New Hybrid Conjugate Gradient Method as A Convex Combination of HS and FR Methods

2018 ◽  
Vol 2 (9) ◽  
Author(s):  
Snezana S. Djordjevic ◽  
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Convex Combination ◽  
Hybrid Conjugate Gradient Method

scholarly journals A comparison on classical-hybrid conjugate gradient method under exact line search

2019 ◽  
Vol 5 (2) ◽  
pp. 150
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 ◽  
Processing Unit ◽  
Central Processing ◽  
Exact Line Search ◽  
Hybrid Conjugate Gradient Method ◽  
Number Of Iterations

One of the popular approaches in modifying the Conjugate Gradient (CG) Method is hybridization. In this paper, a new hybrid CG is introduced and its performance is compared to the classical CG method which are Rivaie-Mustafa-Ismail-Leong (RMIL) and Syarafina-Mustafa-Rivaie (SMR) methods. The proposed hybrid CG is evaluated as a convex combination of RMIL and SMR method. Their performance are analyzed under the exact line search. The comparison performance showed that the hybrid CG is promising and has outperformed the classical CG of RMIL and SMR in terms of the number of iterations and central processing unit per time.

scholarly journals New hybrid conjugate gradient method as a convex combination of FR and PRP methods

Filomat ◽  
2016 ◽  
Vol 30 (11) ◽  
pp. 3083-3100 ◽  
Author(s):  
Snezana Djordjevic
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Convex Combination ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Numerical Comparisons ◽  
Hybrid Conjugate Gradient Method ◽  
Better Than

We consider a newhybrid conjugate gradient algorithm,which is obtained fromthe algorithmof Fletcher-Reeves, and the algorithmof Polak-Ribi?re-Polyak. Numerical comparisons show that the present hybrid conjugate gradient algorithm often behaves better than some known algorithms.

scholarly journals Comments on ”New hybrid conjugate gradient method as a convex combination of FR and PRP methods”

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4573-4574
Author(s):  
Chenna Nasreddine ◽  
Sellami Badreddine
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Convex Combination ◽  
Hybrid Conjugate Gradient Method

In this note, we present a new theory as a modification and an alternative to S.Djordjevic?s Theorem (2.2), Here we rephrase the text of theory (2.2) by deleting condition (2.16), Notations and equation numbers as in S.Djordjevic.

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 A New Hybrid PRPFR Conjugate Gradient Method for Solving Nonlinear Monotone Equations and Image Restoration Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yingjie Zhou ◽  
Yulun Wu ◽  
Xiangrong Li
Keyword(s):  
Image Restoration ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Convex Combination ◽  
Trust Region ◽  
Step Length ◽  
Monotone Equations ◽  
Global Convergence Property ◽  
Sufficient Descent

A new hybrid PRPFR conjugate gradient method is presented in this paper, which is designed such that it owns sufficient descent property and trust region property. This method can be considered as a convex combination of the PRP method and the FR method while using the hyperplane projection technique. Under accelerated step length, the global convergence property is gained with some appropriate assumptions. Comparing with other methods, the numerical experiments show that the PRPFR method is more competitive for solving nonlinear equations and image restoration problems.

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