Scaled diagonal gradient-type method with extra update for large-scale unconstrained optimization
We present a new gradient method that uses scaling and extra updating within the diagonal updating for solving unconstrained optimization problem. The new method is in the frame of Barzilai and Borwein (BB) method, except that the Hessian matrix is approximated by a diagonal matrix rather than the m...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30321/ http://psasir.upm.edu.my/id/eprint/30321/1/30321.pdf |
| _version_ | 1848846644193263616 |
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| author | Farid, Mahboubeh Leong, Wah June Malekmohammadi, Najmeh Mamat, Mustafa |
| author_facet | Farid, Mahboubeh Leong, Wah June Malekmohammadi, Najmeh Mamat, Mustafa |
| author_sort | Farid, Mahboubeh |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | We present a new gradient method that uses scaling and extra updating within the diagonal updating for solving unconstrained optimization problem. The new method is in the frame of Barzilai and Borwein (BB) method, except that the Hessian matrix is approximated by a diagonal matrix rather than the multiple of identity matrix in the BB method. The main idea is to design a new diagonal updating scheme that incorporates scaling to instantly reduce the large eigenvalues of diagonal approximation and otherwise employs extra updates to increase small eigenvalues. These approaches give us a rapid control in the eigenvalues of the updating matrix and thus improve stepwise convergence. We show that our method is globally convergent. The effectiveness of the method is evaluated by means of numerical comparison with the BB method and its variant. |
| first_indexed | 2025-11-15T09:05:59Z |
| format | Article |
| id | upm-30321 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:05:59Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-303212017-10-19T07:58:54Z http://psasir.upm.edu.my/id/eprint/30321/ Scaled diagonal gradient-type method with extra update for large-scale unconstrained optimization Farid, Mahboubeh Leong, Wah June Malekmohammadi, Najmeh Mamat, Mustafa We present a new gradient method that uses scaling and extra updating within the diagonal updating for solving unconstrained optimization problem. The new method is in the frame of Barzilai and Borwein (BB) method, except that the Hessian matrix is approximated by a diagonal matrix rather than the multiple of identity matrix in the BB method. The main idea is to design a new diagonal updating scheme that incorporates scaling to instantly reduce the large eigenvalues of diagonal approximation and otherwise employs extra updates to increase small eigenvalues. These approaches give us a rapid control in the eigenvalues of the updating matrix and thus improve stepwise convergence. We show that our method is globally convergent. The effectiveness of the method is evaluated by means of numerical comparison with the BB method and its variant. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30321/1/30321.pdf Farid, Mahboubeh and Leong, Wah June and Malekmohammadi, Najmeh and Mamat, Mustafa (2013) Scaled diagonal gradient-type method with extra update for large-scale unconstrained optimization. Abstract and Applied Analysis, 2013. art. no. 532041. pp. 1-5. ISSN 1085-3375; ESSN: 1687-0409 https://www.hindawi.com/journals/aaa/2013/532041/abs/ 10.1155/2013/532041 |
| spellingShingle | Farid, Mahboubeh Leong, Wah June Malekmohammadi, Najmeh Mamat, Mustafa Scaled diagonal gradient-type method with extra update for large-scale unconstrained optimization |
| title | Scaled diagonal gradient-type method with extra update for large-scale unconstrained optimization |
| title_full | Scaled diagonal gradient-type method with extra update for large-scale unconstrained optimization |
| title_fullStr | Scaled diagonal gradient-type method with extra update for large-scale unconstrained optimization |
| title_full_unstemmed | Scaled diagonal gradient-type method with extra update for large-scale unconstrained optimization |
| title_short | Scaled diagonal gradient-type method with extra update for large-scale unconstrained optimization |
| title_sort | scaled diagonal gradient-type method with extra update for large-scale unconstrained optimization |
| url | http://psasir.upm.edu.my/id/eprint/30321/ http://psasir.upm.edu.my/id/eprint/30321/ http://psasir.upm.edu.my/id/eprint/30321/ http://psasir.upm.edu.my/id/eprint/30321/1/30321.pdf |