Diagonal quasi-Newton updating formula using log-determinant norm
Quasi-Newton method has been widely used in solving unconstrained optimization problems. The popularity of this method is due to the fact that only the gradient of the objective function is required at each iterate. Since second derivatives (Hessian) are not required, quasi-Newton method is sometime...
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AIP Publishing
2015
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oai:psasir.upm.edu.my:57371 http://psasir.upm.edu.my/id/eprint/57371/ Diagonal quasi-Newton updating formula using log-determinant norm Sim, Hong Seng Leong, Wah June Chen, Chuei Yee Ibrahim, Siti Nur Iqmal Quasi-Newton method has been widely used in solving unconstrained optimization problems. The popularity of this method is due to the fact that only the gradient of the objective function is required at each iterate. Since second derivatives (Hessian) are not required, quasi-Newton method is sometimes more efficient than the Newton method, especially when the computation of Hessian is expensive. On the other hand, standard quasi-Newton methods required full matrix storage that approximates the (inverse) Hessian. Hence, they may not be suitable to handle problems of large-scale. In this paper, we develop quasi-Newton updating formula diagonally using log-determinant norm such that it satisfies the weaker secant equation. The Lagrange multiplier is approximated using the Newton-Raphson method that is associated with weaker secant relation. An executable code is developed to test the efficiency of the proposed method with some standard conjugate-gradient methods. Numerical results show that the proposed method performs better than the conjugate gradient method. AIP Publishing 2015 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57371/1/Diagonal%20quasi-Newton%20updating%20formula%20using%20log-determinant%20norm.pdf Sim, Hong Seng and Leong, Wah June and Chen, Chuei Yee and Ibrahim, Siti Nur Iqmal (2015) Diagonal quasi-Newton updating formula using log-determinant norm. In: 23rd Malaysian National Symposium of Mathematical Sciences (SKSM23), 24-26 Nov. 2015, Johor Bahru, Malaysia. (pp. 1-7). 10.1063/1.4954581 |
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UPM IR |
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UPM IR |
| language |
English |
| description |
Quasi-Newton method has been widely used in solving unconstrained optimization problems. The popularity of this method is due to the fact that only the gradient of the objective function is required at each iterate. Since second derivatives (Hessian) are not required, quasi-Newton method is sometimes more efficient than the Newton method, especially when the computation of Hessian is expensive. On the other hand, standard quasi-Newton methods required full matrix storage that approximates the (inverse) Hessian. Hence, they may not be suitable to handle problems of large-scale. In this paper, we develop quasi-Newton updating formula diagonally using log-determinant norm such that it satisfies the weaker secant equation. The Lagrange multiplier is approximated using the Newton-Raphson method that is associated with weaker secant relation. An executable code is developed to test the efficiency of the proposed method with some standard conjugate-gradient methods. Numerical results show that the proposed method performs better than the conjugate gradient method. |
| format |
Conference or Workshop Item |
| author |
Sim, Hong Seng Leong, Wah June Chen, Chuei Yee Ibrahim, Siti Nur Iqmal |
| spellingShingle |
Sim, Hong Seng Leong, Wah June Chen, Chuei Yee Ibrahim, Siti Nur Iqmal Diagonal quasi-Newton updating formula using log-determinant norm |
| author_facet |
Sim, Hong Seng Leong, Wah June Chen, Chuei Yee Ibrahim, Siti Nur Iqmal |
| author_sort |
Sim, Hong Seng |
| title |
Diagonal quasi-Newton updating formula using log-determinant norm |
| title_short |
Diagonal quasi-Newton updating formula using log-determinant norm |
| title_full |
Diagonal quasi-Newton updating formula using log-determinant norm |
| title_fullStr |
Diagonal quasi-Newton updating formula using log-determinant norm |
| title_full_unstemmed |
Diagonal quasi-Newton updating formula using log-determinant norm |
| title_sort |
diagonal quasi-newton updating formula using log-determinant norm |
| publisher |
AIP Publishing |
| publishDate |
2015 |
| url |
http://psasir.upm.edu.my/id/eprint/57371/1/Diagonal%20quasi-Newton%20updating%20formula%20using%20log-determinant%20norm.pdf |
| _version_ |
1819297739501993984 |
| score |
13.4562235 |