Modified Quasi-Newton Methods For Large-Scale Unconstrained Optimization

The focus of this thesis is on finding the unconstrained minimizer of a function, when the dimension n is large. Specifically, we will focus on the wellknown class of optimization methods called the quasi-Newton methods. First we briefly give some mathematical background. Then we discuss the quas...

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Main Author: Leong, Wah June
Format: Thesis
Language:English
English
Published: 2003
Subjects:
Online Access:http://psasir.upm.edu.my/id/eprint/11702/1/FSAS_2003_60.pdf
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spelling my-upm-ir.117022024-06-25T04:20:34Z Modified Quasi-Newton Methods For Large-Scale Unconstrained Optimization 2003-01 Leong, Wah June The focus of this thesis is on finding the unconstrained minimizer of a function, when the dimension n is large. Specifically, we will focus on the wellknown class of optimization methods called the quasi-Newton methods. First we briefly give some mathematical background. Then we discuss the quasi-Newton's methods, the fundamental method in underlying most approaches to the problems of large-scale unconstrained optimization, as well as the related so-called line search methods. A review of the optimization methods currently available that can be used to solve large-scale problems is also given. The mam practical deficiency of quasi-Newton methods is the high computational cost for search directions, which is the key issue in large-scale unconstrained optimization. Due to the presence of this deficiency, we introduce a variety of techniques for improving the quasi-Newton methods for large-scale problems, including scaling the SR1 update, matrix-storage free methods and the extension of modified BFGS updates to limited-memory scheme. Comprehensive theoretical and experimental results are also given. Finally we comment on some achievements in our researches. Possible extensions are also given to conclude this thesis. Mathematical optimization. 2003-01 Thesis http://psasir.upm.edu.my/id/eprint/11702/ http://psasir.upm.edu.my/id/eprint/11702/1/FSAS_2003_60.pdf text en public doctoral Universiti Putra Malaysia Mathematical optimization. Faculty of Environmental studies Abu Hassan, Malik English
institution Universiti Putra Malaysia
collection PSAS Institutional Repository
language English
English
advisor Abu Hassan, Malik
topic Mathematical optimization.


spellingShingle Mathematical optimization.


Leong, Wah June
Modified Quasi-Newton Methods For Large-Scale Unconstrained Optimization
description The focus of this thesis is on finding the unconstrained minimizer of a function, when the dimension n is large. Specifically, we will focus on the wellknown class of optimization methods called the quasi-Newton methods. First we briefly give some mathematical background. Then we discuss the quasi-Newton's methods, the fundamental method in underlying most approaches to the problems of large-scale unconstrained optimization, as well as the related so-called line search methods. A review of the optimization methods currently available that can be used to solve large-scale problems is also given. The mam practical deficiency of quasi-Newton methods is the high computational cost for search directions, which is the key issue in large-scale unconstrained optimization. Due to the presence of this deficiency, we introduce a variety of techniques for improving the quasi-Newton methods for large-scale problems, including scaling the SR1 update, matrix-storage free methods and the extension of modified BFGS updates to limited-memory scheme. Comprehensive theoretical and experimental results are also given. Finally we comment on some achievements in our researches. Possible extensions are also given to conclude this thesis.
format Thesis
qualification_level Doctorate
author Leong, Wah June
author_facet Leong, Wah June
author_sort Leong, Wah June
title Modified Quasi-Newton Methods For Large-Scale Unconstrained Optimization
title_short Modified Quasi-Newton Methods For Large-Scale Unconstrained Optimization
title_full Modified Quasi-Newton Methods For Large-Scale Unconstrained Optimization
title_fullStr Modified Quasi-Newton Methods For Large-Scale Unconstrained Optimization
title_full_unstemmed Modified Quasi-Newton Methods For Large-Scale Unconstrained Optimization
title_sort modified quasi-newton methods for large-scale unconstrained optimization
granting_institution Universiti Putra Malaysia
granting_department Faculty of Environmental studies
publishDate 2003
url http://psasir.upm.edu.my/id/eprint/11702/1/FSAS_2003_60.pdf
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