scholarly journals A Descent Dai-Liao Conjugate Gradient Method Based on a Modified Secant Equation and Its Global Convergence

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Ioannis E. Livieris ◽  
Panagiotis Pintelas
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
High Order Accuracy ◽  
Secant Condition ◽  
Secant Equation ◽  
Sufficient Descent ◽  
Curvature Information ◽  
Modified Secant Condition

We propose a conjugate gradient method which is based on the study of the Dai-Liao conjugate gradient method. An important property of our proposed method is that it ensures sufficient descent independent of the accuracy of the line search. Moreover, it achieves a high-order accuracy in approximating the second-order curvature information of the objective function by utilizing the modified secant condition proposed by Babaie-Kafaki et al. (2010). Under mild conditions, we establish that the proposed method is globally convergent for general functions provided that the line search satisfies the Wolfe conditions. Numerical experiments are also presented.

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

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Bakhtawar Baluch ◽  
Zabidin Salleh ◽  
Ahmad Alhawarat
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Sufficient Descent Property ◽  
Descent Property ◽  
Sufficient Descent

This paper describes a modified three-term Hestenes–Stiefel (HS) method. The original HS method is the earliest conjugate gradient method. Although the HS method achieves global convergence using an exact line search, this is not guaranteed in the case of an inexact line search. In addition, the HS method does not usually satisfy the descent property. Our modified three-term conjugate gradient method possesses a sufficient descent property regardless of the type of line search and guarantees global convergence using the inexact Wolfe–Powell line search. The numerical efficiency of the modified three-term HS method is checked using 75 standard test functions. It is known that three-term conjugate gradient methods are numerically more efficient than two-term conjugate gradient methods. Importantly, this paper quantifies how much better the three-term performance is compared with two-term methods. Thus, in the numerical results, we compare our new modification with an efficient two-term conjugate gradient method. We also compare our modification with a state-of-the-art three-term HS method. Finally, we conclude that our proposed modification is globally convergent and numerically efficient.

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 .

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 conjugate gradient method based on a modified secant condition with its applications in image processing

2020 ◽  
Author(s):  
Fahimeh Abdollahi ◽  
M. Fatemi
Keyword(s):  
Image Processing ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Secant Condition ◽  
Gradient Parameter ◽  
Function Information ◽  
Modified Secant Condition

We propose an effective conjugate gradient method belonging to the class of Dai-Liao methods for solving unconstrained optimization problems. We employ a variant of the modified secant condition, and introduce a new conjugate gradient parameter by solving an optimization problem. Optimization problem combines the well-known features of the linear conjugate gradient method using some penalty functions. This new parameter takes advantage of function information as well as the gradient information to provide the iterations. Our proposed method is globally convergent under mild assumptions. We examine the ability of the method for solving some real world problems from image processing field. Numerical results show that the proposed method is efficient in the sense of PSNR test. We also compare our proposed method with some well-known existing algorithms using a collection of CUTEr problems to show it's efficiency.

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 Modified Three-Term Conjugate Gradient Method and Its Applications

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Jiankun Liu ◽  
Shouqiang Du
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Unconstrained Optimization Problems ◽  
Armijo Line Search ◽  
Global Convergence Property ◽  
Sufficient Descent ◽  
The Given

We propose a modified three-term conjugate gradient method with the Armijo line search for solving unconstrained optimization problems. The proposed method possesses the sufficient descent property. Under mild assumptions, the global convergence property of the proposed method with the Armijo line search is proved. Due to simplicity, low storage, and nice convergence properties, the proposed method is used to solve M-tensor systems and a kind of nonsmooth optimization problems with l1-norm. Finally, the given numerical experiments show the efficiency of the proposed method.

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 hyhbrid coefficient of conjugate gradient method

2020 ◽  
Vol 18 (3) ◽  
pp. 1454
Author(s):  
Nur Syarafina Mohamed ◽  
Mustafa Mamat ◽  
Mohd Rivaie ◽  
Shazlyn Milleana Shaharudin
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Convex Combination ◽  
Gradient Methods ◽  
Processing Unit ◽  
Central Processing ◽  
Exact Line Search ◽  
Sufficient Descent

<p><span>Hybridization is one of the popular approaches in modifying the conjugate gradient method. In this paper, a new hybrid conjugate gradient is suggested and analyzed in which the parameter <!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1640083713"> </o:OLEObject> </xml><![endif]-->is evaluated as a convex combination of <!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1640083714"> </o:OLEObject> </xml><![endif]--> while using exact line search. The proposed method is shown to possess both sufficient descent and global convergence properties. Numerical performances show that the proposed method is promising and has overpowered other hybrid conjugate gradient methods in its number of iterations and central processing unit per time. </span></p>

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