A new diagonal gradient-type method for large scale unconstrained optimization
The main focus of this paper is to derive new diagonal updating scheme via the direct weak secant equation. This new scheme allows us to improve the accuracy of the Hessian's approximation and is also capable to utilize information gathered about the function in previous iterations. It follows...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Politechnica University of Bucharest
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30325/ http://psasir.upm.edu.my/id/eprint/30325/1/A%20new%20diagonal%20gradient.pdf |
| _version_ | 1848846645298462720 |
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| author | Farid, Mahboubeh Leong, Wah June Zheng, Lihong |
| author_facet | Farid, Mahboubeh Leong, Wah June Zheng, Lihong |
| author_sort | Farid, Mahboubeh |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The main focus of this paper is to derive new diagonal updating scheme via the direct weak secant equation. This new scheme allows us to improve the accuracy of the Hessian's approximation and is also capable to utilize information gathered about the function in previous iterations. It follows by an scaling approach that employs scaling parameter based upon the proposed weak secant equation to guarantee the positive definiteness of the Hessian's approximation. Moreover, we also prove the convergence of the proposed method under a simple monotone strategy. Numerical results show that the method is promising and frequently outperforms its competitors. |
| first_indexed | 2025-11-15T09:06:00Z |
| format | Article |
| id | upm-30325 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:06:00Z |
| publishDate | 2013 |
| publisher | Politechnica University of Bucharest |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-303252019-10-09T08:23:02Z http://psasir.upm.edu.my/id/eprint/30325/ A new diagonal gradient-type method for large scale unconstrained optimization Farid, Mahboubeh Leong, Wah June Zheng, Lihong The main focus of this paper is to derive new diagonal updating scheme via the direct weak secant equation. This new scheme allows us to improve the accuracy of the Hessian's approximation and is also capable to utilize information gathered about the function in previous iterations. It follows by an scaling approach that employs scaling parameter based upon the proposed weak secant equation to guarantee the positive definiteness of the Hessian's approximation. Moreover, we also prove the convergence of the proposed method under a simple monotone strategy. Numerical results show that the method is promising and frequently outperforms its competitors. Politechnica University of Bucharest 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30325/1/A%20new%20diagonal%20gradient.pdf Farid, Mahboubeh and Leong, Wah June and Zheng, Lihong (2013) A new diagonal gradient-type method for large scale unconstrained optimization. UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, 75 (1). pp. 57-64. ISSN 1223-7027 http://www.scientificbulletin.upb.ro/SeriaA_-_Matematica_si_fizica_aplicate.php?page=revistaonline&a=2&arh_an=2013&arh_ser=A&arh_nr=1 |
| spellingShingle | Farid, Mahboubeh Leong, Wah June Zheng, Lihong A new diagonal gradient-type method for large scale unconstrained optimization |
| title | A new diagonal gradient-type method for large scale unconstrained optimization |
| title_full | A new diagonal gradient-type method for large scale unconstrained optimization |
| title_fullStr | A new diagonal gradient-type method for large scale unconstrained optimization |
| title_full_unstemmed | A new diagonal gradient-type method for large scale unconstrained optimization |
| title_short | A new diagonal gradient-type method for large scale unconstrained optimization |
| title_sort | new diagonal gradient-type method for large scale unconstrained optimization |
| url | http://psasir.upm.edu.my/id/eprint/30325/ http://psasir.upm.edu.my/id/eprint/30325/ http://psasir.upm.edu.my/id/eprint/30325/1/A%20new%20diagonal%20gradient.pdf |