Preconditioning on subspace quasi-Newton method for large scale unconstrained optimization
Recently, subspace quasi-Newton (SQN) method has been widely used in solving large scale unconstrained optimization. Besides constructing sub-problems in low dimensions so that the storage requirement as well as computational cost can be reduced, it can also be implemented extremely fast when the ob...
| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
AIP Publishing LLC
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57355/ http://psasir.upm.edu.my/id/eprint/57355/1/Preconditioning%20on%20subspace%20quasi-Newton%20method%20for%20large%20scale%20unconstrained%20optimization.pdf |
| _version_ | 1848853342439079936 |
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| author | Sim, Hong Seng Leong, Wah June Ismail, Fudziah |
| author_facet | Sim, Hong Seng Leong, Wah June Ismail, Fudziah |
| author_sort | Sim, Hong Seng |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Recently, subspace quasi-Newton (SQN) method has been widely used in solving large scale unconstrained optimization. Besides constructing sub-problems in low dimensions so that the storage requirement as well as computational cost can be reduced, it can also be implemented extremely fast when the objective function is a combination of computationally cheap non-linear functions. However, the main deficiency of SQN method is that it can be very slow on certain type of non-linear problem. Hence, a preconditioner which is computationally cheap and is a good approximation to the actual Hessian is constructed to speed up the convergence of the quasi-Newton methods since the evaluation of the actual Hessian is considered as impractical and costly. For this purpose, a diagonal updating matrix has been derived to replace the identity matrix in approximating the initial inverse Hessian. The numerical results show that the preconditioned SQN method performs better than the standard SQN method that without preconditioning. |
| first_indexed | 2025-11-15T10:52:27Z |
| format | Conference or Workshop Item |
| id | upm-57355 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:52:27Z |
| publishDate | 2013 |
| publisher | AIP Publishing LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-573552017-09-26T04:09:52Z http://psasir.upm.edu.my/id/eprint/57355/ Preconditioning on subspace quasi-Newton method for large scale unconstrained optimization Sim, Hong Seng Leong, Wah June Ismail, Fudziah Recently, subspace quasi-Newton (SQN) method has been widely used in solving large scale unconstrained optimization. Besides constructing sub-problems in low dimensions so that the storage requirement as well as computational cost can be reduced, it can also be implemented extremely fast when the objective function is a combination of computationally cheap non-linear functions. However, the main deficiency of SQN method is that it can be very slow on certain type of non-linear problem. Hence, a preconditioner which is computationally cheap and is a good approximation to the actual Hessian is constructed to speed up the convergence of the quasi-Newton methods since the evaluation of the actual Hessian is considered as impractical and costly. For this purpose, a diagonal updating matrix has been derived to replace the identity matrix in approximating the initial inverse Hessian. The numerical results show that the preconditioned SQN method performs better than the standard SQN method that without preconditioning. AIP Publishing LLC 2013 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57355/1/Preconditioning%20on%20subspace%20quasi-Newton%20method%20for%20large%20scale%20unconstrained%20optimization.pdf Sim, Hong Seng and Leong, Wah June and Ismail, Fudziah (2013) Preconditioning on subspace quasi-Newton method for large scale unconstrained optimization. In: Statistics and Operational Research International Conference (SORIC 2013), 3–5 Dec. 2013, Sarawak, Malaysia. (pp. 297-305). 10.1063/1.4894354 |
| spellingShingle | Sim, Hong Seng Leong, Wah June Ismail, Fudziah Preconditioning on subspace quasi-Newton method for large scale unconstrained optimization |
| title | Preconditioning on subspace quasi-Newton method for large scale unconstrained optimization |
| title_full | Preconditioning on subspace quasi-Newton method for large scale unconstrained optimization |
| title_fullStr | Preconditioning on subspace quasi-Newton method for large scale unconstrained optimization |
| title_full_unstemmed | Preconditioning on subspace quasi-Newton method for large scale unconstrained optimization |
| title_short | Preconditioning on subspace quasi-Newton method for large scale unconstrained optimization |
| title_sort | preconditioning on subspace quasi-newton method for large scale unconstrained optimization |
| url | http://psasir.upm.edu.my/id/eprint/57355/ http://psasir.upm.edu.my/id/eprint/57355/ http://psasir.upm.edu.my/id/eprint/57355/1/Preconditioning%20on%20subspace%20quasi-Newton%20method%20for%20large%20scale%20unconstrained%20optimization.pdf |