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.

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.

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 A new accelerated conjugate gradient method for large-scale unconstrained optimization

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yuting Chen ◽  
Mingyuan Cao ◽  
Yueting Yang
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Conjugacy Condition ◽  
Sufficient Descent Condition ◽  
Large Scale Unconstrained Optimization

AbstractIn this paper, we present a new conjugate gradient method using an acceleration scheme for solving large-scale unconstrained optimization. The generated search direction satisfies both the sufficient descent condition and the Dai–Liao conjugacy condition independent of line search. Moreover, the value of the parameter contains more useful information without adding more computational cost and storage requirements, which can improve the numerical performance. Under proper assumptions, the global convergence result of the proposed method with a Wolfe line search is established. Numerical experiments show that the given method is competitive for unconstrained optimization problems, with a maximum dimension of 100,000.

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 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 An Efficient Modified AZPRP Conjugate Gradient Method for Large-Scale Unconstrained Optimization Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Ahmad Alhawarat ◽  
Thoi Trung Nguyen ◽  
Ramadan Sabra ◽  
Zabidin Salleh
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Unconstrained Optimization Problems ◽  
Unconstrained Optimization Problem ◽  
Descent Property ◽  
Large Scale Unconstrained Optimization

To find a solution of unconstrained optimization problems, we normally use a conjugate gradient (CG) method since it does not cost memory or storage of second derivative like Newton’s method or Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. Recently, a new modification of Polak and Ribiere method was proposed with new restart condition to give a so-call AZPRP method. In this paper, we propose a new modification of AZPRP CG method to solve large-scale unconstrained optimization problems based on a modification of restart condition. The new parameter satisfies the descent property and the global convergence analysis with the strong Wolfe-Powell line search. The numerical results prove that the new CG method is strongly aggressive compared with CG_Descent method. The comparisons are made under a set of more than 140 standard functions from the CUTEst library. The comparison includes number of iterations and CPU time.

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 Solving a large scale nonlinear unconstrained optimization problems by using new coefficient of conjugate gradient method with exact line search direction

2018 ◽  
Vol 7 (3.28) ◽  
pp. 92
Author(s):  
Talat Alkouli ◽  
Mustafa Mamat ◽  
Mohd Rivaie ◽  
Puspa Liza Ghazali
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Exact Line Search ◽  
Unconstrained Optimization Problems ◽  
Large Scale Unconstrained Optimization

In this paper, an efficient modification of nonlinear conjugate gradient method and an associated implementation, based on an exact line search, are proposed and analyzed to solve large-scale unconstrained optimization problems. The method satisfies the sufficient descent property. Furthermore, global convergence result is proved. Computational results for a set of unconstrained optimization test problems, some of them from CUTE library, showed that this new conjugate gradient algorithm seems to converge more stable and outperforms the other similar methods in many situations.   

scholarly journals A new modification nonlinear conjugate gradient method with strong wolf-powell line search

2020 ◽  
Vol 18 (1) ◽  
pp. 525
Author(s):  
Chergui Ahmed ◽  
Bouali Tahar
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Convergence Result ◽  
Special Role ◽  
Large Scale Unconstrained Optimization

<span>The conjugate gradient method has played a special role in   solving large-scale unconstrained Optimization problems. In this paper, we propose a new family of CG coefficients that   possess    sufficient descent conditions and global convergence properties this CG method is similar to (Wei et al) [7].  Global convergence   result is established under Strong Wolf-Powell line search. Numerical results to find  the  optimum solution of some test  functions show the   new proposed formula has the best result in CPU time and the number of iterations, and the number of gradient evaluations when it comparing with FR, PRP, DY, and WYL </span>

scholarly journals A Conjugate Gradient Algorithm under Yuan-Wei-Lu Line Search Technique for Large-Scale Minimization Optimization Models

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Xiangrong Li ◽  
Songhua Wang ◽  
Zhongzhou Jin ◽  
Hongtruong Pham
Keyword(s):  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Search Technique ◽  
Inexact Line Search ◽  
Line Search Technique ◽  
Large Scale Unconstrained Optimization

This paper gives a modified Hestenes and Stiefel (HS) conjugate gradient algorithm under the Yuan-Wei-Lu inexact line search technique for large-scale unconstrained optimization problems, where the proposed algorithm has the following properties: (1) the new search direction possesses not only a sufficient descent property but also a trust region feature; (2) the presented algorithm has global convergence for nonconvex functions; (3) the numerical experiment showed that the new algorithm is more effective than similar algorithms.

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