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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主要作者: Abdullah, Nur Azira
格式: Thesis
語言:English
出版: 2014
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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