scholarly journals A Mixed Spectral CD-DY Conjugate Gradient Method

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Liu Jinkui ◽  
Du Xianglin ◽  
Wang Kairong
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Descent Method ◽  
Unconstrained Optimization Problems ◽  
Global Convergence Property ◽  
Wolfe Line Search ◽  
Spectral Conjugate Gradient

A mixed spectral CD-DY conjugate descent method for solving unconstrained optimization problems is proposed, which combines the advantages of the spectral conjugate gradient method, the CD method, and the DY method. Under the Wolfe line search, the proposed method can generate a descent direction in each iteration, and the global convergence property can be also guaranteed. Numerical results show that the new method is efficient and stationary compared to the CD (Fletcher 1987) method, the DY (Dai and Yuan 1999) method, and the SFR (Du and Chen 2008) method; so it can be widely used in scientific computation.

scholarly journals A modified quadratic hybridization of Polak-Ribiere-Polyak and Fletcher-Reeves conjugate gradient method for unconstrained optimization problems

2017 ◽  
Vol 7 (2) ◽  
pp. 177-185 ◽  
Author(s):  
Pro Kaelo ◽  
Sindhu Narayanan ◽  
M.V. Thuto
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Unconstrained Optimization Problems ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search ◽  
Hybrid Conjugate Gradient Method

This article presents a modified quadratic hybridization of the Polak–Ribiere–Polyak and Fletcher–Reeves conjugate gradient method for solving unconstrained optimization problems. Global convergence, with the strong Wolfe line search conditions, of the proposed quadratic hybrid conjugate gradient method is established. We also report some numerical results to show the competitiveness of the new hybrid 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 Global Convergence of a Modified Spectral Conjugate Gradient Method

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Huabin Jiang ◽  
Songhai Deng ◽  
Xiaodong Zheng ◽  
Zhong Wan
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Step Length ◽  
Mild Conditions ◽  
Unconstrained Optimization Problems ◽  
Spectral Conjugate Gradient

A modified spectral PRP conjugate gradient method is presented for solving unconstrained optimization problems. The constructed search direction is proved to be a sufficiently descent direction of the objective function. With an Armijo-type line search to determinate the step length, a new spectral PRP conjugate algorithm is developed. Under some mild conditions, the theory of global convergence is established. Numerical results demonstrate that this algorithm is promising, particularly, compared with the existing similar ones.

scholarly journals Global Convergence of a Nonlinear Conjugate Gradient Method

2011 ◽  
Vol 2011 ◽  
pp. 1-22
Author(s):  
Liu Jin-kui ◽  
Zou Li-min ◽  
Song Xiao-qian
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Nonlinear Conjugate Gradient Method ◽  
Unconstrained Optimization Problems ◽  
Nonlinear Conjugate Gradient ◽  
Wolfe Line Search

A modified PRP nonlinear conjugate gradient method to solve unconstrained optimization problems is proposed. The important property of the proposed method is that the sufficient descent property is guaranteed independent of any line search. By the use of the Wolfe line search, the global convergence of the proposed method is established for nonconvex minimization. Numerical results show that the proposed method is effective and promising by comparing with the VPRP, CG-DESCENT, and DL+methods.

scholarly journals Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained Optimization

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Jinkui Liu ◽  
Youyi Jiang
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
New Method ◽  
Test Problems ◽  
Sufficient Descent Condition ◽  
Spectral Conjugate Gradient

A new nonlinear spectral conjugate descent method for solving unconstrained optimization problems is proposed on the basis of the CD method and the spectral conjugate gradient method. For any line search, the new method satisfies the sufficient descent conditiongkTdk<−∥gk∥2. Moreover, we prove that the new method is globally convergent under the strong Wolfe line search. The numerical results show that the new method is more effective for the given test problems from the CUTE test problem library (Bongartz et al., 1995) in contrast to the famous CD method, FR method, and PRP method.

scholarly journals A Spectral Conjugate Gradient Method with Descent Property

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 280
Author(s):  
Jinbao Jian ◽  
Lin Yang ◽  
Xianzhen Jiang ◽  
Pengjie Liu ◽  
Meixing Liu
Keyword(s):  
Conjugate Gradient Method ◽  
Spectral Parameter ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Descent Property ◽  
Wolfe Line Search ◽  
Spectral Conjugate Gradient ◽  
Two Parameters ◽  
Large Scale Unconstrained Optimization

Spectral conjugate gradient method (SCGM) is an important generalization of the conjugate gradient method (CGM), and it is also one of the effective numerical methods for large-scale unconstrained optimization. The designing for the spectral parameter and the conjugate parameter in SCGM is a core work. And the aim of this paper is to propose a new and effective alternative method for these two parameters. First, motivated by the strong Wolfe line search requirement, we design a new spectral parameter. Second, we propose a hybrid conjugate parameter. Such a way for yielding the two parameters can ensure that the search directions always possess descent property without depending on any line search rule. As a result, a new SCGM with the standard Wolfe line search is proposed. Under usual assumptions, the global convergence of the proposed SCGM is proved. Finally, by testing 108 test instances from 2 to 1,000,000 dimensions in the CUTE library and other classic test collections, a large number of numerical experiments, comparing with both SCGMs and CGMs, for the presented SCGM are executed. The detail results and their corresponding performance profiles are reported, which show that the proposed SCGM is effective and promising.

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.   

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