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.

Convergence of the descent Dai–Yuan conjugate gradient method for unconstrained optimization

2011 ◽  
Vol 18 (9) ◽  
pp. 1249-1253 ◽  
Author(s):  
Mehdi Dehghan ◽  
Masoud Hajarian
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Convergence Result ◽  
Sufficient Descent Condition ◽  
Exact Line Search ◽  
Sufficient Descent

The conjugate gradient method is one of the most useful and the earliest-discovered techniques for solving large-scale nonlinear optimization problems. Many variants of this method have been proposed, and some are widely used in practice. In this article, we study the descent Dai–Yuan conjugate gradient method which guarantees the sufficient descent condition for any line search. With exact line search, the introduced conjugate gradient method reduces to the Dai–Yuan conjugate gradient method. Finally, a global convergence result is established when the line search fulfils the Goldstein conditions.

scholarly journals A New Modified Three-Term Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Bakhtawar Baluch ◽  
Zabidin Salleh ◽  
Ahmad Alhawarat ◽  
U. A. M. Roslan
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Standard Test ◽  
Vital Role ◽  
Sufficient Descent Condition ◽  
Nonconvex Functions ◽  
Sufficient Descent

A new modified three-term conjugate gradient (CG) method is shown for solving the large scale optimization problems. The idea relates to the famous Polak-Ribière-Polyak (PRP) formula. As the numerator of PRP plays a vital role in numerical result and not having the jamming issue, PRP method is not globally convergent. So, for the new three-term CG method, the idea is to use the PRP numerator and combine it with any good CG formula’s denominator that performs well. The new modification of three-term CG method possesses the sufficient descent condition independent of any line search. The novelty is that by using the Wolfe Powell line search the new modification possesses global convergence properties with convex and nonconvex functions. Numerical computation with the Wolfe Powell line search by using the standard test function of optimization shows the efficiency and robustness of the new modification.

scholarly journals New Hybrid Conjugate Gradient Method with Global Convergence Properties under Exact Line Search

2018 ◽  
Vol 7 (3.28) ◽  
pp. 54
Author(s):  
Yasir Salih ◽  
Mustafa Mamat ◽  
Mohd Rivaie ◽  
Abdelrhaman Abashar ◽  
Mohamad Afendee Mohamed
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Convergence Properties ◽  
Exact Line Search ◽  
Sufficient Descent ◽  
Hybrid Conjugate Gradient Method ◽  
New Formula

Conjugate Gradient (CG) method is a very useful technique for solving large-scale nonlinear optimization problems. In this paper, we propose a new formula for 12خ²k"> , which is a hybrid of PRP and WYL methods. This method possesses sufficient descent and global convergence properties when used with exact line search. Numerical results indicate that the new formula has higher efficiency compared with other classical CG methods. 

scholarly journals An Extension of Polak-Ribière-Polyak Method using Exact Line Search

2019 ◽  
Vol 8 (2S3) ◽  
pp. 368-373
Keyword(s):  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Test Problems ◽  
Exact Line Search ◽  
Unconstrained Optimization Problems ◽  
Nonlinear Conjugate Gradient ◽  
Sufficient Descent ◽  
Large Scale Unconstrained Optimization

Lately, many large-scale unconstrained optimization problems rely upon nonlinear conjugate gradient (CG) methods. Many areas such as engineering, and computer science have benefited because of its simplicity, fast and low memory requirements. Many modified coefficients have appeared recently, all of which to improve these methods. This paper considers an extension conjugate gradient method of PolakRibière-Polyak using exact line search to show that it holds for some properties such as sufficient descent and global convergence. A set of 113 test problems is used to evaluate the performance of the proposed method and get compared to other existing methods using the same line search.

scholarly journals Global Convergence of a New Coefficient Nonlinear Conjugate Gradient Method

2018 ◽  
Vol 11 (3) ◽  
pp. 1188
Author(s):  
Nur Syarafina Mohamed ◽  
Mustafa Mamat ◽  
Mohd Rivaie ◽  
Shazlyn Milleana Shaharuddin
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Search Direction ◽  
Nonlinear Conjugate Gradient Method ◽  
Unconstrained Optimization Problems ◽  
Nonlinear Conjugate Gradient ◽  
Large Scale Unconstrained Optimization

Nonlinear conjugate gradient (CG) methods are widely used in optimization field due to its efficiency for solving a large scale unconstrained optimization problems. Many studies and modifications have been developed in order to improve the method. The method is known to possess sufficient descend condition and its global convergence properties under strong Wolfe-Powell search direction. In this paper, the new coefficient of CG method is presented. The global convergence and sufficient descend properties of the new coefficient are established by using strong Wolfe-Powell line search direction. Results show that the new coefficient is able to globally converge under certain assumptions and theories.

scholarly journals The Sufficient Descent Condition of Nonlinear Conjugate Gradient Method

2018 ◽  
Vol 7 (4.30) ◽  
pp. 458
Author(s):  
Srimazzura Basri ◽  
Mustafa Mamat ◽  
Puspa Liza Ghazali
Keyword(s):  
Conjugate Gradient ◽  
Large Scale ◽  
Gradient Methods ◽  
Sufficient Descent Condition ◽  
Nonlinear Conjugate Gradient Method ◽  
Non Linear ◽  
Nonlinear Conjugate Gradient ◽  
Sufficient Descent ◽  
Descent Condition ◽  
Scale Optimization

Non-linear conjugate gradient methods has been widely used instrumental in solving large scale optimization. These methods has been proved that only required very low memory other than its numerical efficiency. Thus, many studies have been conducted to improve these methods to find the most efficient method. In this paper, we proposed a new non-linear conjugate gradient coefficient that guarantees sufficient descent condition. Numerical tests indicate that the proposed coefficient is better than the three classical conjugate gradient coefficients.

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.

scholarly journals Modification of Nonlinear Conjugate Gradient Method with Weak Wolfe-Powell Line Search

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Ahmad Alhawarat ◽  
Zabidin Salleh
Keyword(s):  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Medical Science ◽  
Simple Algorithm ◽  
Sufficient Descent Condition ◽  
Nonlinear Conjugate Gradient Method ◽  
Optimum Solution ◽  
Large Scale Unconstrained Optimization

Conjugate gradient (CG) method is used to find the optimum solution for the large scale unconstrained optimization problems. Based on its simple algorithm, low memory requirement, and the speed of obtaining the solution, this method is widely used in many fields, such as engineering, computer science, and medical science. In this paper, we modified CG method to achieve the global convergence with various line searches. In addition, it passes the sufficient descent condition without any line search. The numerical computations under weak Wolfe-Powell line search shows that the efficiency of the new method is superior to other conventional 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.

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