Multi-spectral gradient method via variational technique under log-determinant norm for large-scale optimization
The spectral gradient method is popular due to the fact that only the gradient of the objective function is required at each iterate. Besides that, it is more efficient than the quasi-Newton method as the storage of second derivatives (Hessian) approximation are not required especially when the dime...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Malaysian Mathematical Science Society
2017
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| Online Access: | http://psasir.upm.edu.my/id/eprint/62502/ http://psasir.upm.edu.my/id/eprint/62502/1/SPECTRAL.pdf |
| _version_ | 1848854634408443904 |
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| author | Hong, Seng Sim Leong, Wah June Chen, Chuei Yee Ibrahim, Siti Nur Iqmal |
| author_facet | Hong, Seng Sim Leong, Wah June Chen, Chuei Yee Ibrahim, Siti Nur Iqmal |
| author_sort | Hong, Seng Sim |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The spectral gradient method is popular due to the fact that only the gradient of the objective function is required at each iterate. Besides that, it is more efficient than the quasi-Newton method as the storage of second derivatives (Hessian) approximation are not required especially when the dimension of the problem is large. In this paper, we propose a spectral gradient method via variational technique under log-determinant measure such that it satisfies the weaker secant equation. The corresponding variational problem is solved and the Lagrange multiplier is approximated using the Newton-Raphson method and solved following interior point method that is associated with weaker secant relation. An executable code is developed to test the efficiency of the proposed method with some standard conjugate-gradient methods. Numerical results are presented which suggest a better performance has been achieved. |
| first_indexed | 2025-11-15T11:12:59Z |
| format | Article |
| id | upm-62502 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T11:12:59Z |
| publishDate | 2017 |
| publisher | Malaysian Mathematical Science Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-625022020-12-03T20:07:49Z http://psasir.upm.edu.my/id/eprint/62502/ Multi-spectral gradient method via variational technique under log-determinant norm for large-scale optimization Hong, Seng Sim Leong, Wah June Chen, Chuei Yee Ibrahim, Siti Nur Iqmal The spectral gradient method is popular due to the fact that only the gradient of the objective function is required at each iterate. Besides that, it is more efficient than the quasi-Newton method as the storage of second derivatives (Hessian) approximation are not required especially when the dimension of the problem is large. In this paper, we propose a spectral gradient method via variational technique under log-determinant measure such that it satisfies the weaker secant equation. The corresponding variational problem is solved and the Lagrange multiplier is approximated using the Newton-Raphson method and solved following interior point method that is associated with weaker secant relation. An executable code is developed to test the efficiency of the proposed method with some standard conjugate-gradient methods. Numerical results are presented which suggest a better performance has been achieved. Malaysian Mathematical Science Society 2017 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/62502/1/SPECTRAL.pdf Hong, Seng Sim and Leong, Wah June and Chen, Chuei Yee and Ibrahim, Siti Nur Iqmal (2017) Multi-spectral gradient method via variational technique under log-determinant norm for large-scale optimization. Discovering Mathematics (Menemui Matematik), 39 (1). 22 - 29. ISSN 2231-7023 https://einspem.upm.edu.my/ojs/index.php/dismath/article/view/8 |
| spellingShingle | Hong, Seng Sim Leong, Wah June Chen, Chuei Yee Ibrahim, Siti Nur Iqmal Multi-spectral gradient method via variational technique under log-determinant norm for large-scale optimization |
| title | Multi-spectral gradient method via variational technique under log-determinant norm for large-scale optimization |
| title_full | Multi-spectral gradient method via variational technique under log-determinant norm for large-scale optimization |
| title_fullStr | Multi-spectral gradient method via variational technique under log-determinant norm for large-scale optimization |
| title_full_unstemmed | Multi-spectral gradient method via variational technique under log-determinant norm for large-scale optimization |
| title_short | Multi-spectral gradient method via variational technique under log-determinant norm for large-scale optimization |
| title_sort | multi-spectral gradient method via variational technique under log-determinant norm for large-scale optimization |
| url | http://psasir.upm.edu.my/id/eprint/62502/ http://psasir.upm.edu.my/id/eprint/62502/ http://psasir.upm.edu.my/id/eprint/62502/1/SPECTRAL.pdf |