A New Modified Three-Term Hestenes–Stiefel Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence
Joint Authors
Salleh, Zabidin
Alhawarat, Ahmad
Baluch, Bakhtawar
Source
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-09-27
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
This paper describes a modified three-term Hestenes–Stiefel (HS) method.
The original HS method is the earliest conjugate gradient method.
Although the HS method achieves global convergence using an exact line search, this is not guaranteed in the case of an inexact line search.
In addition, the HS method does not usually satisfy the descent property.
Our modified three-term conjugate gradient method possesses a sufficient descent property regardless of the type of line search and guarantees global convergence using the inexact Wolfe–Powell line search.
The numerical efficiency of the modified three-term HS method is checked using 75 standard test functions.
It is known that three-term conjugate gradient methods are numerically more efficient than two-term conjugate gradient methods.
Importantly, this paper quantifies how much better the three-term performance is compared with two-term methods.
Thus, in the numerical results, we compare our new modification with an efficient two-term conjugate gradient method.
We also compare our modification with a state-of-the-art three-term HS method.
Finally, we conclude that our proposed modification is globally convergent and numerically efficient.
American Psychological Association (APA)
Baluch, Bakhtawar& Salleh, Zabidin& Alhawarat, Ahmad. 2018. A New Modified Three-Term Hestenes–Stiefel Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence. Journal of Optimization،Vol. 2018, no. 2018, pp.1-13.
https://search.emarefa.net/detail/BIM-1197253
Modern Language Association (MLA)
Baluch, Bakhtawar…[et al.]. A New Modified Three-Term Hestenes–Stiefel Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence. Journal of Optimization No. 2018 (2018), pp.1-13.
https://search.emarefa.net/detail/BIM-1197253
American Medical Association (AMA)
Baluch, Bakhtawar& Salleh, Zabidin& Alhawarat, Ahmad. A New Modified Three-Term Hestenes–Stiefel Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence. Journal of Optimization. 2018. Vol. 2018, no. 2018, pp.1-13.
https://search.emarefa.net/detail/BIM-1197253
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1197253