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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
http://psasir.upm.edu.my/id/eprint/85444/
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spelling my.upm.eprints.854442021-12-16T02:28:34Z http://psasir.upm.edu.my/id/eprint/85444/ Conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization 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. 2015-11 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/85444/1/FS%202016%2091%20ir.pdf Ling, Mei Mei (2015) Conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization. Masters thesis, Universiti Putra Malaysia. Conjugate gradient methods
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
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
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
publishDate 2015
url http://psasir.upm.edu.my/id/eprint/85444/1/FS%202016%2091%20ir.pdf
http://psasir.upm.edu.my/id/eprint/85444/
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score 13.244745

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