Generalized Barzilai and Borwein method for large-scale unconstrained optimization.

The focus of the thesis is on finding the unconstrained minimizer of a function by using the fixed steps gradient method. Specifically, we will focus on the Barzilai and Borwein (BB) method. In this thesis, we propose a generalized Barzilai and Borwein (GBB) method that can overcome some disadvantag...

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Main Author:	Koo, Boon Yuan
Format:	Thesis
Language:	English English
Published:	2011
Subjects:	Method of steepest descent (Numerical analysis) Method of steepest descent (Numerical analysis) Mathematical optimization
Online Access:	http://psasir.upm.edu.my/id/eprint/27372/1/FS%202011%20107R.pdf
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id	my-upm-ir.27372
record_format	uketd_dc
spelling	my-upm-ir.273722014-02-27T01:48:02Z Generalized Barzilai and Borwein method for large-scale unconstrained optimization. 2011-12 Koo, Boon Yuan The focus of the thesis is on finding the unconstrained minimizer of a function by using the fixed steps gradient method. Specifically, we will focus on the Barzilai and Borwein (BB) method. In this thesis, we propose a generalized Barzilai and Borwein (GBB) method that can overcome some disadvantages of the standard BB methods. The generalized Barzilai and Borwein method presented a special choice of steplength for the gradient method, which is a convex combination of two standard BB methods. Generally, the standard BB method does not guarantee a descent in the objective function at each iteration. We choose different scalar of combination between 0 and 1 to ensure that are descending in function value. This property is shown to be able to reduce the number of iteration in obtaining an approximate minimizer. The relationship between any gradient method and the shifted power method is considered. This relationship allows us to establish the convergence of the generalized Barzilai and Borwein method when applied to the problem of minimizing any strictly convex quadratic function. To highlight the performance of the generalized Barzilai and Borwein method, we applied them in solving the convex quadratic problem for the cases n = 2, 3, and 4. The results shown the number of iteration is decreasing for almost all cases. Finally, we concluded the achievements in our research and some future extensions are given at the end of thesis Method of steepest descent (Numerical analysis) Differential equations, Elliptic - Numerical solutions Mathematical optimization 2011-12 Thesis http://psasir.upm.edu.my/id/eprint/27372/ http://psasir.upm.edu.my/id/eprint/27372/1/FS%202011%20107R.pdf application/pdf en public masters Universiti Putra Malaysia Method of steepest descent (Numerical analysis) Differential equations, Elliptic - Numerical solutions Mathematical optimization Faculty of Science English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
topic	Method of steepest descent (Numerical analysis) Method of steepest descent (Numerical analysis) Mathematical optimization
spellingShingle	Method of steepest descent (Numerical analysis) Method of steepest descent (Numerical analysis) Mathematical optimization Koo, Boon Yuan Generalized Barzilai and Borwein method for large-scale unconstrained optimization.
description	The focus of the thesis is on finding the unconstrained minimizer of a function by using the fixed steps gradient method. Specifically, we will focus on the Barzilai and Borwein (BB) method. In this thesis, we propose a generalized Barzilai and Borwein (GBB) method that can overcome some disadvantages of the standard BB methods. The generalized Barzilai and Borwein method presented a special choice of steplength for the gradient method, which is a convex combination of two standard BB methods. Generally, the standard BB method does not guarantee a descent in the objective function at each iteration. We choose different scalar of combination between 0 and 1 to ensure that are descending in function value. This property is shown to be able to reduce the number of iteration in obtaining an approximate minimizer. The relationship between any gradient method and the shifted power method is considered. This relationship allows us to establish the convergence of the generalized Barzilai and Borwein method when applied to the problem of minimizing any strictly convex quadratic function. To highlight the performance of the generalized Barzilai and Borwein method, we applied them in solving the convex quadratic problem for the cases n = 2, 3, and 4. The results shown the number of iteration is decreasing for almost all cases. Finally, we concluded the achievements in our research and some future extensions are given at the end of thesis
format	Thesis
qualification_level	Master's degree
author	Koo, Boon Yuan
author_facet	Koo, Boon Yuan
author_sort	Koo, Boon Yuan
title	Generalized Barzilai and Borwein method for large-scale unconstrained optimization.
title_short	Generalized Barzilai and Borwein method for large-scale unconstrained optimization.
title_full	Generalized Barzilai and Borwein method for large-scale unconstrained optimization.
title_fullStr	Generalized Barzilai and Borwein method for large-scale unconstrained optimization.
title_full_unstemmed	Generalized Barzilai and Borwein method for large-scale unconstrained optimization.
title_sort	generalized barzilai and borwein method for large-scale unconstrained optimization.
granting_institution	Universiti Putra Malaysia
granting_department	Faculty of Science
publishDate	2011
url	http://psasir.upm.edu.my/id/eprint/27372/1/FS%202011%20107R.pdf
_version_	1747811588251844608

Generalized Barzilai and Borwein method for large-scale unconstrained optimization.

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