Convergence of a positive definite symmetric rank one method with restart
The paper investigates convergence properties of a positive definite symmetric rank one method with the line search. The method is applied to find a local minimum of the unconstrained minimization problem, the objective function of which is defined on ℝ n and is assumed to be twice continuously diff...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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ICI Publishing House
2009
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| Online Access: | http://psasir.upm.edu.my/id/eprint/13791/ http://psasir.upm.edu.my/id/eprint/13791/1/Convergence%20of%20a%20positive%20definite%20symmetric%20rank%20one%20method%20with%20restart.pdf |
| _version_ | 1848842211334029312 |
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| author | Leong, Wah June Abu Hassan, Malik |
| author_facet | Leong, Wah June Abu Hassan, Malik |
| author_sort | Leong, Wah June |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The paper investigates convergence properties of a positive definite symmetric rank one method with the line search. The method is applied to find a local minimum of the unconstrained minimization problem, the objective function of which is defined on ℝ n and is assumed to be twice continuously differentiable. The authors show that the method is (n+1)-step q-superlinearly convergent without the assumption of linearly independent iterates. It is only assumed that the Hessian approximations are positive definite and asymptotically bounded. Computational experience shows that the method satisfies well these requirements in practical computations.
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| first_indexed | 2025-11-15T07:55:31Z |
| format | Article |
| id | upm-13791 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T07:55:31Z |
| publishDate | 2009 |
| publisher | ICI Publishing House |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-137912015-10-05T06:10:39Z http://psasir.upm.edu.my/id/eprint/13791/ Convergence of a positive definite symmetric rank one method with restart Leong, Wah June Abu Hassan, Malik The paper investigates convergence properties of a positive definite symmetric rank one method with the line search. The method is applied to find a local minimum of the unconstrained minimization problem, the objective function of which is defined on ℝ n and is assumed to be twice continuously differentiable. The authors show that the method is (n+1)-step q-superlinearly convergent without the assumption of linearly independent iterates. It is only assumed that the Hessian approximations are positive definite and asymptotically bounded. Computational experience shows that the method satisfies well these requirements in practical computations. ICI Publishing House 2009 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/13791/1/Convergence%20of%20a%20positive%20definite%20symmetric%20rank%20one%20method%20with%20restart.pdf Leong, Wah June and Abu Hassan, Malik (2009) Convergence of a positive definite symmetric rank one method with restart. Advance Modeling and Optimization, 11 (4). pp. 423-433. ISSN 1841-4311 http://camo.ici.ro/journal/v11n4.htm |
| spellingShingle | Leong, Wah June Abu Hassan, Malik Convergence of a positive definite symmetric rank one method with restart |
| title | Convergence of a positive definite symmetric rank one method with restart |
| title_full | Convergence of a positive definite symmetric rank one method with restart |
| title_fullStr | Convergence of a positive definite symmetric rank one method with restart |
| title_full_unstemmed | Convergence of a positive definite symmetric rank one method with restart |
| title_short | Convergence of a positive definite symmetric rank one method with restart |
| title_sort | convergence of a positive definite symmetric rank one method with restart |
| url | http://psasir.upm.edu.my/id/eprint/13791/ http://psasir.upm.edu.my/id/eprint/13791/ http://psasir.upm.edu.my/id/eprint/13791/1/Convergence%20of%20a%20positive%20definite%20symmetric%20rank%20one%20method%20with%20restart.pdf |