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Modified Quasi-Newton Methods For Large-Scale Unconstrained Optimization


Leong, Wah June (2003) Modified Quasi-Newton Methods For Large-Scale Unconstrained Optimization. PhD thesis, Universiti Putra Malaysia.


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.

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Additional Metadata

Item Type: Thesis (PhD)
Subject: Mathematical optimization.
Call Number: FSAS 2003 60
Chairman Supervisor: Associate Professor Malik Hj. Abu Hassan, PhD
Divisions: Faculty of Environmental Studies
Depositing User: Mohd Nezeri Mohamad
Date Deposited: 21 Jul 2011 03:43
Last Modified: 28 Aug 2012 02:49
URI: http://psasir.upm.edu.my/id/eprint/11702
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