scholarly journals An Efficient Hybrid Conjugate Gradient Method with the Strong Wolfe-Powell Line Search

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Ahmad Alhawarat ◽  
Mustafa Mamat ◽  
Mohd Rivaie ◽  
Zabidin Salleh
Keyword(s):  
Conjugate Gradient ◽  
Line Search ◽  
Optimization Problems ◽  
Standard Test ◽  
Sufficient Descent Condition ◽  
Sufficient Descent ◽  
Descent Condition ◽  
Hybrid Conjugate Gradient Method ◽  
New Formula ◽  
Better Than

Conjugate gradient (CG) method is an interesting tool to solve optimization problems in many fields, such as design, economics, physics, and engineering. In this paper, we depict a new hybrid of CG method which relates to the famous Polak-Ribière-Polyak (PRP) formula. It reveals a solution for the PRP case which is not globally convergent with the strong Wolfe-Powell (SWP) line search. The new formula possesses the sufficient descent condition and the global convergent properties. In addition, we further explained about the cases where PRP method failed with SWP line search. Furthermore, we provide numerical computations for the new hybrid CG method which is almost better than other related PRP formulas in both the number of iterations and the CPU time under some standard test functions.

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 Global convergence of conjugate gradient method in unconstrained optimization problems

2019 ◽  
Vol 38 (7) ◽  
pp. 227-231
Author(s):  
Huda Younus Najm ◽  
Eman T. Hamed ◽  
Huda I. Ahmed
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Inexact Line Search ◽  
Sufficient Descent Condition ◽  
Unconstrained Optimization Problems ◽  
Sufficient Descent ◽  
Descent Condition

In this study, we propose a new parameter in the conjugate gradient method. It is shown that the new method fulfils the sufficient descent condition with the strong Wolfe condition when inexact line search has been used. The numerical results of this suggested method also shown that this method outperforms to other standard conjugate gradient method.

scholarly journals A NEW HYBRID PRP-MMSIS CONJUGATE GRADIENT METHOD AND ITS APPLICATION IN PORTOFOLIO SELECTION

2021 ◽  
Vol 5 (1) ◽  
pp. 47
Author(s):  
Sindy Devila ◽  
Maulana Malik ◽  
Wed Giyarti
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
New Method ◽  
Convergence Properties ◽  
Sufficient Descent Condition ◽  
Exact Line Search ◽  
Sufficient Descent ◽  
Descent Condition

In this paper, we propose a new hybrid coefficient of conjugate gradient method (CG) for solving unconstrained optimization model.  The new coefficient is combination of part the MMSIS (Malik et.al, 2020) and PRP (Polak, Ribi'ere \& Polyak, 1969) coefficients.  Under exact line search, the search direction of new method satisfies the sufficient descent condition and based on certain assumption, we establish the global convergence properties.  Using some test functions, numerical results show that the proposed method is more efficient than MMSIS method.  Besides, the new method can be used to solve problem in minimizing portfolio selection risk .

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 Descent Condition for a Scalar Parameter of Spectral HS (SpHS) Conjugate Gradient Method

2019 ◽  
Vol 8 (4) ◽  
pp. 11464-11467
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Standard Test ◽  
Exact Line Search ◽  
Sufficient Descent ◽  
Descent Condition ◽  
Spectral Conjugate Gradient ◽  
Unconstrained Problems

Spectral conjugate gradient method has been used in most cases as an alternative to the conjugate gradient (CG) method in order to solve nonlinear unconstrained problems. In this paper, we introduced a spectral parameter of HS conjugate gradient method resultant from the classical CG search direction and used some of the standard test functions with numerous variables to prove its sufficient descent and global convergence properties, the numerical outcome is verified by exact line search procedures.

scholarly journals A NEW THREE–TERM CONJUGATE GRADIENT METHOD WITH DESCENT DIRECTION FOR UNCONSTRAINED OPTIMIZATION

2016 ◽  
Vol 21 (3) ◽  
pp. 399-411 ◽  
Author(s):  
XiaoLiang Dong ◽  
HongWei Liu ◽  
YuBo He ◽  
Saman Babaie-Kafaki ◽  
Reza Ghanbari
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Numerical Comparison ◽  
Conjugacy Condition ◽  
Sufficient Descent Condition ◽  
Line Searches ◽  
Sufficient Descent ◽  
Descent Condition

In this paper, we propose a three–term PRP–type conjugate gradient method which always satisfies the sufficient descent condition independently of line searches employed. An important property of our method is that its direction is closest to the direction of the Newton method or satisfies conjugacy condition as the iterations evolve. In addition, under mild condition, we prove global convergence properties of the proposed method. Numerical comparison illustrates that our proposed method is efficient for solving the optimization problems.

Sign in / Sign up

Export Citation Format

Share Document