New Conjugacy Conditions and Related Nonlinear Conjugate Gradient Methods

Conjugate gradient methods are a class of important methods for unconstrained optimization, especially when the dimension is large. This paper proposes a new conjugacy condition, which considers an inexact line search scheme but reduces to the old one if the line search is exact. Based on the new co...

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Bibliographic Details
Published in:Applied mathematics & optimization 2001-01, Vol.43 (1), p.87-101
Main Authors: Dai, Y.-H., E-mail: dyh@lsec.cc.ac.cn, Liao, L.-Z.
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Conjugate gradient method
CONVERGENCE
NONLINEAR PROBLEMS
Numerical methods
OPTIMIZATION
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Summary:Conjugate gradient methods are a class of important methods for unconstrained optimization, especially when the dimension is large. This paper proposes a new conjugacy condition, which considers an inexact line search scheme but reduces to the old one if the line search is exact. Based on the new conjugacy condition, two nonlinear conjugate gradient methods are constructed. Convergence analysis for the two methods is provided. Our numerical results show that one of the methods is very efficient for the given test problems.
ISSN:0095-4616
1432-0606
DOI:10.1007/s002450010019