A conjugate gradient algorithm for large-scale nonlinear equations and image restoration problems

Nonlinear systems present a quite complicate problem. As the number of dimensions increases, it becomes more difficult to find the solution of the problem. In this paper, a modified conjugate gradient method is designed that has a sufficient descent property and trust region property. It is interest...

Full description

Saved in:
Bibliographic Details
Published in:Applied numerical mathematics 2020-01, Vol.147, p.129-141
Main Authors: Yuan, Gonglin, Li, Tingting, Hu, Wujie
Format: Article
Language:English
Subjects:
Conjugate gradient
Global convergence
Nonlinear system
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Nonlinear systems present a quite complicate problem. As the number of dimensions increases, it becomes more difficult to find the solution of the problem. In this paper, a modified conjugate gradient method is designed that has a sufficient descent property and trust region property. It is interesting that the formula for search direction makes full use of the property of convex combination between the deepest descent algorithm and the classical LS conjugate gradient (CG) method. The global convergence property is established under certain conditions, and the numerical results show that the modified method is effective for normal nonlinear equations and image restoration problems.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2019.08.022