Descent three-term conjugate gradient methods based on secant conditions for unconstrained optimization

The conjugate gradient method is an effective method for large-scale unconstrained optimization problems. Recent research has proposed conjugate gradient methods based on secant conditions to establish fast convergence of the methods. However, these methods do not always generate a descent search di...

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Bibliographic Details
Published inOptimization methods & software Vol. 32; no. 6; pp. 1313 - 1329
Main Authors Kobayashi, Hiroshi, Narushima, Yasushi, Yabe, Hiroshi
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.11.2017
Taylor & Francis Ltd
Subjects
Conjugate gradient method
Convergence
Descent
Distributed processing
global convergence
Methods
Multiprocessing
Optimization
Queuing theory
secant condition
sufficient descent property
three-term conjugate gradient method
unconstrained optimization
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Summary:The conjugate gradient method is an effective method for large-scale unconstrained optimization problems. Recent research has proposed conjugate gradient methods based on secant conditions to establish fast convergence of the methods. However, these methods do not always generate a descent search direction. In contrast, Y. Narushima, H. Yabe, and J.A. Ford [A three-term conjugate gradient method with sufficient descent property for unconstrained optimization, SIAM J. Optim. 21 (2011), pp. 212-230] proposed a three-term conjugate gradient method which always satisfies the sufficient descent condition. This paper makes use of both ideas to propose descent three-term conjugate gradient methods based on particular secant conditions, and then shows their global convergence properties. Finally, numerical results are given.
ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2017.1338288