A Class of Diagonally Preconditioned Limited Memory Quasi-Newton Methods for Large-Scale Unconstrained Optimization

The focus of this thesis is to diagonally precondition on the limited memory quasi-Newton method for large scale unconstrained optimization problem. Particularly, the centre of discussion is on diagonally preconditioned limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method. L-BFGS method h...

Full description

Saved in:

Bibliographic Details
Main Author:	Chen, Chuei Yee
Format:	Thesis
Language:	English English
Published:	2009
Subjects:	Mathematical optimization - Case studies
Online Access:	http://psasir.upm.edu.my/id/eprint/7547/1/ABS_---__FS_2009_29.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-upm-ir.7547
record_format	uketd_dc
spelling	my-upm-ir.75472013-05-27T07:35:31Z A Class of Diagonally Preconditioned Limited Memory Quasi-Newton Methods for Large-Scale Unconstrained Optimization 2009 Chen, Chuei Yee The focus of this thesis is to diagonally precondition on the limited memory quasi-Newton method for large scale unconstrained optimization problem. Particularly, the centre of discussion is on diagonally preconditioned limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method. L-BFGS method has been widely used in large scale unconstrained optimization due to its effectiveness. However, a major drawback of the L-BFGS method is that it can be very slow on certain type of problems. Scaling and preconditioning have been used to boost the performance of the L-BFGS method. In this study, a class of diagonally preconditioned L-BFGS method will be proposed. Contrary to the standard L-BFGS method where its initial inverse Hessian approximation is the identity matrix, a class of diagonal preconditioners has been derived based upon the weak-quasi-Newton relation with an additional parameter. Choosing different parameters leads the research to some well-known diagonal updating formulae which enable the R-linear convergent for the L-BFGS method. Numerical experiments were performed on a set of large scale unconstrained minimization problem to examine the impact of each choice of parameter. The computational results suggest that the proposed diagonally preconditioned L-BFGS methods outperform the standard L-BFGS method without any preconditioning. Finally, we discuss on the impact of the diagonal preconditioners on the L-BFGS method as compared to the standard L-BFGS method in terms of the number of iterations, the number of function/gradient evaluations and the CPU time in second. Mathematical optimization - Case studies 2009 Thesis http://psasir.upm.edu.my/id/eprint/7547/ http://psasir.upm.edu.my/id/eprint/7547/1/ABS_---__FS_2009_29.pdf application/pdf en public masters Universiti Putra Malaysia Mathematical optimization - Case studies Faculty of Science English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
topic	Mathematical optimization - Case studies
spellingShingle	Mathematical optimization - Case studies Chen, Chuei Yee A Class of Diagonally Preconditioned Limited Memory Quasi-Newton Methods for Large-Scale Unconstrained Optimization
description	The focus of this thesis is to diagonally precondition on the limited memory quasi-Newton method for large scale unconstrained optimization problem. Particularly, the centre of discussion is on diagonally preconditioned limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method. L-BFGS method has been widely used in large scale unconstrained optimization due to its effectiveness. However, a major drawback of the L-BFGS method is that it can be very slow on certain type of problems. Scaling and preconditioning have been used to boost the performance of the L-BFGS method. In this study, a class of diagonally preconditioned L-BFGS method will be proposed. Contrary to the standard L-BFGS method where its initial inverse Hessian approximation is the identity matrix, a class of diagonal preconditioners has been derived based upon the weak-quasi-Newton relation with an additional parameter. Choosing different parameters leads the research to some well-known diagonal updating formulae which enable the R-linear convergent for the L-BFGS method. Numerical experiments were performed on a set of large scale unconstrained minimization problem to examine the impact of each choice of parameter. The computational results suggest that the proposed diagonally preconditioned L-BFGS methods outperform the standard L-BFGS method without any preconditioning. Finally, we discuss on the impact of the diagonal preconditioners on the L-BFGS method as compared to the standard L-BFGS method in terms of the number of iterations, the number of function/gradient evaluations and the CPU time in second.
format	Thesis
qualification_level	Master's degree
author	Chen, Chuei Yee
author_facet	Chen, Chuei Yee
author_sort	Chen, Chuei Yee
title	A Class of Diagonally Preconditioned Limited Memory Quasi-Newton Methods for Large-Scale Unconstrained Optimization
title_short	A Class of Diagonally Preconditioned Limited Memory Quasi-Newton Methods for Large-Scale Unconstrained Optimization
title_full	A Class of Diagonally Preconditioned Limited Memory Quasi-Newton Methods for Large-Scale Unconstrained Optimization
title_fullStr	A Class of Diagonally Preconditioned Limited Memory Quasi-Newton Methods for Large-Scale Unconstrained Optimization
title_full_unstemmed	A Class of Diagonally Preconditioned Limited Memory Quasi-Newton Methods for Large-Scale Unconstrained Optimization
title_sort	class of diagonally preconditioned limited memory quasi-newton methods for large-scale unconstrained optimization
granting_institution	Universiti Putra Malaysia
granting_department	Faculty of Science
publishDate	2009
url	http://psasir.upm.edu.my/id/eprint/7547/1/ABS_---__FS_2009_29.pdf
_version_	1747810698397745152

A Class of Diagonally Preconditioned Limited Memory Quasi-Newton Methods for Large-Scale Unconstrained Optimization

Similar Items