scholarly journals Nonlinear conjugate gradient methods with sufficient descent properties for unconstrained optimization

2013 ◽  
Vol 9 (3) ◽  
pp. 595-619 ◽  
Author(s):  
Wataru Nakamura ◽  
◽  
Yasushi Narushima ◽  
Hiroshi Yabe ◽  
◽  
...  
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Nonlinear Conjugate Gradient ◽  
Sufficient Descent ◽  
Nonlinear Conjugate Gradient Methods

scholarly journals Nonlinear Conjugate Gradient Methods with Wolfe Type Line Search

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yuan-Yuan Chen ◽  
Shou-Qiang Du
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Line Search ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Unconstrained Optimization Problems ◽  
Convergence Results ◽  
Nonlinear Conjugate Gradient ◽  
Nonlinear Conjugate Gradient Methods

Nonlinear conjugate gradient method is one of the useful methods for unconstrained optimization problems. In this paper, we consider three kinds of nonlinear conjugate gradient methods with Wolfe type line search for unstrained optimization problems. Under some mild assumptions, the global convergence results of the given methods are proposed. The numerical results show that the nonlinear conjugate gradient methods with Wolfe type line search are efficient for some unconstrained optimization problems.

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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