A symmetric rank-one method based on extra updating techniques for unconstrained optimization.
In this paper, we present a new symmetric rank-one (SR1) method for the solution of unconstrained optimization problems. The proposed method involves an algorithm in which the usual SR1 Hessian is updated a number of times in a way to be specified in some iterations, to improve the performance of th...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English English |
| Published: |
Elsevier
2011
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| Online Access: | http://psasir.upm.edu.my/id/eprint/24645/1/A%20symmetric%20rank.pdf |
| _version_ | 1796970600647884800 |
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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 new symmetric rank-one (SR1) method for the solution of unconstrained optimization problems. The proposed method involves an algorithm in which the usual SR1 Hessian is updated a number of times in a way to be specified in some iterations, to improve the performance of the Hessian approximation. In particular, we discuss how to consider a criterion for indicating at each iteration whether it is necessary to employ extra updates. However it is well known that there are some theoretical difficulties when applying the SR1 update. Even for a current positive definite Hessian approximation, it is possible that the SR1 update may not be defined or the SR1 update may not preserve positive definiteness at some iterations. We then employ a restarting procedure that guarantees that updated matrices will be well-defined while preserving positive definiteness of updates. Numerical results support these theoretical considerations. They show that the implementation of the SR1 method using extra updating techniques improves the performance of the SR1 method substantially for a number of test problems from the literature. |
| first_indexed | 2024-03-06T08:00:28Z |
| format | Article |
| id | upm.eprints-24645 |
| institution | Universiti Putra Malaysia |
| language | English English |
| last_indexed | 2024-03-06T08:00:28Z |
| publishDate | 2011 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | upm.eprints-246452015-10-16T07:07:49Z http://psasir.upm.edu.my/id/eprint/24645/ A symmetric rank-one method based on extra updating techniques for unconstrained optimization. Modarres, Farzin Abu Hassan, Malik Leong, Wah June In this paper, we present a new symmetric rank-one (SR1) method for the solution of unconstrained optimization problems. The proposed method involves an algorithm in which the usual SR1 Hessian is updated a number of times in a way to be specified in some iterations, to improve the performance of the Hessian approximation. In particular, we discuss how to consider a criterion for indicating at each iteration whether it is necessary to employ extra updates. However it is well known that there are some theoretical difficulties when applying the SR1 update. Even for a current positive definite Hessian approximation, it is possible that the SR1 update may not be defined or the SR1 update may not preserve positive definiteness at some iterations. We then employ a restarting procedure that guarantees that updated matrices will be well-defined while preserving positive definiteness of updates. Numerical results support these theoretical considerations. They show that the implementation of the SR1 method using extra updating techniques improves the performance of the SR1 method substantially for a number of test problems from the literature. Elsevier 2011-07 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/24645/1/A%20symmetric%20rank.pdf Modarres, Farzin and Abu Hassan, Malik and Leong, Wah June (2011) A symmetric rank-one method based on extra updating techniques for unconstrained optimization. Computers and Mathematics with Applications, 62 (1). pp. 392-400. ISSN 0898-1221 http://www.elsevier.com/ 10.1016/j.camwa.2011.05.022 English |
| spellingShingle | Modarres, Farzin Abu Hassan, Malik Leong, Wah June A symmetric rank-one method based on extra updating techniques for unconstrained optimization. |
| title | A symmetric rank-one method based on extra updating techniques for unconstrained optimization. |
| title_full | A symmetric rank-one method based on extra updating techniques for unconstrained optimization. |
| title_fullStr | A symmetric rank-one method based on extra updating techniques for unconstrained optimization. |
| title_full_unstemmed | A symmetric rank-one method based on extra updating techniques for unconstrained optimization. |
| title_short | A symmetric rank-one method based on extra updating techniques for unconstrained optimization. |
| title_sort | symmetric rank one method based on extra updating techniques for unconstrained optimization |
| url | http://psasir.upm.edu.my/id/eprint/24645/1/A%20symmetric%20rank.pdf |
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