A scaled three-term conjugate gradient method for unconstrained optimization
Conjugate gradient methods play an important role in many fields of application due to their simplicity, low memory requirements, and global convergence properties. In this paper, we propose an efficient three-term conjugate gradient method by utilizing the DFP update for the inverse Hessian approxi...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2016
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/54932/1/A%20scaled%20three-term%20conjugate%20gradient%20method%20for%20unconstrained%20optimization.pdf |
| _version_ | 1796976172949569536 |
|---|---|
| author | Arzuka, Ibrahim Abu Bakar, Mohd Rizam Leong, Wah June |
| author_facet | Arzuka, Ibrahim Abu Bakar, Mohd Rizam Leong, Wah June |
| author_sort | Arzuka, Ibrahim |
| collection | UPM |
| description | Conjugate gradient methods play an important role in many fields of application due to their simplicity, low memory requirements, and global convergence properties. In this paper, we propose an efficient three-term conjugate gradient method by utilizing the DFP update for the inverse Hessian approximation which satisfies both the sufficient descent and the conjugacy conditions. The basic philosophy is that the DFP update is restarted with a multiple of the identity matrix in every iteration. An acceleration scheme is incorporated in the proposed method to enhance the reduction in function value. Numerical results from an implementation of the proposed method on some standard unconstrained optimization problem show that the proposed method is promising and exhibits a superior numerical performance in comparison with other well-known conjugate gradient methods. |
| first_indexed | 2024-03-06T09:21:59Z |
| format | Article |
| id | upm.eprints-54932 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:21:59Z |
| publishDate | 2016 |
| publisher | SpringerOpen |
| record_format | dspace |
| spelling | upm.eprints-549322019-10-09T08:54:51Z http://psasir.upm.edu.my/id/eprint/54932/ A scaled three-term conjugate gradient method for unconstrained optimization Arzuka, Ibrahim Abu Bakar, Mohd Rizam Leong, Wah June Conjugate gradient methods play an important role in many fields of application due to their simplicity, low memory requirements, and global convergence properties. In this paper, we propose an efficient three-term conjugate gradient method by utilizing the DFP update for the inverse Hessian approximation which satisfies both the sufficient descent and the conjugacy conditions. The basic philosophy is that the DFP update is restarted with a multiple of the identity matrix in every iteration. An acceleration scheme is incorporated in the proposed method to enhance the reduction in function value. Numerical results from an implementation of the proposed method on some standard unconstrained optimization problem show that the proposed method is promising and exhibits a superior numerical performance in comparison with other well-known conjugate gradient methods. SpringerOpen 2016 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/54932/1/A%20scaled%20three-term%20conjugate%20gradient%20method%20for%20unconstrained%20optimization.pdf Arzuka, Ibrahim and Abu Bakar, Mohd Rizam and Leong, Wah June (2016) A scaled three-term conjugate gradient method for unconstrained optimization. Journal of Inequalities and Applications, 2016. art. no. 325. pp. 1-16. ISSN 1025-5834; ESSN: 1029-242X 10.1186/s13660-016-1239-1 |
| spellingShingle | Arzuka, Ibrahim Abu Bakar, Mohd Rizam Leong, Wah June A scaled three-term conjugate gradient method for unconstrained optimization |
| title | A scaled three-term conjugate gradient method for unconstrained optimization |
| title_full | A scaled three-term conjugate gradient method for unconstrained optimization |
| title_fullStr | A scaled three-term conjugate gradient method for unconstrained optimization |
| title_full_unstemmed | A scaled three-term conjugate gradient method for unconstrained optimization |
| title_short | A scaled three-term conjugate gradient method for unconstrained optimization |
| title_sort | scaled three term conjugate gradient method for unconstrained optimization |
| url | http://psasir.upm.edu.my/id/eprint/54932/1/A%20scaled%20three-term%20conjugate%20gradient%20method%20for%20unconstrained%20optimization.pdf |
| work_keys_str_mv | AT arzukaibrahim ascaledthreetermconjugategradientmethodforunconstrainedoptimization AT abubakarmohdrizam ascaledthreetermconjugategradientmethodforunconstrainedoptimization AT leongwahjune ascaledthreetermconjugategradientmethodforunconstrainedoptimization AT arzukaibrahim scaledthreetermconjugategradientmethodforunconstrainedoptimization AT abubakarmohdrizam scaledthreetermconjugategradientmethodforunconstrainedoptimization AT leongwahjune scaledthreetermconjugategradientmethodforunconstrainedoptimization |