Efficiency of subgradient method in solving nonsmootth optimization problems

Nonsmooth optimization is one of the hardest type of problems to solve in optimization area. This is because of the non-differentiability of the function itself. Subgradient method is generally known as the method to solve nonsmooth optimization problems, where it was first discovered by Shor [17]....

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Main Author:	Abdullah, Nur Azira
Format:	Thesis
Language:	English
Published:	2014
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/38863/1/NurAziraAbdullahMFS2014.pdf
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spelling	my-utm-ep.388632017-09-06T00:48:50Z Efficiency of subgradient method in solving nonsmootth optimization problems 2014-01 Abdullah, Nur Azira QA Mathematics Nonsmooth optimization is one of the hardest type of problems to solve in optimization area. This is because of the non-differentiability of the function itself. Subgradient method is generally known as the method to solve nonsmooth optimization problems, where it was first discovered by Shor [17]. The main purpose of this study is to analyze the efficiency of subgradient method by implementing it on these nonsmooth problems. This study considers two different types of problems, the first of which is Shor’s piecewise quadratic function type of problem and the other is L1-regularized form type of problems. The objectives of this study are to apply the subgradient method on nonsmooth optimization problems and to develop matlab code for the subgradient method and to compare the performance of the method using various step sizes and matrix dimensions. In order to achieve the result, we will use matlab software. At the end of this study we can conclude that subgradient method can solve nonsmooth optimization problems and the rate of convergence varies based on the step size used. 2014-01 Thesis http://eprints.utm.my/id/eprint/38863/ http://eprints.utm.my/id/eprint/38863/1/NurAziraAbdullahMFS2014.pdf application/pdf en public masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Abdullah, Nur Azira Efficiency of subgradient method in solving nonsmootth optimization problems
description	Nonsmooth optimization is one of the hardest type of problems to solve in optimization area. This is because of the non-differentiability of the function itself. Subgradient method is generally known as the method to solve nonsmooth optimization problems, where it was first discovered by Shor [17]. The main purpose of this study is to analyze the efficiency of subgradient method by implementing it on these nonsmooth problems. This study considers two different types of problems, the first of which is Shor’s piecewise quadratic function type of problem and the other is L1-regularized form type of problems. The objectives of this study are to apply the subgradient method on nonsmooth optimization problems and to develop matlab code for the subgradient method and to compare the performance of the method using various step sizes and matrix dimensions. In order to achieve the result, we will use matlab software. At the end of this study we can conclude that subgradient method can solve nonsmooth optimization problems and the rate of convergence varies based on the step size used.
format	Thesis
qualification_level	Master's degree
author	Abdullah, Nur Azira
author_facet	Abdullah, Nur Azira
author_sort	Abdullah, Nur Azira
title	Efficiency of subgradient method in solving nonsmootth optimization problems
title_short	Efficiency of subgradient method in solving nonsmootth optimization problems
title_full	Efficiency of subgradient method in solving nonsmootth optimization problems
title_fullStr	Efficiency of subgradient method in solving nonsmootth optimization problems
title_full_unstemmed	Efficiency of subgradient method in solving nonsmootth optimization problems
title_sort	efficiency of subgradient method in solving nonsmootth optimization problems
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2014
url	http://eprints.utm.my/id/eprint/38863/1/NurAziraAbdullahMFS2014.pdf
_version_	1747816531916488704

Efficiency of subgradient method in solving nonsmootth optimization problems

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