Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained Optimization

Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained Optimization

A new nonlinear spectral conjugate descent method for solving unconstrained optimization problems is proposed on the basis of the CD method and the spectral conjugate gradient method. For any line search, the new method satisfies the sufficient descent condition gkTdk<−∥gk∥2. Moreover, we prove t...

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Main Authors: Jinkui Liu, Youyi Jiang
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/758287
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spelling doaj-361c964c45044025ad602233b7e8a7662020-11-24T22:38:03ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/758287758287Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained OptimizationJinkui Liu0Youyi Jiang1College of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000, ChinaCollege of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000, ChinaA new nonlinear spectral conjugate descent method for solving unconstrained optimization problems is proposed on the basis of the CD method and the spectral conjugate gradient method. For any line search, the new method satisfies the sufficient descent condition gkTdk<−∥gk∥2. Moreover, we prove that the new method is globally convergent under the strong Wolfe line search. The numerical results show that the new method is more effective for the given test problems from the CUTE test problem library (Bongartz et al., 1995) in contrast to the famous CD method, FR method, and PRP method.http://dx.doi.org/10.1155/2012/758287
collection DOAJ
language English
format Article
sources DOAJ
author Jinkui Liu
Youyi Jiang
spellingShingle Jinkui Liu
Youyi Jiang
Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained Optimization
Abstract and Applied Analysis
author_facet Jinkui Liu
Youyi Jiang
author_sort Jinkui Liu
title Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained Optimization
title_short Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained Optimization
title_full Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained Optimization
title_fullStr Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained Optimization
title_full_unstemmed Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained Optimization
title_sort global convergence of a spectral conjugate gradient method for unconstrained optimization
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description A new nonlinear spectral conjugate descent method for solving unconstrained optimization problems is proposed on the basis of the CD method and the spectral conjugate gradient method. For any line search, the new method satisfies the sufficient descent condition gkTdk<−∥gk∥2. Moreover, we prove that the new method is globally convergent under the strong Wolfe line search. The numerical results show that the new method is more effective for the given test problems from the CUTE test problem library (Bongartz et al., 1995) in contrast to the famous CD method, FR method, and PRP method.
url http://dx.doi.org/10.1155/2012/758287
work_keys_str_mv AT jinkuiliu globalconvergenceofaspectralconjugategradientmethodforunconstrainedoptimization
AT youyijiang globalconvergenceofaspectralconjugategradientmethodforunconstrainedoptimization
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