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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my-upm-ir.117022012-08-28T02:49:28Z 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_A.pdf application/pdf en public phd doctoral Universiti Putra Malaysia Mathematical optimization. Faculty of Environmental studies English |
| institution |
Universiti Putra Malaysia |
| collection |
PSAS Institutional Repository |
| language |
English English |
| 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_name |
Doctor of Philosophy (PhD.) |
| 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_A.pdf |
| _version_ |
1747811252171702272 |