Efficient ODE-based methods for unconstrained optimization
This paper presents some efficient methods for unconstrained optimization based upon approximating the gradient flow of the objective function. Most ODE-based methods would generate Levenberg-Marquardt-like steps that require the solution of linear systems. On the other hand our proposed methods use...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Faculty of Science, Universiti Putra Malaysia
2018
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| Online Access: | http://psasir.upm.edu.my/id/eprint/72536/ http://psasir.upm.edu.my/id/eprint/72536/1/Efficient%20ODE.pdf |
| _version_ | 1848857142407200768 |
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| author | Yap, Chui Ying Leong, Wah June |
| author_facet | Yap, Chui Ying Leong, Wah June |
| author_sort | Yap, Chui Ying |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper presents some efficient methods for unconstrained optimization based upon approximating the gradient flow of the objective function. Most ODE-based methods would generate Levenberg-Marquardt-like steps that require the solution of linear systems. On the other hand our proposed methods used some quasi-Newton matrices to approximate the solution of these linear systems, thus avoiding the solution of linear systems repeatedly. Two implementations of the modified ODE-based methods - line search and trust region implementation are proposed. Under some suitable assumptions, the convergence of the proposed methods is then established. Numerical results indicate that the modified methods are more effective and comparable than the standard line search and trust region method using the well-known BFGS formula. |
| first_indexed | 2025-11-15T11:52:51Z |
| format | Article |
| id | upm-72536 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T11:52:51Z |
| publishDate | 2018 |
| publisher | Faculty of Science, Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-725362020-10-22T05:00:12Z http://psasir.upm.edu.my/id/eprint/72536/ Efficient ODE-based methods for unconstrained optimization Yap, Chui Ying Leong, Wah June This paper presents some efficient methods for unconstrained optimization based upon approximating the gradient flow of the objective function. Most ODE-based methods would generate Levenberg-Marquardt-like steps that require the solution of linear systems. On the other hand our proposed methods used some quasi-Newton matrices to approximate the solution of these linear systems, thus avoiding the solution of linear systems repeatedly. Two implementations of the modified ODE-based methods - line search and trust region implementation are proposed. Under some suitable assumptions, the convergence of the proposed methods is then established. Numerical results indicate that the modified methods are more effective and comparable than the standard line search and trust region method using the well-known BFGS formula. Faculty of Science, Universiti Putra Malaysia 2018 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/72536/1/Efficient%20ODE.pdf Yap, Chui Ying and Leong, Wah June (2018) Efficient ODE-based methods for unconstrained optimization. Discovering Mathematics, 40 (1). 31 - 45. ISSN 2231-7023 https://einspem.upm.edu.my/ojs/index.php/dismath/article/view/28 |
| spellingShingle | Yap, Chui Ying Leong, Wah June Efficient ODE-based methods for unconstrained optimization |
| title | Efficient ODE-based methods for unconstrained optimization |
| title_full | Efficient ODE-based methods for unconstrained optimization |
| title_fullStr | Efficient ODE-based methods for unconstrained optimization |
| title_full_unstemmed | Efficient ODE-based methods for unconstrained optimization |
| title_short | Efficient ODE-based methods for unconstrained optimization |
| title_sort | efficient ode-based methods for unconstrained optimization |
| url | http://psasir.upm.edu.my/id/eprint/72536/ http://psasir.upm.edu.my/id/eprint/72536/ http://psasir.upm.edu.my/id/eprint/72536/1/Efficient%20ODE.pdf |