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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| Format: | Thesis |
| Language: | English English |
| Published: |
2003
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| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/11702/1/FSAS_2003_60.pdf |
| _version_ | 1825944924853370880 |
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| author | Leong, Wah June |
| author_facet | Leong, Wah June |
| author_sort | Leong, Wah June |
| collection | UPM |
| 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. |
| first_indexed | 2024-03-06T07:23:31Z |
| format | Thesis |
| id | upm.eprints-11702 |
| institution | Universiti Putra Malaysia |
| language | English English |
| last_indexed | 2024-09-25T03:32:19Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | upm.eprints-117022024-06-25T04:20:34Z http://psasir.upm.edu.my/id/eprint/11702/ Modified Quasi-Newton Methods For Large-Scale Unconstrained Optimization 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. 2003-01 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/11702/1/FSAS_2003_60.pdf Leong, Wah June (2003) Modified Quasi-Newton Methods For Large-Scale Unconstrained Optimization. Doctoral thesis, Universiti Putra Malaysia. Mathematical optimization. English |
| spellingShingle | Mathematical optimization. Leong, Wah June Modified Quasi-Newton Methods For Large-Scale Unconstrained Optimization |
| title | 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_short | Modified Quasi-Newton Methods For Large-Scale Unconstrained Optimization |
| title_sort | modified quasi newton methods for large scale unconstrained optimization |
| topic | Mathematical optimization. |
| url | http://psasir.upm.edu.my/id/eprint/11702/1/FSAS_2003_60.pdf |
| work_keys_str_mv | AT leongwahjune modifiedquasinewtonmethodsforlargescaleunconstrainedoptimization |