scholarly journals Anew Conjugate Gradient Algorithm Based on The (Dai-Liao) Conjugate Gradient Method

2020 ◽  
Vol 25 (1) ◽  
pp. 128
Author(s):  
SHAHER QAHTAN HUSSEIN1 ◽  
GHASSAN EZZULDDIN ARIF1 ◽  
YOKSAL ABDLL SATTAR2
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Numerical Results ◽  
Conjugate Gradient Algorithm ◽  
New Method ◽  
Gradient Algorithm ◽  
Search Direction ◽  
Descent Property

In this paper we can derive a new search direction of conjugating gradient method associated with (Dai-Liao method ) the new algorithm becomes converged by assuming some hypothesis. We are also able to prove the Descent property for the new method, numerical results showed for the proposed method is effective comparing with the (FR, HS and DY) methods.   http://dx.doi.org/10.25130/tjps.25.2020.019    

scholarly journals A Modified Three-Term Type CD Conjugate Gradient Algorithm for Unconstrained Optimization Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Zhan Wang ◽  
Pengyuan Li ◽  
Xiangrong Li ◽  
Hongtruong Pham
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Trust Region ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
General Function ◽  
Term Type

Conjugate gradient methods are well-known methods which are widely applied in many practical fields. CD conjugate gradient method is one of the classical types. In this paper, a modified three-term type CD conjugate gradient algorithm is proposed. Some good features are presented as follows: (i) A modified three-term type CD conjugate gradient formula is presented. (ii) The given algorithm possesses sufficient descent property and trust region property. (iii) The algorithm has global convergence with the modified weak Wolfe–Powell (MWWP) line search technique and projection technique for general function. The new algorithm has made great progress in numerical experiments. It shows that the modified three-term type CD conjugate gradient method is more competitive than the classical CD conjugate gradient method.

scholarly journals Spectral CG Algorithm for Solving Fuzzy Nonlinear Equations

2022 ◽  
pp. 1-10
Author(s):  
Mezher M. Abed ◽  
Ufuk Öztürk ◽  
Hisham M. Khudhur
Keyword(s):  
Nonlinear Equations ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Conjugacy Condition ◽  
Wide Range ◽  
Non Linear ◽  
Fuzzy Equations

The nonlinear conjugate gradient method is an effective technique for solving large-scale minimizations problems, and has a wide range of applications in various fields, such as mathematics, chemistry, physics, engineering and medicine. This study presents a novel spectral conjugate gradient algorithm (non-linear conjugate gradient algorithm), which is derived based on the Hisham–Khalil (KH) and Newton algorithms. Based on pure conjugacy condition The importance of this research lies in finding an appropriate method to solve all types of linear and non-linear fuzzy equations because the Buckley and Qu method is ineffective in solving fuzzy equations. Moreover, the conjugate gradient method does not need a Hessian matrix (second partial derivatives of functions) in the solution. The descent property of the proposed method is shown provided that the step size at meets the strong Wolfe conditions. In numerous circumstances, numerical results demonstrate that the proposed technique is more efficient than the Fletcher–Reeves and KH algorithms in solving fuzzy nonlinear equations.

scholarly journals A Modified Liu and Storey Conjugate Gradient Method for Large Scale Unconstrained Optimization Problems

Algorithms ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 227
Author(s):  
Zabidin Salleh ◽  
Ghaliah Alhamzi ◽  
Ibitsam Masmali ◽  
Ahmad Alhawarat
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Numerical Results ◽  
New Method ◽  
Unconstrained Optimization Problems ◽  
Large Scale Unconstrained Optimization

The conjugate gradient method is one of the most popular methods to solve large-scale unconstrained optimization problems since it does not require the second derivative, such as Newton’s method or approximations. Moreover, the conjugate gradient method can be applied in many fields such as neural networks, image restoration, etc. Many complicated methods are proposed to solve these optimization functions in two or three terms. In this paper, we propose a simple, easy, efficient, and robust conjugate gradient method. The new method is constructed based on the Liu and Storey method to overcome the convergence problem and descent property. The new modified method satisfies the convergence properties and the sufficient descent condition under some assumptions. The numerical results show that the new method outperforms famous CG methods such as CG-Descent5.3, Liu and Storey, and Dai and Liao. The numerical results include the number of iterations and CPU 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 Conjugate gradient algorithm and fractals

2006 ◽  
Vol 2006 ◽  
pp. 1-15 ◽  
Author(s):  
Mohamed Lamine Sahari ◽  
Ilhem Djellit
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Fractal Structures

This work is an extension of the survey on Cayley's problem in case where the conjugate gradient method is used. We show that for certain values of parameters, this method produces beautiful fractal structures.

MATRIX ANALYSES ON THE DAI–LIAO CONJUGATE GRADIENT METHOD

2019 ◽  
Vol 61 (02) ◽  
pp. 195-203
Author(s):  
Z. AMINIFARD ◽  
S. BABAIE-KAFAKI
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Search Direction ◽  
Condition Numbers ◽  
Test Problems ◽  
Spectral Condition ◽  
Testing Environment ◽  
Measure Function ◽  
Descent Property

Some optimal choices for a parameter of the Dai–Liao conjugate gradient method are proposed by conducting matrix analyses of the method. More precisely, first the $\ell _{1}$ and $\ell _{\infty }$ norm condition numbers of the search direction matrix are minimized, yielding two adaptive choices for the Dai–Liao parameter. Then we show that a recent formula for computing this parameter which guarantees the descent property can be considered as a minimizer of the spectral condition number as well as the well-known measure function for a symmetrized version of the search direction matrix. Brief convergence analyses are also carried out. Finally, some numerical experiments on a set of test problems related to constrained and unconstrained testing environment, are conducted using a well-known performance profile.

Tomographic inversion via the conjugate gradient method

Geophysics ◽  
1987 ◽  
Vol 52 (2) ◽  
pp. 179-185 ◽  
Author(s):  
John A. Scales
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Sparse Matrices ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Algebraic Equations ◽  
Tomographic Inversion ◽  
Linear Algebraic Equations ◽  
The Matrix

Tomographic inversion of seismic traveltime residuals is now an established and widely used technique for imaging the Earth’s interior. This inversion procedure results in large, but sparse, rectangular systems of linear algebraic equations; in practice there may be tens or even hundreds of thousands of simultaneous equations. This paper applies the classic conjugate gradient algorithm of Hestenes and Stiefel to the least‐squares solution of large, sparse systems of traveltime equations. The conjugate gradient method is fast, accurate, and easily adapted to take advantage of the sparsity of the matrix. The techniques necessary for manipulating sparse matrices are outlined in the Appendix. In addition, the results of the conjugate gradient algorithm are compared to results from two of the more widely used tomographic inversion algorithms.

scholarly journals A New Nonlinear Conjugate Gradient Method Based on the Scaled Matrix

2017 ◽  
Vol 27 (5) ◽  
pp. 68
Author(s):  
Basim A. Hassan ◽  
Haneen A. Alashoor
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Numerical Results ◽  
New Method ◽  
Test Problems ◽  
Nonlinear Conjugate Gradient Method ◽  
Nonlinear Conjugate Gradient ◽  
New Type ◽  
The Given

In this paper, a new type nonlinear conjugate gradient method based on the ScaleMatrix is derived. The new method has the decent and globally convergentproperties under some assumptions. Numerical results indicate the efficiency ofthis method to solve the given test problems.

Sign in / Sign up

Export Citation Format

Share Document