A monotone gradient method via weak secant equation for unconstrained optimization
In this paper we present a new algorithm of steepest descent type. A new technique for steplength computation and a monotone strategy are provided in the framework of the Barzilai and Borwein method. In contrast with Barzilai and Borwein approach's in which the steplength is computed by means o...
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| Format: | Article |
| Language: | English |
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Mathematical Society of the Republic of China (Taiwan)
2010
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| Online Access: | http://psasir.upm.edu.my/id/eprint/17677/ http://psasir.upm.edu.my/id/eprint/17677/1/A%20monotone%20gradient%20method%20via%20weak%20secant%20equation%20for%20unconstrained%20optimization.pdf |
| _version_ | 1848843307869798400 |
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| author | Leong, Wah June Abu Hassan, Malik Farid, Mahboubeh |
| author_facet | Leong, Wah June Abu Hassan, Malik Farid, Mahboubeh |
| author_sort | Leong, Wah June |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper we present a new algorithm of steepest descent type. A new technique for steplength computation and a monotone strategy are provided in the framework of the Barzilai and Borwein method. In contrast with Barzilai and Borwein approach's in which the steplength is computed by means of a simple approximation of the Hessian in the form of scalar multiple of identity and an interpretation of the secant equation, the new proposed algorithm considers another approximation of the Hessian based on the weak secant equation. By incorporating a simple monotone strategy, the resulting algorithm belongs to the class of monotone gradient methods with linearly convergence. Numerical results suggest that for non-quadratic minimization problem, the new method clearly outperforms the Barzilai-Borwein method. |
| first_indexed | 2025-11-15T08:12:57Z |
| format | Article |
| id | upm-17677 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T08:12:57Z |
| publishDate | 2010 |
| publisher | Mathematical Society of the Republic of China (Taiwan) |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-176772017-07-18T03:41:53Z http://psasir.upm.edu.my/id/eprint/17677/ A monotone gradient method via weak secant equation for unconstrained optimization Leong, Wah June Abu Hassan, Malik Farid, Mahboubeh In this paper we present a new algorithm of steepest descent type. A new technique for steplength computation and a monotone strategy are provided in the framework of the Barzilai and Borwein method. In contrast with Barzilai and Borwein approach's in which the steplength is computed by means of a simple approximation of the Hessian in the form of scalar multiple of identity and an interpretation of the secant equation, the new proposed algorithm considers another approximation of the Hessian based on the weak secant equation. By incorporating a simple monotone strategy, the resulting algorithm belongs to the class of monotone gradient methods with linearly convergence. Numerical results suggest that for non-quadratic minimization problem, the new method clearly outperforms the Barzilai-Borwein method. Mathematical Society of the Republic of China (Taiwan) 2010 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/17677/1/A%20monotone%20gradient%20method%20via%20weak%20secant%20equation%20for%20unconstrained%20optimization.pdf Leong, Wah June and Abu Hassan, Malik and Farid, Mahboubeh (2010) A monotone gradient method via weak secant equation for unconstrained optimization. Taiwanese Journal of Mathematics, 14 (2). pp. 413-423. ISSN 1027-5487; ESSN: 2224-6851 http://journal.tms.org.tw/index.php/TJM/article/view/367 |
| spellingShingle | Leong, Wah June Abu Hassan, Malik Farid, Mahboubeh A monotone gradient method via weak secant equation for unconstrained optimization |
| title | A monotone gradient method via weak secant equation for unconstrained optimization |
| title_full | A monotone gradient method via weak secant equation for unconstrained optimization |
| title_fullStr | A monotone gradient method via weak secant equation for unconstrained optimization |
| title_full_unstemmed | A monotone gradient method via weak secant equation for unconstrained optimization |
| title_short | A monotone gradient method via weak secant equation for unconstrained optimization |
| title_sort | monotone gradient method via weak secant equation for unconstrained optimization |
| url | http://psasir.upm.edu.my/id/eprint/17677/ http://psasir.upm.edu.my/id/eprint/17677/ http://psasir.upm.edu.my/id/eprint/17677/1/A%20monotone%20gradient%20method%20via%20weak%20secant%20equation%20for%20unconstrained%20optimization.pdf |