Higher order curvature information and its application in a modified diagonal Secant method
A secant equation (quasi-Newton) has one of the most important rule to find an optimal solution in nonlinear optimization. Curvature information must satisfy the usual secant equation to ensure positive definiteness of the Hessian approximation. In this work, we present a new diagonal updating to im...
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis
2018
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| Online Access: | http://psasir.upm.edu.my/id/eprint/74506/ http://psasir.upm.edu.my/id/eprint/74506/1/Higher%20order.pdf |
| _version_ | 1848857510240321536 |
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| author | Enshaei, Sharareh Farid, Mahboubeh Wah, June Leong Ardestani, S. Mohsen Hashemi |
| author_facet | Enshaei, Sharareh Farid, Mahboubeh Wah, June Leong Ardestani, S. Mohsen Hashemi |
| author_sort | Enshaei, Sharareh |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | A secant equation (quasi-Newton) has one of the most important rule to find an optimal solution in nonlinear optimization. Curvature information must satisfy the usual secant equation to ensure positive definiteness of the Hessian approximation. In this work, we present a new diagonal updating to improve the Hessian approximation with a modifying weak secant equation for the diagonal quasi-Newton (DQN) method. The gradient and function evaluation are utilized to obtain a new weak secant equation and achieve a higher order accuracy in curvature information in the proposed method. Modified DQN methods based on the modified weak secant equation are globally convergent. Extended numerical results indicate the advantages of modified DQN methods over the usual ones and some classical conjugate gradient methods. |
| first_indexed | 2025-11-15T11:58:42Z |
| format | Article |
| id | upm-74506 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T11:58:42Z |
| publishDate | 2018 |
| publisher | Taylor & Francis |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-745062020-02-27T01:54:47Z http://psasir.upm.edu.my/id/eprint/74506/ Higher order curvature information and its application in a modified diagonal Secant method Enshaei, Sharareh Farid, Mahboubeh Wah, June Leong Ardestani, S. Mohsen Hashemi A secant equation (quasi-Newton) has one of the most important rule to find an optimal solution in nonlinear optimization. Curvature information must satisfy the usual secant equation to ensure positive definiteness of the Hessian approximation. In this work, we present a new diagonal updating to improve the Hessian approximation with a modifying weak secant equation for the diagonal quasi-Newton (DQN) method. The gradient and function evaluation are utilized to obtain a new weak secant equation and achieve a higher order accuracy in curvature information in the proposed method. Modified DQN methods based on the modified weak secant equation are globally convergent. Extended numerical results indicate the advantages of modified DQN methods over the usual ones and some classical conjugate gradient methods. Taylor & Francis 2018 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/74506/1/Higher%20order.pdf Enshaei, Sharareh and Farid, Mahboubeh and Wah, June Leong and Ardestani, S. Mohsen Hashemi (2018) Higher order curvature information and its application in a modified diagonal Secant method. Optimization, 67 (12). 2229 - 2246. ISSN 0233-1934; ESSN: 1029-4945 10.1080/02331934.2018.1527840 |
| spellingShingle | Enshaei, Sharareh Farid, Mahboubeh Wah, June Leong Ardestani, S. Mohsen Hashemi Higher order curvature information and its application in a modified diagonal Secant method |
| title | Higher order curvature information and its application in a modified diagonal Secant method |
| title_full | Higher order curvature information and its application in a modified diagonal Secant method |
| title_fullStr | Higher order curvature information and its application in a modified diagonal Secant method |
| title_full_unstemmed | Higher order curvature information and its application in a modified diagonal Secant method |
| title_short | Higher order curvature information and its application in a modified diagonal Secant method |
| title_sort | higher order curvature information and its application in a modified diagonal secant method |
| url | http://psasir.upm.edu.my/id/eprint/74506/ http://psasir.upm.edu.my/id/eprint/74506/ http://psasir.upm.edu.my/id/eprint/74506/1/Higher%20order.pdf |