Diagonal preconditioned conjugate gradient algorithm for unconstrained optimization
The nonlinear conjugate gradient (CG) methods have widely been used in solving unconstrained optimization problems. They are well-suited for large-scale optimization problems due to their low memory requirements and least computational costs. In this paper, a new diagonal preconditioned conjugate gr...
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| Format: | Article |
| Language: | English |
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Universiti Putra Malaysia Press
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/40566/ http://psasir.upm.edu.my/id/eprint/40566/1/48.%20Diagonal%20Preconditioned%20Conjugate%20Gradient%20Algorithm%20for.pdf |
| _version_ | 1848849463654744064 |
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| author | Ng, Choong Boon Leong, Wah June Monsi, Mansor |
| author_facet | Ng, Choong Boon Leong, Wah June Monsi, Mansor |
| author_sort | Ng, Choong Boon |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The nonlinear conjugate gradient (CG) methods have widely been used in solving unconstrained optimization problems. They are well-suited for large-scale optimization problems due to their low memory requirements and least computational costs. In this paper, a new diagonal preconditioned conjugate gradient (PRECG) algorithm is designed, and this is motivated by the fact that a pre-conditioner can greatly enhance the performance of the CG method. Under mild conditions, it is shown that the algorithm is globally convergent for strongly convex functions. Numerical results are presented to show that the new diagonal PRECG method works better than the standard CG method. |
| first_indexed | 2025-11-15T09:50:48Z |
| format | Article |
| id | upm-40566 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:50:48Z |
| publishDate | 2014 |
| publisher | Universiti Putra Malaysia Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-405662019-10-09T08:28:00Z http://psasir.upm.edu.my/id/eprint/40566/ Diagonal preconditioned conjugate gradient algorithm for unconstrained optimization Ng, Choong Boon Leong, Wah June Monsi, Mansor The nonlinear conjugate gradient (CG) methods have widely been used in solving unconstrained optimization problems. They are well-suited for large-scale optimization problems due to their low memory requirements and least computational costs. In this paper, a new diagonal preconditioned conjugate gradient (PRECG) algorithm is designed, and this is motivated by the fact that a pre-conditioner can greatly enhance the performance of the CG method. Under mild conditions, it is shown that the algorithm is globally convergent for strongly convex functions. Numerical results are presented to show that the new diagonal PRECG method works better than the standard CG method. Universiti Putra Malaysia Press 2014 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/40566/1/48.%20Diagonal%20Preconditioned%20Conjugate%20Gradient%20Algorithm%20for.pdf Ng, Choong Boon and Leong, Wah June and Monsi, Mansor (2014) Diagonal preconditioned conjugate gradient algorithm for unconstrained optimization. Pertanika Journal of Science & Technology, 22 (1). pp. 213-224. ISSN 0128-7680; ESSN: 2231-8526 http://pertanika.upm.edu.my/Pertanika%20PAPERS/JST%20Vol.%2022%20(1)%20Jan.%202014/18%20Page%20213-224%20(JST%200385-2012).pdf |
| spellingShingle | Ng, Choong Boon Leong, Wah June Monsi, Mansor Diagonal preconditioned conjugate gradient algorithm for unconstrained optimization |
| title | Diagonal preconditioned conjugate gradient algorithm for unconstrained optimization |
| title_full | Diagonal preconditioned conjugate gradient algorithm for unconstrained optimization |
| title_fullStr | Diagonal preconditioned conjugate gradient algorithm for unconstrained optimization |
| title_full_unstemmed | Diagonal preconditioned conjugate gradient algorithm for unconstrained optimization |
| title_short | Diagonal preconditioned conjugate gradient algorithm for unconstrained optimization |
| title_sort | diagonal preconditioned conjugate gradient algorithm for unconstrained optimization |
| url | http://psasir.upm.edu.my/id/eprint/40566/ http://psasir.upm.edu.my/id/eprint/40566/ http://psasir.upm.edu.my/id/eprint/40566/1/48.%20Diagonal%20Preconditioned%20Conjugate%20Gradient%20Algorithm%20for.pdf |