Conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization

This thesis focuses on solving conjugate gradient methods for large-scale uncon- strained optimization problems. The main objective of this study is to propose some modifications to the standard conjugate gradient methods so that its search direction satisfies the sufficient descent and the bo...

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Main Author:	Ling, Mei Mei
Format:	Thesis
Language:	English
Published:	2015
Subjects:	Conjugate gradient methods
Online Access:	http://psasir.upm.edu.my/id/eprint/85444/1/FS%202016%2091%20ir.pdf
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id	my-upm-ir.85444
record_format	uketd_dc
spelling	my-upm-ir.854442021-12-16T02:28:34Z Conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization 2015-11 Ling, Mei Mei This thesis focuses on solving conjugate gradient methods for large-scale uncon- strained optimization problems. The main objective of this study is to propose some modifications to the standard conjugate gradient methods so that its search direction satisfies the sufficient descent and the boundedness condition. These two conditions appear to be a natural way of guaranteeing convergence for the conjugate gradient methods. We also propose some techniques for improving the conjugate gradient methods. The techniques in consideration include scaling parameters proposed by Oren and Luenberger, preconditioner suggested by Powell and memoryless symmetric rank one. In addition, the modified scaled conjugate gradient method is also implemented using nonmonotone line search. The convergence results for all of the modified conjugate gradient methods are also established. To validate the usefulness of our proposed improvement strategies, numerical ex- periments on a set of standard test problems were performed and presented. The results showed that our proposed methods can be good alternatives to the conju- gate gradient method in solving large-scale unconstrained optimization problems. Conjugate gradient methods 2015-11 Thesis http://psasir.upm.edu.my/id/eprint/85444/ http://psasir.upm.edu.my/id/eprint/85444/1/FS%202016%2091%20ir.pdf text en public masters Universiti Putra Malaysia Conjugate gradient methods Leong, Wah June
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
advisor	Leong, Wah June
topic	Conjugate gradient methods
spellingShingle	Conjugate gradient methods Ling, Mei Mei Conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization
description	This thesis focuses on solving conjugate gradient methods for large-scale uncon- strained optimization problems. The main objective of this study is to propose some modifications to the standard conjugate gradient methods so that its search direction satisfies the sufficient descent and the boundedness condition. These two conditions appear to be a natural way of guaranteeing convergence for the conjugate gradient methods. We also propose some techniques for improving the conjugate gradient methods. The techniques in consideration include scaling parameters proposed by Oren and Luenberger, preconditioner suggested by Powell and memoryless symmetric rank one. In addition, the modified scaled conjugate gradient method is also implemented using nonmonotone line search. The convergence results for all of the modified conjugate gradient methods are also established. To validate the usefulness of our proposed improvement strategies, numerical ex- periments on a set of standard test problems were performed and presented. The results showed that our proposed methods can be good alternatives to the conju- gate gradient method in solving large-scale unconstrained optimization problems.
format	Thesis
qualification_level	Master's degree
author	Ling, Mei Mei
author_facet	Ling, Mei Mei
author_sort	Ling, Mei Mei
title	Conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization
title_short	Conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization
title_full	Conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization
title_fullStr	Conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization
title_full_unstemmed	Conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization
title_sort	conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization
granting_institution	Universiti Putra Malaysia
publishDate	2015
url	http://psasir.upm.edu.my/id/eprint/85444/1/FS%202016%2091%20ir.pdf
_version_	1747813541802409984

Conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization

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