SECANT CONDITION FREE OF A SPECTRAL WYL CONJUGATE GRADIENT (CG) METHOD AND ITS GLOBAL CONVERGENCE PROPERTIES

2018 ◽  
Vol 103 (12) ◽  
pp. 1889-1902
Author(s):  
Usman Abbas Yakubu ◽  
Mustafa Mamat ◽  
Mohamad Afendee Mohamad ◽  
Mohd Rivaie ◽  
Rabi’u Bashir Yunus
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient ◽  
Convergence Properties ◽  
Secant Condition

scholarly journals New Hybrid Conjugate Gradient Method with Global Convergence Properties under Exact Line Search

2018 ◽  
Vol 7 (3.28) ◽  
pp. 54
Author(s):  
Yasir Salih ◽  
Mustafa Mamat ◽  
Mohd Rivaie ◽  
Abdelrhaman Abashar ◽  
Mohamad Afendee Mohamed
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Convergence Properties ◽  
Exact Line Search ◽  
Sufficient Descent ◽  
Hybrid Conjugate Gradient Method ◽  
New Formula

Conjugate Gradient (CG) method is a very useful technique for solving large-scale nonlinear optimization problems. In this paper, we propose a new formula for 12خ²k"> , which is a hybrid of PRP and WYL methods. This method possesses sufficient descent and global convergence properties when used with exact line search. Numerical results indicate that the new formula has higher efficiency compared with other classical CG methods. 

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