scholarly journals The application of new conjugate gradient methods in estimating data

2018 ◽  
Vol 7 (2.14) ◽  
pp. 25 ◽  
Author(s):  
Syazni Shoid ◽  
Norrlaili Shapiee ◽  
Norhaslinda Zull ◽  
Nur Hamizah Abdul Ghani ◽  
Nur Syarafina Mohamed ◽  
...  
Keyword(s):  
Conjugate Gradient ◽  
Numerical Experiments ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Real Life ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Large Scale Optimization ◽  
Scale Optimization

Many researchers are intended to improve the conjugate gradient (CG) methods as well as their applications in real life. Besides, CG become more interesting and useful in many disciplines and has important role for solving large-scale optimization problems. In this paper, three types of new CG coefficients are presented with application in estimating data. Numerical experiments show that the proposed methods have succeeded in solving problems under strong Wolfe Powell line search conditions. 

A new three-term spectral conjugate gradient algorithm with higher numerical performance for solving large scale optimization problems based on Quasi-Newton equation

2021 ◽  
pp. 2150053
Author(s):  
Jie Guo ◽  
Zhong Wan
Keyword(s):  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Gradient Algorithm ◽  
Large Scale Optimization ◽  
Newton Equation ◽  
Numerical Performance ◽  
Scale Optimization ◽  
Quasi Newton

A new spectral three-term conjugate gradient algorithm in virtue of the Quasi-Newton equation is developed for solving large-scale unconstrained optimization problems. It is proved that the search directions in this algorithm always satisfy a sufficiently descent condition independent of any line search. Global convergence is established for general objective functions if the strong Wolfe line search is used. Numerical experiments are employed to show its high numerical performance in solving large-scale optimization problems. Particularly, the developed algorithm is implemented to solve the 100 benchmark test problems from CUTE with different sizes from 1000 to 10,000, in comparison with some similar ones in the literature. The numerical results demonstrate that our algorithm outperforms the state-of-the-art ones in terms of less CPU time, less number of iteration or less number of function evaluation.

scholarly journals Several Guaranteed Descent Conjugate Gradient Methods for Unconstrained Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
San-Yang Liu ◽  
Yuan-Yuan Huang
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Gradient Methods ◽  
Numerical Results ◽  
Conjugate Gradient Methods ◽  
Descent Condition ◽  
Wolfe Line Search ◽  
Large Scale Unconstrained Optimization

This paper investigates a general form of guaranteed descent conjugate gradient methods which satisfies the descent conditiongkTdk≤-1-1/4θkgk2  θk>1/4and which is strongly convergent whenever the weak Wolfe line search is fulfilled. Moreover, we present several specific guaranteed descent conjugate gradient methods and give their numerical results for large-scale unconstrained optimization.

scholarly journals Nonlinear Conjugate Gradient Methods with Wolfe Type Line Search

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yuan-Yuan Chen ◽  
Shou-Qiang Du
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Line Search ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Unconstrained Optimization Problems ◽  
Convergence Results ◽  
Nonlinear Conjugate Gradient ◽  
Nonlinear Conjugate Gradient Methods

Nonlinear conjugate gradient method is one of the useful methods for unconstrained optimization problems. In this paper, we consider three kinds of nonlinear conjugate gradient methods with Wolfe type line search for unstrained optimization problems. Under some mild assumptions, the global convergence results of the given methods are proposed. The numerical results show that the nonlinear conjugate gradient methods with Wolfe type line search are efficient for some unconstrained optimization problems.

GLOBAL CONVERGENCE OF TWO KINDS OF THREE-TERM CONJUGATE GRADIENT METHODS WITHOUT LINE SEARCH

2013 ◽  
Vol 30 (01) ◽  
pp. 1250043
Author(s):  
LIANG YIN ◽  
XIONGDA CHEN
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Search Procedure ◽  
Computational Results ◽  
Large Scale Problems ◽  
Sufficient Descent

The conjugate gradient method is widely used in unconstrained optimization, especially for large-scale problems. Recently, Zhang et al. proposed a three-term PRP method (TTPRP) and a three-term HS method (TTHS), both of which can produce sufficient descent conditions. In this paper, the global convergence of the TTPRP and TTHS methods is studied, in which the line search procedure is replaced by a fixed formula of stepsize. This character is of significance when the line search is expensive in some particular applications. In addition, relevant computational results are also presented.

scholarly journals A COMPARATIVE STUDY OF SOME MODIFICATIONS OF CG METHODS UNDER EXACT LINE SEARCH

2020 ◽  
Vol 1 (1) ◽  
pp. 12-17
Author(s):  
Yasir Salih ◽  
Mustafa Mamat ◽  
Sukono Sukono
Keyword(s):  
Conjugate Gradient ◽  
Numerical Experiments ◽  
Line Search ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Test Problems ◽  
Convergence Properties ◽  
Exact Line Search ◽  
Unconstrained Optimization Problems ◽  
Nonlinear Unconstrained Optimization

Conjugate Gradient (CG) method is a technique used in solving nonlinear unconstrained optimization problems. In this paper, we analysed the performance of two modifications and compared the results with the classical conjugate gradient methods of. These proposed methods possesse global convergence properties for general functions using exact line search. Numerical experiments show that the two modifications are more efficient for the test problems compared to classical CG coefficients.

scholarly journals Two New Conjugate Gradient Methods for Unconstrained Optimization

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Meixing Liu ◽  
Guodong Ma ◽  
Jianghua Yin
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Globally Convergent ◽  
Sufficient Descent ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search

The conjugate gradient method is very effective in solving large-scale unconstrained optimal problems. In this paper, on the basis of the conjugate parameter of the conjugate descent (CD) method and the second inequality in the strong Wolfe line search, two new conjugate parameters are devised. Using the strong Wolfe line search to obtain the step lengths, two modified conjugate gradient methods are proposed for general unconstrained optimization. Under the standard assumptions, the two presented methods are proved to be sufficient descent and globally convergent. Finally, preliminary numerical results are reported to show that the proposed methods are promising.

scholarly journals The Hybrid BFGS-CG Method in Solving Unconstrained Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Mohd Asrul Hery Ibrahim ◽  
Mustafa Mamat ◽  
Wah June Leong
Keyword(s):  
Unconstrained Optimization ◽  
Hybrid Method ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Unconstrained Optimization Problems ◽  
Large Scale Unconstrained Optimization ◽  
Quasi Newton

In solving large scale problems, the quasi-Newton method is known as the most efficient method in solving unconstrained optimization problems. Hence, a new hybrid method, known as the BFGS-CG method, has been created based on these properties, combining the search direction between conjugate gradient methods and quasi-Newton methods. In comparison to standard BFGS methods and conjugate gradient methods, the BFGS-CG method shows significant improvement in the total number of iterations and CPU time required to solve large scale unconstrained optimization problems. We also prove that the hybrid method is globally convergent.

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