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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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প্রধান লেখক: Sim, Hong Seng, Leong, Wah June, Chen, Chuei Yee, Ibrahim, Siti Nur Iqmal
বিন্যাস: Conference or Workshop Item
ভাষা:English
প্রকাশিত: AIP Publishing 2015
অনলাইন ব্যবহার করুন:http://psasir.upm.edu.my/id/eprint/57371/1/Diagonal%20quasi-Newton%20updating%20formula%20using%20log-determinant%20norm.pdf
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id oai:psasir.upm.edu.my:57371
record_format eprints
spelling 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
institution UPM IR
collection 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

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