A NEW COEFFICIENT OF CONJUGATE GRADIENT METHODS FOR NONLINEAR UNCONSTRAINED OPTIMIZATION

2016 ◽  
Vol 78 (6-4) ◽  
Author(s):  
Nur Syarafina Mohamed ◽  
Mustafa Mamat ◽  
Fatma Susilawati Mohamad ◽  
Mohd Rivaie
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Standard Test ◽  
Processing Unit ◽  
Central Processing ◽  
Exact Line Search ◽  
Unconstrained Optimization Problems ◽  
Nonlinear Unconstrained Optimization

Conjugate gradient (CG) methods are widely used in solving nonlinear unconstrained optimization problems such as designs, economics, physics and engineering due to its low computational memory requirement. In this paper, a new modifications of CG coefficient ( ) which possessed global convergence properties is proposed by using exact line search. Based on the number of iterations and central processing unit (CPU) time, the numerical results show that the new  performs better than some other well known CG methods under some standard test functions.

scholarly journals A COMPARATIVE STUDY OF SOME MODIFICATIONS OF CG METHODS UNDER EXACT LINE SEARCH

2020 ◽  
Vol 1 (1) ◽  
pp. 12-17
Author(s):  
Yasir Salih ◽  
Mustafa Mamat ◽  
Sukono Sukono
Keyword(s):  
Conjugate Gradient ◽  
Numerical Experiments ◽  
Line Search ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Test Problems ◽  
Convergence Properties ◽  
Exact Line Search ◽  
Unconstrained Optimization Problems ◽  
Nonlinear Unconstrained Optimization

Conjugate Gradient (CG) method is a technique used in solving nonlinear unconstrained optimization problems. In this paper, we analysed the performance of two modifications and compared the results with the classical conjugate gradient methods of. These proposed methods possesse global convergence properties for general functions using exact line search. Numerical experiments show that the two modifications are more efficient for the test problems compared to classical CG coefficients.

scholarly journals Application of spectral conjugate gradient methods for solving unconstrained optimization problems

2020 ◽  
Vol 10 (2) ◽  
pp. 198-205
Author(s):  
Sulaiman Mohammed Ibrahim ◽  
Usman Abbas Yakubu ◽  
Mustafa Mamat
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Optimization Problems ◽  
Computational Cost ◽  
Real Life ◽  
Gradient Methods ◽  
Nonlinear Problems ◽  
Exact Line Search ◽  
Unconstrained Optimization Problems

Conjugate gradient (CG) methods are among the most efficient numerical methods for solving unconstrained optimization problems. This is due to their simplicty and  less computational cost in solving large-scale nonlinear problems. In this paper, we proposed some spectral CG methods using the classical CG search direction. The proposed methods are applied to real-life problems in regression analysis. Their convergence proof was establised under exact line search. Numerical results has shown that the proposed methods are efficient and promising.

scholarly journals Nonlinear Conjugate Gradient Methods with Wolfe Type Line Search

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yuan-Yuan Chen ◽  
Shou-Qiang Du
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Line Search ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Unconstrained Optimization Problems ◽  
Convergence Results ◽  
Nonlinear Conjugate Gradient ◽  
Nonlinear Conjugate Gradient Methods

Nonlinear conjugate gradient method is one of the useful methods for unconstrained optimization problems. In this paper, we consider three kinds of nonlinear conjugate gradient methods with Wolfe type line search for unstrained optimization problems. Under some mild assumptions, the global convergence results of the given methods are proposed. The numerical results show that the nonlinear conjugate gradient methods with Wolfe type line search are efficient for some unconstrained optimization problems.

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 q-Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shashi Kant Mishra ◽  
Suvra Kanti Chakraborty ◽  
Mohammad Esmael Samei ◽  
Bhagwat Ram
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Optimization Problems ◽  
Gradient Algorithm ◽  
Test Problems ◽  
Conjugate Gradient Algorithms ◽  
Gradient Algorithms ◽  
Unconstrained Optimization Problems ◽  
Wolfe Conditions ◽  
Nonlinear Unconstrained Optimization

AbstractA Polak–Ribière–Polyak (PRP) algorithm is one of the oldest and popular conjugate gradient algorithms for solving nonlinear unconstrained optimization problems. In this paper, we present a q-variant of the PRP (q-PRP) method for which both the sufficient and conjugacy conditions are satisfied at every iteration. The proposed method is convergent globally with standard Wolfe conditions and strong Wolfe conditions. The numerical results show that the proposed method is promising for a set of given test problems with different starting points. Moreover, the method reduces to the classical PRP method as the parameter q approaches 1.

scholarly journals A New conjugate gradient method for unconstrained optimization problems with descent property

2020 ◽  
Vol 9 (2) ◽  
pp. 101-105
Author(s):  
Hussein Ageel Khatab ◽  
Salah Gazi Shareef
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Conjugacy Condition ◽  
Sufficient Descent Condition ◽  
Unconstrained Optimization Problems ◽  
Descent Condition ◽  
Nonlinear Unconstrained Optimization

In this paper, we propose a new conjugate gradient method for solving nonlinear unconstrained optimization. The new method consists of three parts, the first part of them is the parameter of Hestenes-Stiefel (HS). The proposed method is satisfying the descent condition, sufficient descent condition and conjugacy condition. We give some numerical results to show the efficiency of the suggested method.

Sign in / Sign up

Export Citation Format

Share Document