Sultan Qaboos University House of Expertise Home
A family of three-term conjugate gradient methods with sufficient descent property for unconstrained optimization
Mehiddin Al-Baali, Yasushi Narushima*, Hiroshi Yabe
Recently, conjugate gradient methods, which usually generate descent search directions, are useful for large-scale optimization. Narushima et al. (SIAM J Optim 21:212–230, 2011) have proposed a three-term conjugate gradient method which satisfies a sufficient descent condition. We extend this method to two parameters family of three-term conjugate gradient methods which can be used to control the magnitude of the directional derivative. We show that these methods converge globally and work well for suitable choices of the parameters. Numerical results are also presented.
Computational Optimization and Applications
Global convergence
Sufficient descent condition
Three-term conjugate gradient method
Unconstrained optimization
Dive into the research topics of 'A family of three-term conjugate gradient methods with sufficient descent property for unconstrained optimization'. Together they form a unique fingerprint.
Conjugate gradient method Engineering & Materials Science 100%
Unconstrained Optimization Mathematics 88%
Conjugate Gradient Method Mathematics 85%
Descent Mathematics 80%
Sufficient Mathematics 58%
Term Mathematics 42%
Family Mathematics 37%
Large-scale Optimization Mathematics 34%
Al-Baali, M., Narushima, Y., & Yabe, H. (2014). A family of three-term conjugate gradient methods with sufficient descent property for unconstrained optimization. Computational Optimization and Applications, 60(1), 89-110. https://doi.org/10.1007/s10589-014-9662-z
A family of three-term conjugate gradient methods with sufficient descent property for unconstrained optimization. / Al-Baali, Mehiddin; Narushima, Yasushi; Yabe, Hiroshi.
In: Computational Optimization and Applications, Vol. 60, No. 1, 01.2014, p. 89-110.
Al-Baali, M, Narushima, Y & Yabe, H 2014, 'A family of three-term conjugate gradient methods with sufficient descent property for unconstrained optimization', Computational Optimization and Applications, vol. 60, no. 1, pp. 89-110. https://doi.org/10.1007/s10589-014-9662-z
Al-Baali M, Narushima Y, Yabe H. A family of three-term conjugate gradient methods with sufficient descent property for unconstrained optimization. Computational Optimization and Applications. 2014 Jan;60(1):89-110. https://doi.org/10.1007/s10589-014-9662-z
Al-Baali, Mehiddin ; Narushima, Yasushi ; Yabe, Hiroshi. / A family of three-term conjugate gradient methods with sufficient descent property for unconstrained optimization. In: Computational Optimization and Applications. 2014 ; Vol. 60, No. 1. pp. 89-110.
@article{7892bba7e3544a638134c93ac9f442cd,
title = "A family of three-term conjugate gradient methods with sufficient descent property for unconstrained optimization",
abstract = "Recently, conjugate gradient methods, which usually generate descent search directions, are useful for large-scale optimization. Narushima et al. (SIAM J Optim 21:212–230, 2011) have proposed a three-term conjugate gradient method which satisfies a sufficient descent condition. We extend this method to two parameters family of three-term conjugate gradient methods which can be used to control the magnitude of the directional derivative. We show that these methods converge globally and work well for suitable choices of the parameters. Numerical results are also presented.",
keywords = "Global convergence, Sufficient descent condition, Three-term conjugate gradient method, Unconstrained optimization",
author = "Mehiddin Al-Baali and Yasushi Narushima and Hiroshi Yabe",
note = "Funding Information: The authors would like to thank Prof. William W. Hager, the Editor-in-Chief of the journal, and the anonymous reviewers for valuable comments on a draft of this paper. We would also like to thank Prof. Yu-Hong Dai for providing his program code of conjugate gradient methods. The second and third authors are supported in part by the Grant-in-Aid for Scientific Research (C) 25330030 of Japan Society for the Promotion of Science Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media New York.",
journal = "Computational Optimization and Applications",
T1 - A family of three-term conjugate gradient methods with sufficient descent property for unconstrained optimization
AU - Al-Baali, Mehiddin
AU - Narushima, Yasushi
AU - Yabe, Hiroshi
N1 - Funding Information: The authors would like to thank Prof. William W. Hager, the Editor-in-Chief of the journal, and the anonymous reviewers for valuable comments on a draft of this paper. We would also like to thank Prof. Yu-Hong Dai for providing his program code of conjugate gradient methods. The second and third authors are supported in part by the Grant-in-Aid for Scientific Research (C) 25330030 of Japan Society for the Promotion of Science Publisher Copyright: © 2014, Springer Science+Business Media New York.
N2 - Recently, conjugate gradient methods, which usually generate descent search directions, are useful for large-scale optimization. Narushima et al. (SIAM J Optim 21:212–230, 2011) have proposed a three-term conjugate gradient method which satisfies a sufficient descent condition. We extend this method to two parameters family of three-term conjugate gradient methods which can be used to control the magnitude of the directional derivative. We show that these methods converge globally and work well for suitable choices of the parameters. Numerical results are also presented.
AB - Recently, conjugate gradient methods, which usually generate descent search directions, are useful for large-scale optimization. Narushima et al. (SIAM J Optim 21:212–230, 2011) have proposed a three-term conjugate gradient method which satisfies a sufficient descent condition. We extend this method to two parameters family of three-term conjugate gradient methods which can be used to control the magnitude of the directional derivative. We show that these methods converge globally and work well for suitable choices of the parameters. Numerical results are also presented.
KW - Global convergence
KW - Sufficient descent condition
KW - Three-term conjugate gradient method
KW - Unconstrained optimization
JO - Computational Optimization and Applications
JF - Computational Optimization and Applications