Performance Profiles of Conjugate-Gradient Algorithms for Unconstrained Optimization

2012 ◽  
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Conjugate Gradient Algorithms ◽  
Gradient Algorithms ◽  
Performance Profiles

scholarly journals Global convergence of new three terms conjugate gradient for unconstrained optimization

2021 ◽  
Vol 11 (1) ◽  
pp. 1-9
Author(s):  
Ahmed Anwer Mustafa ◽  
Salah Gazi Shareef
Keyword(s):  
Global Convergence ◽  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Optimization Problems ◽  
Step Size ◽  
Conjugacy Condition ◽  
Sufficient Descent Condition ◽  
Conjugate Gradient Algorithms ◽  
Gradient Algorithms ◽  
Descent Condition

In this paper, a new formula of 𝛽𝑘 is suggested for the conjugate gradient method of solving unconstrained optimization problems based on three terms and step size of cubic. Our new proposed CG method has descent condition, sufficient descent condition, conjugacy condition, and global convergence properties. Numerical comparisons with two standard conjugate gradient algorithms show that this algorithm is very effective depending on the number of iterations and the number of functions evaluated.

scholarly journals A q-Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shashi Kant Mishra ◽  
Suvra Kanti Chakraborty ◽  
Mohammad Esmael Samei ◽  
Bhagwat Ram
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Optimization Problems ◽  
Gradient Algorithm ◽  
Test Problems ◽  
Conjugate Gradient Algorithms ◽  
Gradient Algorithms ◽  
Unconstrained Optimization Problems ◽  
Wolfe Conditions ◽  
Nonlinear Unconstrained Optimization

AbstractA Polak–Ribière–Polyak (PRP) algorithm is one of the oldest and popular conjugate gradient algorithms for solving nonlinear unconstrained optimization problems. In this paper, we present a q-variant of the PRP (q-PRP) method for which both the sufficient and conjugacy conditions are satisfied at every iteration. The proposed method is convergent globally with standard Wolfe conditions and strong Wolfe conditions. The numerical results show that the proposed method is promising for a set of given test problems with different starting points. Moreover, the method reduces to the classical PRP method as the parameter q approaches 1.

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