Newton based homotopy optimization method for solving global optimization problem

Optimization method is widely used in mechanics and engineering, economics, operations research and engineering controls. Various methods have been introduced to solve the optimization problem and mostly it will get a local optimum. One of the most commonly used method is the Newton-Raphson method....

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Main Author:	Mohd. Taha, Ahmad Zharif Salami
Format:	Thesis
Language:	English
Published:	2013
Subjects:	QA75 Electronic computers Computer science
Online Access:	http://eprints.utm.my/id/eprint/33234/1/AhmadZharifSalamiMFS2013.pdf
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id	my-utm-ep.33234
record_format	uketd_dc
spelling	my-utm-ep.332342017-09-14T03:58:16Z Newton based homotopy optimization method for solving global optimization problem 2013-01 Mohd. Taha, Ahmad Zharif Salami QA75 Electronic computers. Computer science Optimization method is widely used in mechanics and engineering, economics, operations research and engineering controls. Various methods have been introduced to solve the optimization problem and mostly it will get a local optimum. One of the most commonly used method is the Newton-Raphson method. In this method, there are some circumstances where it is unable to solve the optimization problem. With the help of homotopy, the problems faced by the Newton-Raphson method can be overcome and thus solve the optimization problem. Therefore, the aim of this study is to investigate the Newton-Raphson method as the basis for the homotopy optimization method for finding local minimum and also the global minimum. There are several auxiliary homotopy functions that should be selected and this project using the Newton Homotopy and Fixed-Point Homotopy. The ability for these two functions are compared in solving optimization. To strengthen these findings, the project is programmed using MATLAB to implement the Newton’s based Homotopy Optimization Method. The four functions of univariate and multivariate are provided for illustrative purposes. This project has succeeded to compare the ability of these two auxiliary homotopy functions in solving global optimization method. 2013-01 Thesis http://eprints.utm.my/id/eprint/33234/ http://eprints.utm.my/id/eprint/33234/1/AhmadZharifSalamiMFS2013.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:71535?site_name=Restricted Repository masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA75 Electronic computers Computer science
spellingShingle	QA75 Electronic computers Computer science Mohd. Taha, Ahmad Zharif Salami Newton based homotopy optimization method for solving global optimization problem
description	Optimization method is widely used in mechanics and engineering, economics, operations research and engineering controls. Various methods have been introduced to solve the optimization problem and mostly it will get a local optimum. One of the most commonly used method is the Newton-Raphson method. In this method, there are some circumstances where it is unable to solve the optimization problem. With the help of homotopy, the problems faced by the Newton-Raphson method can be overcome and thus solve the optimization problem. Therefore, the aim of this study is to investigate the Newton-Raphson method as the basis for the homotopy optimization method for finding local minimum and also the global minimum. There are several auxiliary homotopy functions that should be selected and this project using the Newton Homotopy and Fixed-Point Homotopy. The ability for these two functions are compared in solving optimization. To strengthen these findings, the project is programmed using MATLAB to implement the Newton’s based Homotopy Optimization Method. The four functions of univariate and multivariate are provided for illustrative purposes. This project has succeeded to compare the ability of these two auxiliary homotopy functions in solving global optimization method.
format	Thesis
qualification_level	Master's degree
author	Mohd. Taha, Ahmad Zharif Salami
author_facet	Mohd. Taha, Ahmad Zharif Salami
author_sort	Mohd. Taha, Ahmad Zharif Salami
title	Newton based homotopy optimization method for solving global optimization problem
title_short	Newton based homotopy optimization method for solving global optimization problem
title_full	Newton based homotopy optimization method for solving global optimization problem
title_fullStr	Newton based homotopy optimization method for solving global optimization problem
title_full_unstemmed	Newton based homotopy optimization method for solving global optimization problem
title_sort	newton based homotopy optimization method for solving global optimization problem
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2013
url	http://eprints.utm.my/id/eprint/33234/1/AhmadZharifSalamiMFS2013.pdf
_version_	1747816111914614784

Newton based homotopy optimization method for solving global optimization problem

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