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.

scholarly journals Global Convergence of a Nonlinear Conjugate Gradient Method

2011 ◽  
Vol 2011 ◽  
pp. 1-22
Author(s):  
Liu Jin-kui ◽  
Zou Li-min ◽  
Song Xiao-qian
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Nonlinear Conjugate Gradient Method ◽  
Unconstrained Optimization Problems ◽  
Nonlinear Conjugate Gradient ◽  
Wolfe Line Search

A modified PRP nonlinear conjugate gradient method to solve unconstrained optimization problems is proposed. The important property of the proposed method is that the sufficient descent property is guaranteed independent of any line search. By the use of the Wolfe line search, the global convergence of the proposed method is established for nonconvex minimization. Numerical results show that the proposed method is effective and promising by comparing with the VPRP, CG-DESCENT, and DL+methods.

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.

scholarly journals A modified quadratic hybridization of Polak-Ribiere-Polyak and Fletcher-Reeves conjugate gradient method for unconstrained optimization problems

2017 ◽  
Vol 7 (2) ◽  
pp. 177-185 ◽  
Author(s):  
Pro Kaelo ◽  
Sindhu Narayanan ◽  
M.V. Thuto
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Unconstrained Optimization Problems ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search ◽  
Hybrid Conjugate Gradient Method

This article presents a modified quadratic hybridization of the Polak–Ribiere–Polyak and Fletcher–Reeves conjugate gradient method for solving unconstrained optimization problems. Global convergence, with the strong Wolfe line search conditions, of the proposed quadratic hybrid conjugate gradient method is established. We also report some numerical results to show the competitiveness of the new hybrid method.

A modified nonlinear conjugate gradient method for unconstrained optimization

2015 ◽  
Vol 9 ◽  
pp. 2671-2682 ◽  
Author(s):  
Ibrahim S. Mohammed ◽  
Mustafa Mamat ◽  
Abdelrhaman Abashar ◽  
Mohd Rivaie ◽  
Zabidin Salleh
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Nonlinear Conjugate Gradient Method ◽  
Nonlinear Conjugate Gradient
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