A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.

A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.

It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new P...

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Main Authors: Xiangrong Li, Xupei Zhao, Xiabin Duan, Xiaoliang Wang
Format: Article
Language:English
Published: Public Library of Science (PLoS) 2015-01-01
Series:PLoS ONE
Online Access:http://europepmc.org/articles/PMC4575111?pdf=render
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spelling doaj-4dac5b5e37374c34bc9ecd600c457da62020-11-24T21:27:11ZengPublic Library of Science (PLoS)PLoS ONE1932-62032015-01-01109e013716610.1371/journal.pone.0137166A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.Xiangrong LiXupei ZhaoXiabin DuanXiaoliang WangIt is generally acknowledged that the conjugate gradient (CG) method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.http://europepmc.org/articles/PMC4575111?pdf=render
collection DOAJ
language English
format Article
sources DOAJ
author Xiangrong Li
Xupei Zhao
Xiabin Duan
Xiaoliang Wang
spellingShingle Xiangrong Li
Xupei Zhao
Xiabin Duan
Xiaoliang Wang
A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.
PLoS ONE
author_facet Xiangrong Li
Xupei Zhao
Xiabin Duan
Xiaoliang Wang
author_sort Xiangrong Li
title A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.
title_short A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.
title_full A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.
title_fullStr A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.
title_full_unstemmed A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.
title_sort conjugate gradient algorithm with function value information and n-step quadratic convergence for unconstrained optimization.
publisher Public Library of Science (PLoS)
series PLoS ONE
issn 1932-6203
publishDate 2015-01-01
description It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.
url http://europepmc.org/articles/PMC4575111?pdf=render
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AT xiaoliangwang aconjugategradientalgorithmwithfunctionvalueinformationandnstepquadraticconvergenceforunconstrainedoptimization
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AT xupeizhao conjugategradientalgorithmwithfunctionvalueinformationandnstepquadraticconvergenceforunconstrainedoptimization
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