On the Modifications of a Broyden's Single Parameter Rank-Two Quasi-Newton Method for Unconstrained Minimization
The thesis concerns mainly in finding the numerical solution of non-linear unconstrained problems. We consider a well-known class of optimization methods called the quasi-Newton methods, or variable metric methods. In particular, a class of quasi-Newton method named Broyden's single paramete...
| Main Author: | |
|---|---|
| Format: | Thesis |
| Language: | English English |
| Published: |
1999
|
| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/8655/ http://psasir.upm.edu.my/id/eprint/8655/1/FSAS_1999_7_A.pdf |
| _version_ | 1848840930585477120 |
|---|---|
| author | Leong, Wah June |
| author_facet | Leong, Wah June |
| author_sort | Leong, Wah June |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The thesis concerns mainly in finding the numerical solution of non-linear
unconstrained problems. We consider a well-known class of optimization methods
called the quasi-Newton methods, or variable metric methods. In particular, a class of
quasi-Newton method named Broyden's single parameter rank two method is
focussed.
We also investigate the global convergence properties for some step-length
procedures. Immediately from the investigations, a global convergence proof of the
Armijo quasi-Newton method is given.
Some preliminary modifications and numerical experiments are carried out to
gain useful numerical experiences for the improvements of the quasi-Ne"-'ton updates.We then derived two improvement techniques: the first we employ a switching
criteria between quasi-Newton Broyden-Fletcher-Goldfrab-Shanno or BFGS and
steepest descent direction and in the second we introduce a reduced trace-norm
condition BFGS update. The thesis includes results illustrating the numerical
performance of the modified methods on a chosen set of test problems.
Limitations and some possible extensions are also given to conclude this thesis. |
| first_indexed | 2025-11-15T07:35:10Z |
| format | Thesis |
| id | upm-8655 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T07:35:10Z |
| publishDate | 1999 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-86552012-05-11T01:18:09Z http://psasir.upm.edu.my/id/eprint/8655/ On the Modifications of a Broyden's Single Parameter Rank-Two Quasi-Newton Method for Unconstrained Minimization Leong, Wah June The thesis concerns mainly in finding the numerical solution of non-linear unconstrained problems. We consider a well-known class of optimization methods called the quasi-Newton methods, or variable metric methods. In particular, a class of quasi-Newton method named Broyden's single parameter rank two method is focussed. We also investigate the global convergence properties for some step-length procedures. Immediately from the investigations, a global convergence proof of the Armijo quasi-Newton method is given. Some preliminary modifications and numerical experiments are carried out to gain useful numerical experiences for the improvements of the quasi-Ne"-'ton updates.We then derived two improvement techniques: the first we employ a switching criteria between quasi-Newton Broyden-Fletcher-Goldfrab-Shanno or BFGS and steepest descent direction and in the second we introduce a reduced trace-norm condition BFGS update. The thesis includes results illustrating the numerical performance of the modified methods on a chosen set of test problems. Limitations and some possible extensions are also given to conclude this thesis. 1999 Thesis NonPeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/8655/1/FSAS_1999_7_A.pdf Leong, Wah June (1999) On the Modifications of a Broyden's Single Parameter Rank-Two Quasi-Newton Method for Unconstrained Minimization. Masters thesis, Universiti Putra Malaysia. Numerical analysis Variables (Mathematics) English |
| spellingShingle | Numerical analysis Variables (Mathematics) Leong, Wah June On the Modifications of a Broyden's Single Parameter Rank-Two Quasi-Newton Method for Unconstrained Minimization |
| title | On the Modifications of a Broyden's Single Parameter Rank-Two Quasi-Newton Method for Unconstrained Minimization |
| title_full | On the Modifications of a Broyden's Single Parameter Rank-Two Quasi-Newton Method for Unconstrained Minimization |
| title_fullStr | On the Modifications of a Broyden's Single Parameter Rank-Two Quasi-Newton Method for Unconstrained Minimization |
| title_full_unstemmed | On the Modifications of a Broyden's Single Parameter Rank-Two Quasi-Newton Method for Unconstrained Minimization |
| title_short | On the Modifications of a Broyden's Single Parameter Rank-Two Quasi-Newton Method for Unconstrained Minimization |
| title_sort | on the modifications of a broyden's single parameter rank-two quasi-newton method for unconstrained minimization |
| topic | Numerical analysis Variables (Mathematics) |
| url | http://psasir.upm.edu.my/id/eprint/8655/ http://psasir.upm.edu.my/id/eprint/8655/1/FSAS_1999_7_A.pdf |