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.
|Item Type:||Thesis (PhD)|
|Chairman Supervisor:||Associate Professor Malik Hj. Abu Hassan, PhD|
|Call Number:||FSAS 2003 60|
|Faculty or Institute:||Faculty of Environmental Studies|
|Deposited By:||Mohd Nezeri Mohamad|
|Deposited On:||21 Jul 2011 03:43|
|Last Modified:||28 Aug 2012 02:49|
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