An improved multi-step gradient-type method for large scale optimization
In this paper, we propose an improved multi-step diagonal updating method for large scale unconstrained optimization. Our approach is based on constructing a new gradient-type method by means of interpolating curves. We measure the distances required to parameterize the interpolating polynomials via...
| 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/24643/ http://psasir.upm.edu.my/id/eprint/24643/1/An%20improved%20multi.pdf |
| _version_ | 1848845092062756864 |
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| author | Farid, Mahboubeh Leong, Wah June |
| author_facet | Farid, Mahboubeh Leong, Wah June |
| author_sort | Farid, Mahboubeh |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, we propose an improved multi-step diagonal updating method for large scale unconstrained optimization. Our approach is based on constructing a new gradient-type method by means of interpolating curves. We measure the distances required to parameterize the interpolating polynomials via a norm defined by a positive-definite matrix. By developing on implicit updating approach we can obtain an improved version of Hessian approximation in diagonal matrix form, while avoiding the computational expenses of actually calculating the improved version of the approximation matrix. The effectiveness of our proposed method is evaluated by means of computational comparison with the BB method and its variants. We show that our method is globally convergent and only requires O(n) memory allocations. |
| first_indexed | 2025-11-15T08:41:19Z |
| format | Article |
| id | upm-24643 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T08:41:19Z |
| publishDate | 2011 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-246432019-10-11T00:43:03Z http://psasir.upm.edu.my/id/eprint/24643/ An improved multi-step gradient-type method for large scale optimization Farid, Mahboubeh Leong, Wah June In this paper, we propose an improved multi-step diagonal updating method for large scale unconstrained optimization. Our approach is based on constructing a new gradient-type method by means of interpolating curves. We measure the distances required to parameterize the interpolating polynomials via a norm defined by a positive-definite matrix. By developing on implicit updating approach we can obtain an improved version of Hessian approximation in diagonal matrix form, while avoiding the computational expenses of actually calculating the improved version of the approximation matrix. The effectiveness of our proposed method is evaluated by means of computational comparison with the BB method and its variants. We show that our method is globally convergent and only requires O(n) memory allocations. Elsevier 2011 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/24643/1/An%20improved%20multi.pdf Farid, Mahboubeh and Leong, Wah June (2011) An improved multi-step gradient-type method for large scale optimization. Computers and Mathematics with Applications, 61 (11). pp. 3312-3318. ISSN 0898-1221; ESSN: 1873-7668 https://www.sciencedirect.com/science/article/pii/S0898122111003312?via%3Dihub 10.1016/j.camwa.2011.04.030 |
| spellingShingle | Farid, Mahboubeh Leong, Wah June An improved multi-step gradient-type method for large scale optimization |
| title | An improved multi-step gradient-type method for large scale optimization |
| title_full | An improved multi-step gradient-type method for large scale optimization |
| title_fullStr | An improved multi-step gradient-type method for large scale optimization |
| title_full_unstemmed | An improved multi-step gradient-type method for large scale optimization |
| title_short | An improved multi-step gradient-type method for large scale optimization |
| title_sort | improved multi-step gradient-type method for large scale optimization |
| url | http://psasir.upm.edu.my/id/eprint/24643/ http://psasir.upm.edu.my/id/eprint/24643/ http://psasir.upm.edu.my/id/eprint/24643/ http://psasir.upm.edu.my/id/eprint/24643/1/An%20improved%20multi.pdf |