Some diagonal preconditioners for limited memory quasi-Newton method for large Scale optimization
One of the well-known methods in solving large scale unconstrained optimization is limited memory quasi-Newton (LMQN) method. This method is derived from a subproblem in low dimension so that the storage requirement as well as the computation cost can be reduced. In this paper, we propose a precondi...
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| Format: | Article |
| Language: | English |
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Institute for Mathematical Research, Universiti Putra Malaysia
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/38928/ http://psasir.upm.edu.my/id/eprint/38928/1/38928.pdf |
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| author | Sim, Hong Seng Leong, Wah June Abu Hassan, Malik Ismail, Fudziah |
| author_facet | Sim, Hong Seng Leong, Wah June Abu Hassan, Malik Ismail, Fudziah |
| author_sort | Sim, Hong Seng |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | One of the well-known methods in solving large scale unconstrained optimization is limited memory quasi-Newton (LMQN) method. This method is derived from a subproblem in low dimension so that the storage requirement as well as the computation cost can be reduced. In this paper, we propose a preconditioned LMQN method which is generally more effective than the LMQN method dueto the main defect of the LMQN method that it can be very slow on certain type of nonlinear problem such as ill-conditioned problems. In order to do this, we propose to use a diagonal updating matrix that has been derived based on the weak quasi-Newton relation to replace the identity matrix to approximate the initial inverse Hessian. The computational results show that the proposed preconditioned LMQN method performs better than LMQN method that without preconditioning. |
| first_indexed | 2025-11-15T09:43:33Z |
| format | Article |
| id | upm-38928 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:43:33Z |
| publishDate | 2013 |
| publisher | Institute for Mathematical Research, Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-389282015-09-04T13:16:53Z http://psasir.upm.edu.my/id/eprint/38928/ Some diagonal preconditioners for limited memory quasi-Newton method for large Scale optimization Sim, Hong Seng Leong, Wah June Abu Hassan, Malik Ismail, Fudziah One of the well-known methods in solving large scale unconstrained optimization is limited memory quasi-Newton (LMQN) method. This method is derived from a subproblem in low dimension so that the storage requirement as well as the computation cost can be reduced. In this paper, we propose a preconditioned LMQN method which is generally more effective than the LMQN method dueto the main defect of the LMQN method that it can be very slow on certain type of nonlinear problem such as ill-conditioned problems. In order to do this, we propose to use a diagonal updating matrix that has been derived based on the weak quasi-Newton relation to replace the identity matrix to approximate the initial inverse Hessian. The computational results show that the proposed preconditioned LMQN method performs better than LMQN method that without preconditioning. Institute for Mathematical Research, Universiti Putra Malaysia 2013-07 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/38928/1/38928.pdf Sim, Hong Seng and Leong, Wah June and Abu Hassan, Malik and Ismail, Fudziah (2013) Some diagonal preconditioners for limited memory quasi-Newton method for large Scale optimization. Malaysian Journal of Mathematical Sciences, 7 (2). pp. 181-201. ISSN 1823-8343; ESSN: 2289-750X http://einspem.upm.edu.my/journal/fullpaper/vol7no2/3.%20Hong%20Seng%20Sim,%20Wah%20June%20Leong,%20Fudziah%20Ismail.pdf |
| spellingShingle | Sim, Hong Seng Leong, Wah June Abu Hassan, Malik Ismail, Fudziah Some diagonal preconditioners for limited memory quasi-Newton method for large Scale optimization |
| title | Some diagonal preconditioners for limited memory quasi-Newton method for large Scale optimization |
| title_full | Some diagonal preconditioners for limited memory quasi-Newton method for large Scale optimization |
| title_fullStr | Some diagonal preconditioners for limited memory quasi-Newton method for large Scale optimization |
| title_full_unstemmed | Some diagonal preconditioners for limited memory quasi-Newton method for large Scale optimization |
| title_short | Some diagonal preconditioners for limited memory quasi-Newton method for large Scale optimization |
| title_sort | some diagonal preconditioners for limited memory quasi-newton method for large scale optimization |
| url | http://psasir.upm.edu.my/id/eprint/38928/ http://psasir.upm.edu.my/id/eprint/38928/ http://psasir.upm.edu.my/id/eprint/38928/1/38928.pdf |