Multi-steps symmetric rank-one update for unconstrained optimization
In this paper, we present a generalized Symmetric Rank-one (SR1) method by employing interpolatory polynomials in order to possess a more accurate information from more than one previous step. The basic idea is to incorporate the SR1 update within the framework of multi-step methods. Hence iterates...
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| Format: | Article |
| Language: | English |
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IDOSI Publications
2009
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| Online Access: | http://psasir.upm.edu.my/id/eprint/15755/1/Multi-steps%20symmetric%20rank-one%20update%20for%20unconstrained%20optimization..pdf |
| _version_ | 1825945682859524096 |
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| author | Modarres, Farzin Abu Hassan, Malik Leong, Wah June |
| author_facet | Modarres, Farzin Abu Hassan, Malik Leong, Wah June |
| author_sort | Modarres, Farzin |
| collection | UPM |
| description | In this paper, we present a generalized Symmetric Rank-one (SR1) method by employing interpolatory polynomials in order to possess a more accurate information from more than one previous step. The basic idea is to incorporate the SR1 update within the framework of multi-step methods. Hence iterates could be interpolated by a curve in such a way that the consecutive points define the curves. However to preserve the positive definiteness of the SR1 updates a restart procedure is applied, in which we restart the SR1 update by a scale of the identity. Comparison to multi-steps BFGS method, the proposed algorithm shows significant improvements in numerical results. |
| first_indexed | 2024-03-06T07:35:17Z |
| format | Article |
| id | upm.eprints-15755 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T07:35:17Z |
| publishDate | 2009 |
| publisher | IDOSI Publications |
| record_format | dspace |
| spelling | upm.eprints-157552020-06-16T02:14:58Z http://psasir.upm.edu.my/id/eprint/15755/ Multi-steps symmetric rank-one update for unconstrained optimization Modarres, Farzin Abu Hassan, Malik Leong, Wah June In this paper, we present a generalized Symmetric Rank-one (SR1) method by employing interpolatory polynomials in order to possess a more accurate information from more than one previous step. The basic idea is to incorporate the SR1 update within the framework of multi-step methods. Hence iterates could be interpolated by a curve in such a way that the consecutive points define the curves. However to preserve the positive definiteness of the SR1 updates a restart procedure is applied, in which we restart the SR1 update by a scale of the identity. Comparison to multi-steps BFGS method, the proposed algorithm shows significant improvements in numerical results. IDOSI Publications 2009 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/15755/1/Multi-steps%20symmetric%20rank-one%20update%20for%20unconstrained%20optimization..pdf Modarres, Farzin and Abu Hassan, Malik and Leong, Wah June (2009) Multi-steps symmetric rank-one update for unconstrained optimization. World Applied Sciences Journal, 7 (5). pp. 610-615. ISSN 1818-4952; ESSN: 1991-6426 https://www.idosi.org/wasj/wasj7(5)2009.htm |
| spellingShingle | Modarres, Farzin Abu Hassan, Malik Leong, Wah June Multi-steps symmetric rank-one update for unconstrained optimization |
| title | Multi-steps symmetric rank-one update for unconstrained optimization |
| title_full | Multi-steps symmetric rank-one update for unconstrained optimization |
| title_fullStr | Multi-steps symmetric rank-one update for unconstrained optimization |
| title_full_unstemmed | Multi-steps symmetric rank-one update for unconstrained optimization |
| title_short | Multi-steps symmetric rank-one update for unconstrained optimization |
| title_sort | multi steps symmetric rank one update for unconstrained optimization |
| url | http://psasir.upm.edu.my/id/eprint/15755/1/Multi-steps%20symmetric%20rank-one%20update%20for%20unconstrained%20optimization..pdf |
| work_keys_str_mv | AT modarresfarzin multistepssymmetricrankoneupdateforunconstrainedoptimization AT abuhassanmalik multistepssymmetricrankoneupdateforunconstrainedoptimization AT leongwahjune multistepssymmetricrankoneupdateforunconstrainedoptimization |