scholarly journals A Modified Nonlinear Conjugate Gradient Method for Engineering Computation

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Tiefeng Zhu ◽  
Zaizai Yan ◽  
Xiuyun Peng
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Numerical Experiments ◽  
General Criterion ◽  
Mild Conditions ◽  
Nonlinear Conjugate Gradient Method ◽  
Engineering Computation ◽  
Nonlinear Conjugate Gradient

A general criterion for the global convergence of the nonlinear conjugate gradient method is established, based on which the global convergence of a new modified three-parameter nonlinear conjugate gradient method is proved under some mild conditions. A large amount of numerical experiments is executed and reported, which show that the proposed method is competitive and alternative. Finally, one engineering example has been analyzed for illustrative purposes.

scholarly journals The Global Convergence of a New Mixed Conjugate Gradient Method for Unconstrained Optimization

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Yang Yueting ◽  
Cao Mingyuan
Keyword(s):  
Global Convergence ◽  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Nonlinear Conjugate Gradient Method ◽  
Nonlinear Conjugate Gradient ◽  
Wolfe Line Search ◽  
Theoretical Analyses

We propose and generalize a new nonlinear conjugate gradient method for unconstrained optimization. The global convergence is proved with the Wolfe line search. Numerical experiments are reported which support the theoretical analyses and show the presented methods outperforming CGDESCENT method.

A Hybrid Nonlinear Conjugate Gradient Method with Sufficient Descent Property

2011 ◽  
Vol 58-60 ◽  
pp. 943-949
Author(s):  
Wan You Cheng ◽  
Xue Jie Liu
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Numerical Experiments ◽  
Test Problems ◽  
Sufficient Descent Property ◽  
Nonlinear Conjugate Gradient Method ◽  
Descent Property ◽  
Nonlinear Conjugate Gradient ◽  
Sufficient Descent

In this paper, on the basis of the recently developed HZ (Hager-Zhang) method [SIAM J. Optim., 16 (2005), pp. 170-192], we propose a hybrid descent conjugate gradient method which reserves the sufficient descent property of the HZ method. Under suitable conditions, we prove the global convergence of the proposed method. Extensive numerical experiments show that the method is promising for the test problems from the CUTE library.

scholarly journals Global convergence of new conjugate gradient method with inexact line search

2021 ◽  
Vol 11 (2) ◽  
pp. 1469
Author(s):  
Chergui Ahmed ◽  
Bouali Tahar
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Inexact Line Search ◽  
Sufficient Descent Condition ◽  
Nonlinear Conjugate Gradient Method ◽  
Nonlinear Conjugate Gradient ◽  
New Formula

In this paper, We propose a new nonlinear conjugate gradient method (FRA) that satisfies a sufficient descent condition and global convergence under the inexact line search of strong wolf powell. Our numerical experiment shaw the efficiency of the new method in solving a set of problems from the CUTEst package, the proposed new formula gives excellent numerical results at CPU time, number of iterations, number of gradient ratings when compared to WYL, DY, PRP, and FR methods.

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