scholarly journals A Globally Convergent Hybrid Conjugate Gradient Method and Its Numerical Behaviors

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Yuan-Yuan Huang ◽  
San-Yang Liu ◽  
Xue-Wu Du ◽  
Xiao-Liang Dong
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Globally Convergent ◽  
Numerical Performance ◽  
Hybrid Conjugate Gradient Method

We consider a hybrid Dai-Yuan conjugate gradient method. We confirm that its numerical performance can be improved provided that this method uses a practical steplength rule developed by Dong, and the associated convergence is analyzed as well.

scholarly journals A comparison on classical-hybrid conjugate gradient method under exact line search

2019 ◽  
Vol 5 (2) ◽  
pp. 150
Author(s):  
Nur Syarafina Mohamed ◽  
Mustafa Mamat ◽  
Mohd Rivaie ◽  
Shazlyn Milleana Shaharudin
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Convex Combination ◽  
Processing Unit ◽  
Central Processing ◽  
Exact Line Search ◽  
Hybrid Conjugate Gradient Method ◽  
Number Of Iterations

One of the popular approaches in modifying the Conjugate Gradient (CG) Method is hybridization. In this paper, a new hybrid CG is introduced and its performance is compared to the classical CG method which are Rivaie-Mustafa-Ismail-Leong (RMIL) and Syarafina-Mustafa-Rivaie (SMR) methods. The proposed hybrid CG is evaluated as a convex combination of RMIL and SMR method. Their performance are analyzed under the exact line search. The comparison performance showed that the hybrid CG is promising and has outperformed the classical CG of RMIL and SMR in terms of the number of iterations and central processing unit per time.

scholarly journals A modified quadratic hybridization of Polak-Ribiere-Polyak and Fletcher-Reeves conjugate gradient method for unconstrained optimization problems

2017 ◽  
Vol 7 (2) ◽  
pp. 177-185 ◽  
Author(s):  
Pro Kaelo ◽  
Sindhu Narayanan ◽  
M.V. Thuto
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Unconstrained Optimization Problems ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search ◽  
Hybrid Conjugate Gradient Method

This article presents a modified quadratic hybridization of the Polak–Ribiere–Polyak and Fletcher–Reeves conjugate gradient method for solving unconstrained optimization problems. Global convergence, with the strong Wolfe line search conditions, of the proposed quadratic hybrid conjugate gradient method is established. We also report some numerical results to show the competitiveness of the new hybrid method.

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