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.

A new hybrid conjugate gradient method of unconstrained optimization methods

2021 ◽  
pp. 2250070
Author(s):  
Chenna Nasreddine ◽  
Sellami Badreddine ◽  
Belloufi Mohammed
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Convex Combination ◽  
Optimization Methods ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search ◽  
Hybrid Conjugate Gradient Method

In this paper, we present a new hybrid method to solve a nonlinear unconstrained optimization problem by using conjugate gradient, which is a convex combination of Liu–Storey (LS) conjugate gradient method and Hager–Zhang (HZ) conjugate gradient method. This method possesses the sufficient descent property with Strong Wolfe line search and the global convergence with the strong Wolfe line search. In the end of this paper, we illustrate our method by giving some numerical examples.

scholarly journals Global convergence analysis of a new hybrid conjugate gradient method for unconstrained optimization problems

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Ibrahim Abdullahi ◽  
Rohanin Ahmad
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Unconstrained Optimization Problems ◽  
Numerical Experimentation ◽  
Hybrid Conjugate Gradient Method

In this paper, we propose a new hybrid conjugate gradient method for unconstrained optimization problems. The proposed method comprises of beta (DY), beta (WHY), beta (RAMI)  and beta (New). The beta (New)  was constructed purposely for this proposed hybrid method.The method possesses sufficient descent property irrespective of the line search. Under Strong Wolfe-Powell line search, we proved that the method is globally convergent. Numerical experimentation shows the effectiveness and robustness of the proposed method when compare with some hybrid as well as some modified conjugate gradient methods.

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 globally convergent hybrid conjugate gradient method with strong Wolfe conditions for unconstrained optimization

2019 ◽  
Vol 14 (1) ◽  
pp. 1-9
Author(s):  
P. Kaelo ◽  
P. Mtagulwa ◽  
M. V. Thuto
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Gradient Methods ◽  
Convergence Properties ◽  
Good Convergence ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search ◽  
Hybrid Conjugate Gradient Method

Abstract In this paper, we develop a new hybrid conjugate gradient method that inherits the features of the Liu and Storey (LS), Hestenes and Stiefel (HS), Dai and Yuan (DY) and Conjugate Descent (CD) conjugate gradient methods. The new method generates a descent direction independently of any line search and possesses good convergence properties under the strong Wolfe line search conditions. Numerical results show that the proposed method is robust and efficient.

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 hybrid conjugate gradient method for dynamic force reconstruction

2019 ◽  
Vol 11 (1) ◽  
pp. 168781401882236
Author(s):  
Linjun Wang ◽  
Liu Xu ◽  
Youxiang Xie ◽  
Yixian Du ◽  
Xiao Han
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Present Method ◽  
Line Search ◽  
Dynamic Force ◽  
Load Identification ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search ◽  
Hybrid Conjugate Gradient Method

A new hybrid conjugate gradient method is proposed in this article based on the gradient operator and applied to the structural dynamic load identification problem. It has proved that the present method with the strong Wolfe line search possesses sufficient descent property. In addition, the present method is globally convergent when the parameter in the strong Wolfe line search conditions is restricted in some suitable intervals. Three example problems from engineering are solved by the newly developed conjugate gradient method to demonstrate the robustness and effectiveness of conjugate gradient method in solving multi-source dynamic load identification problems. Compared with the traditional Landweber iteration regularization method (Landweber), the proposed conjugate gradient method can more stably and effectively overcome the influences of noise, largely reduce the number of iterations, and provide accurate results in identifying multi-source dynamic force in practical engineering structure.

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