Global convergence of a new class nonlinear conjugate gradient method with exact line search

2021 ◽  
Author(s):  
Nur Haziqah Mohd Dani ◽  
Srimazzura Basri ◽  
Mustafa Mamat
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
New Class ◽  
Nonlinear Conjugate Gradient Method ◽  
Exact Line Search ◽  
Nonlinear Conjugate Gradient

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 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 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.

A new class of nonlinear conjugate gradient coefficients for unconstrained optimization

2021 ◽  
Author(s):  
Amina Boumediene ◽  
Tahar Bechouat ◽  
Rachid Benzine ◽  
Ghania Hadji
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Sufficient Descent Condition ◽  
Nonlinear Conjugate Gradient Method ◽  
Exact Line Search ◽  
Nonlinear Conjugate Gradient ◽  
Sufficient Descent

The nonlinear Conjugate gradient method (CGM) is a very effective way in solving large-scale optimization problems. Zhang et al. proposed a new CG coefficient which is defined by [Formula: see text]. They proved the sufficient descent condition and the global convergence for nonconvex minimization in strong Wolfe line search. In this paper, we prove that this CG coefficient possesses sufficient descent conditions and global convergence properties under the exact line search.

Global convergence properties of the BBB conjugate gradient method

2018 ◽  
Vol 13 (03) ◽  
pp. 2050059
Author(s):  
Amina Boumediene ◽  
Rachid Benzine ◽  
Mohammed Belloufi
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Exact Line Search ◽  
Unconstrained Optimization Problems ◽  
Nonlinear Conjugate Gradient ◽  
Large Scale Unconstrained Optimization

Nonlinear conjugate gradient (CG) methods are widely used for solving large scale unconstrained optimization problems. Many studies have been devoted to develop and improve these methods. In this paper, we aim to study the global convergence of the BBB conjugate gradient method with exact line search.

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