On the Modifications of a Broyden's Single Parameter Rank-Two Quasi-Newton Method for Unconstrained Minimization

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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Main Author: Leong, Wah June
Format: Thesis
Language:English
English
Published: 1999
Subjects:
Numerical analysis
Variables (Mathematics)
Online Access:http://psasir.upm.edu.my/id/eprint/8655/1/FSAS_1999_7_A.pdf
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spelling my-upm-ir.86552012-05-11T01:18:09Z On the Modifications of a Broyden's Single Parameter Rank-Two Quasi-Newton Method for Unconstrained Minimization 1999 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. Numerical analysis Variables (Mathematics) 1999 Thesis http://psasir.upm.edu.my/id/eprint/8655/ http://psasir.upm.edu.my/id/eprint/8655/1/FSAS_1999_7_A.pdf application/pdf en public masters Universiti Putra Malaysia Numerical analysis Variables (Mathematics) Faculty of Environmental Studies English
institution Universiti Putra Malaysia
collection PSAS Institutional Repository
language English
English
topic Numerical analysis
Variables (Mathematics)
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
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.
format Thesis
qualification_level Master's degree
author Leong, Wah June
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
granting_institution Universiti Putra Malaysia
granting_department Faculty of Environmental Studies
publishDate 1999
url http://psasir.upm.edu.my/id/eprint/8655/1/FSAS_1999_7_A.pdf
_version_ 1747810849489158144

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