A new two-step gradient-type method for large-scale unconstrained optimization
In this paper, we propose some improvements on a new gradient-type method for solving large-scale unconstrained optimization problems, in which we use data from two previous steps to revise the current approximate Hessian. The new method which we considered, resembles to that of Barzilai and Borwein...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Pergamon Press
2010
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| Online Access: | http://psasir.upm.edu.my/id/eprint/12759/ http://psasir.upm.edu.my/id/eprint/12759/1/A%20new%20two.pdf |
| _version_ | 1848841922916909056 |
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| author | Farid, Mahboubeh Leong, Wah June Abu Hassan, Malik |
| author_facet | Farid, Mahboubeh Leong, Wah June Abu Hassan, Malik |
| author_sort | Farid, Mahboubeh |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, we propose some improvements on a new gradient-type method for solving large-scale unconstrained optimization problems, in which we use data from two previous steps to revise the current approximate Hessian. The new method which we considered, resembles to that of Barzilai and Borwein (BB) method. The innovation features of this approach consist in using approximation of the Hessian in diagonal matrix form based on the modified weak secant equation rather than the multiple of the identity matrix in the BB method. Using this approach, we can obtain a higher order accuracy of Hessian approximation when compares to other existing BB-type method. By incorporating a simple monotone strategy, the global convergence of the new method is achieved. Practical insights into the effectiveness of the proposed method are given by numerical comparison with the BB method and its variant. |
| first_indexed | 2025-11-15T07:50:56Z |
| format | Article |
| id | upm-12759 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T07:50:56Z |
| publishDate | 2010 |
| publisher | Pergamon Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-127592015-09-22T03:38:42Z http://psasir.upm.edu.my/id/eprint/12759/ A new two-step gradient-type method for large-scale unconstrained optimization Farid, Mahboubeh Leong, Wah June Abu Hassan, Malik In this paper, we propose some improvements on a new gradient-type method for solving large-scale unconstrained optimization problems, in which we use data from two previous steps to revise the current approximate Hessian. The new method which we considered, resembles to that of Barzilai and Borwein (BB) method. The innovation features of this approach consist in using approximation of the Hessian in diagonal matrix form based on the modified weak secant equation rather than the multiple of the identity matrix in the BB method. Using this approach, we can obtain a higher order accuracy of Hessian approximation when compares to other existing BB-type method. By incorporating a simple monotone strategy, the global convergence of the new method is achieved. Practical insights into the effectiveness of the proposed method are given by numerical comparison with the BB method and its variant. Pergamon Press 2010-05 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/12759/1/A%20new%20two.pdf Farid, Mahboubeh and Leong, Wah June and Abu Hassan, Malik (2010) A new two-step gradient-type method for large-scale unconstrained optimization. Computers and Mathematics with Applications, 59 (10). pp. 3301-3307. ISSN 0898-1221; ESSN: 1873-7668 10.1016/j.camwa.2010.03.014 |
| spellingShingle | Farid, Mahboubeh Leong, Wah June Abu Hassan, Malik A new two-step gradient-type method for large-scale unconstrained optimization |
| title | A new two-step gradient-type method for large-scale unconstrained optimization |
| title_full | A new two-step gradient-type method for large-scale unconstrained optimization |
| title_fullStr | A new two-step gradient-type method for large-scale unconstrained optimization |
| title_full_unstemmed | A new two-step gradient-type method for large-scale unconstrained optimization |
| title_short | A new two-step gradient-type method for large-scale unconstrained optimization |
| title_sort | new two-step gradient-type method for large-scale unconstrained optimization |
| url | http://psasir.upm.edu.my/id/eprint/12759/ http://psasir.upm.edu.my/id/eprint/12759/ http://psasir.upm.edu.my/id/eprint/12759/1/A%20new%20two.pdf |