Improved Hessian approximations with modified secant equations for symmetric rank-one method
Symmetric rank-one (SR1) is one of the competitive formulas among the quasi-Newton (QN) methods. In this paper, we propose some modified SR1 updates based on the modified secant equations, which use both gradient and function information. Furthermore, to avoid the loss of positive definiteness and z...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2011
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| Online Access: | http://psasir.upm.edu.my/id/eprint/24640/ http://psasir.upm.edu.my/id/eprint/24640/1/Improved%20Hessian%20approximations%20with%20modified%20secant%20equations%20for%20symmetric%20rank.pdf |
| _version_ | 1848845091306733568 |
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| author | Modarres, Farzin Abu Hassan, Malik Leong, Wah June |
| author_facet | Modarres, Farzin Abu Hassan, Malik Leong, Wah June |
| author_sort | Modarres, Farzin |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Symmetric rank-one (SR1) is one of the competitive formulas among the quasi-Newton (QN) methods. In this paper, we propose some modified SR1 updates based on the modified secant equations, which use both gradient and function information. Furthermore, to avoid the loss of positive definiteness and zero denominators of the new SR1 updates, we apply a restart procedure to this update. Three new algorithms are given to improve the Hessian approximation with modified secant equations for the SR1 method. Numerical results show that the proposed algorithms are very encouraging and the advantage of the proposed algorithms over the standard SR1 and BFGS updates is clearly observed. |
| first_indexed | 2025-11-15T08:41:18Z |
| format | Article |
| id | upm-24640 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T08:41:18Z |
| publishDate | 2011 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-246402017-08-16T09:35:26Z http://psasir.upm.edu.my/id/eprint/24640/ Improved Hessian approximations with modified secant equations for symmetric rank-one method Modarres, Farzin Abu Hassan, Malik Leong, Wah June Symmetric rank-one (SR1) is one of the competitive formulas among the quasi-Newton (QN) methods. In this paper, we propose some modified SR1 updates based on the modified secant equations, which use both gradient and function information. Furthermore, to avoid the loss of positive definiteness and zero denominators of the new SR1 updates, we apply a restart procedure to this update. Three new algorithms are given to improve the Hessian approximation with modified secant equations for the SR1 method. Numerical results show that the proposed algorithms are very encouraging and the advantage of the proposed algorithms over the standard SR1 and BFGS updates is clearly observed. Elsevier 2011 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/24640/1/Improved%20Hessian%20approximations%20with%20modified%20secant%20equations%20for%20symmetric%20rank.pdf Modarres, Farzin and Abu Hassan, Malik and Leong, Wah June (2011) Improved Hessian approximations with modified secant equations for symmetric rank-one method. Journal of Computational and Applied Mathematics, 235 (8). pp. 2423-2431. ISSN 0377-0427; ESSN: 1879-1778 http://www.sciencedirect.com/science/article/pii/S0377042710006084?via%3Dihub#! 10.1016/j.cam.2010.10.042 |
| spellingShingle | Modarres, Farzin Abu Hassan, Malik Leong, Wah June Improved Hessian approximations with modified secant equations for symmetric rank-one method |
| title | Improved Hessian approximations with modified secant equations for symmetric rank-one method |
| title_full | Improved Hessian approximations with modified secant equations for symmetric rank-one method |
| title_fullStr | Improved Hessian approximations with modified secant equations for symmetric rank-one method |
| title_full_unstemmed | Improved Hessian approximations with modified secant equations for symmetric rank-one method |
| title_short | Improved Hessian approximations with modified secant equations for symmetric rank-one method |
| title_sort | improved hessian approximations with modified secant equations for symmetric rank-one method |
| url | http://psasir.upm.edu.my/id/eprint/24640/ http://psasir.upm.edu.my/id/eprint/24640/ http://psasir.upm.edu.my/id/eprint/24640/ http://psasir.upm.edu.my/id/eprint/24640/1/Improved%20Hessian%20approximations%20with%20modified%20secant%20equations%20for%20symmetric%20rank.pdf |