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 new conjugate gradient algorithms using conjugacy condition for solving unconstrained optimization

2021 ◽  
Vol 24 (3) ◽  
pp. 1647
Author(s):  
Aseel M. Qasim ◽  
Zinah F. Salih ◽  
Basim A. Hassan
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Conjugacy Condition ◽  
Simple Modification ◽  
Conjugate Gradient Algorithms ◽  
Gradient Algorithms ◽  
Nonlinear Conjugate Gradient ◽  
Nonlinear Conjugate Gradient Methods

The primarily objective of this paper which is indicated in the field of conjugate gradient algorithms for unconstrained optimization problems and algorithms is to show the advantage of the new proposed algorithm in comparison with the standard method which is denoted as. Hestenes Stiefel method, as we know the coefficient conjugate parameter is very crucial for this reason, we proposed a simple modification of the coefficient conjugate gradient which is used to derived the new formula for the conjugate gradient update parameter described in this paper. Our new modification is based on the conjugacy situation for nonlinear conjugate gradient methods which is given by the conjugacy condition for nonlinear conjugate gradient methods and added a nonnegative parameter to suggest the new extension of the method. Under mild Wolfe conditions, the global convergence theorem and lemmas are also defined and proved. The proposed method's efficiency is programming and demonstrated by the numerical instances, which were very encouraging.

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