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 Nonlinear Conjugate Gradient Methods with Sufficient Descent Condition for Large-Scale Unconstrained Optimization

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Jianguo Zhang ◽  
Yunhai Xiao ◽  
Zengxin Wei
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Sufficient Descent Condition ◽  
Convergence Results ◽  
Nonlinear Conjugate Gradient ◽  
Large Scale Unconstrained Optimization ◽  
Nonlinear Conjugate Gradient Methods

Two nonlinear conjugate gradient-type methods for solving unconstrained optimization problems are proposed. An attractive property of the methods, is that, without any line search, the generated directions always descend. Under some mild conditions, global convergence results for both methods are established. Preliminary numerical results show that these proposed methods are promising, and competitive with the well-known PRP method.

scholarly journals Some generalized three-term conjugate gradient methods based on CD approach for unconstrained optimization problems

2021 ◽  
Vol 3 (2) ◽  
pp. 67-82
Author(s):  
Ladan Arman ◽  
Yuanming Xu ◽  
Long Liping
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Line Search ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Sufficient Descent Condition ◽  
Unconstrained Optimization Problems ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search

Abstract In this paper, based on the efficient Conjugate Descent (CD) method, two generalized CD algorithms are proposed to solve the unconstrained optimization problems. These methods are three-term conjugate gradient methods which the generated directions by using the conjugate gradient parameters and independent of the line search satisfy in the sufficient descent condition. Furthermore, under the strong Wolfe line search, the global convergence of the proposed methods are proved. Also, the preliminary numerical results on the CUTEst collection are presented to show effectiveness of our methods.

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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