ◽  
Author(s):  
HUI ZHU ◽  
XIONGDA CHEN
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient ◽  
Line Search ◽  
Gradient Methods ◽  
Parameter Family ◽  
Conjugate Gradient Methods ◽  
Objective Functions ◽  
Nonlinear Conjugate Gradient ◽  
Nonlinear Conjugate Gradient Methods ◽  
Special Case

Conjugate gradient methods are efficient to minimize differentiable objective functions in large dimension spaces. Recently, Dai and Yuan introduced a tree-parameter family of nonlinear conjugate gradient methods and show their convergence. However, line search strategies usually bring computational burden. To overcome this problem, in this paper, we study the global convergence of a special case of three-parameter family(the CD-DY family) in which the line search procedures are replaced by fixed formulae of stepsize.

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