Sufficient descent conjugate gradient methods for large-scale optimization problems

2011 ◽  
Vol 88 (16) ◽  
pp. 3436-3447 ◽  
Author(s):  
Xiuyun Zheng ◽  
Hongwei Liu ◽  
Aiguo Lu
Keyword(s):  
Conjugate Gradient ◽  
Large Scale ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Large Scale Optimization ◽  
Sufficient Descent ◽  
Scale Optimization

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 Sufficient Descent Conjugate Gradient Methods for Solving Convex Constrained Nonlinear Monotone Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
San-Yang Liu ◽  
Yuan-Yuan Huang ◽  
Hong-Wei Jiao
Keyword(s):  
Global Convergence ◽  
Projection Method ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Monotone Equations ◽  
Mild Conditions ◽  
Sufficient Descent ◽  
Nonlinear Monotone Equations

Two unified frameworks of some sufficient descent conjugate gradient methods are considered. Combined with the hyperplane projection method of Solodov and Svaiter, they are extended to solve convex constrained nonlinear monotone equations. Their global convergence is proven under some mild conditions. Numerical results illustrate that these methods are efficient and can be applied to solve large-scale nonsmooth equations.

scholarly journals The Sufficient Descent Condition of Nonlinear Conjugate Gradient Method

2018 ◽  
Vol 7 (4.30) ◽  
pp. 458
Author(s):  
Srimazzura Basri ◽  
Mustafa Mamat ◽  
Puspa Liza Ghazali
Keyword(s):  
Conjugate Gradient ◽  
Large Scale ◽  
Gradient Methods ◽  
Sufficient Descent Condition ◽  
Nonlinear Conjugate Gradient Method ◽  
Non Linear ◽  
Nonlinear Conjugate Gradient ◽  
Sufficient Descent ◽  
Descent Condition ◽  
Scale Optimization

Non-linear conjugate gradient methods has been widely used instrumental in solving large scale optimization. These methods has been proved that only required very low memory other than its numerical efficiency. Thus, many studies have been conducted to improve these methods to find the most efficient method. In this paper, we proposed a new non-linear conjugate gradient coefficient that guarantees sufficient descent condition. Numerical tests indicate that the proposed coefficient is better than the three classical conjugate gradient coefficients.

scholarly journals A New Conjugate Gradient Method with Sufficient Descent Property

2021 ◽  
pp. 163-174
Author(s):  
O.B. Akinduko
Keyword(s):  
Conjugate Gradient ◽  
Large Scale ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Superior Performance ◽  
Sufficient Descent Property ◽  
Unconstrained Optimization Problems ◽  
Descent Property ◽  
Sufficient Descent ◽  
Large Scale Unconstrained Optimization

In this paper, by linearly combining the numerator and denominator terms of the Dai-Liao (DL) and Bamigbola-Ali-Nwaeze (BAN) conjugate gradient methods (CGMs), a general form of DL-BAN method has been proposed. From this general form, a new hybrid CGM, which was found to possess a sufficient descent property is generated. Numerical experiment was carried out on the new CGM in comparison with four existing CGMs, using some set of large scale unconstrained optimization problems. The result showed a superior performance of new method over majority of the existing methods.

Sign in / Sign up

Export Citation Format

Share Document