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...
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1999
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my.upm.eprints.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. English |
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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. |
format |
Thesis |
author |
Leong, Wah June |
spellingShingle |
Leong, Wah June On the Modifications of a Broyden's Single Parameter Rank-Two Quasi-Newton Method for Unconstrained Minimization |
author_facet |
Leong, Wah June |
author_sort |
Leong, Wah June |
title |
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_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_sort |
on the modifications of a broyden's single parameter rank-two quasi-newton method for unconstrained minimization |
publishDate |
1999 |
url |
http://psasir.upm.edu.my/id/eprint/8655/1/FSAS_1999_7_A.pdf http://psasir.upm.edu.my/id/eprint/8655/ |
_version_ |
1643824081132322816 |
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13.160551 |