Comparisons between Newton and Quasi-Newton method in solving unconstrained optimization problems / Naznin Faiqa Khirul Fozi & Hanis Sofia Mohd Rodi

Newton and Quasi-Newton methods are widely used in solving unconstrained optimization problems. The solution to optimization problems are known as local optimum solutions and global minimum solutions. For Newton method, if the initial points are far from the solution points, it may fail to converge....

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Main Authors:	Khirul Fozi, Naznin Faiqa, Mohd Rodi, Hanis Sofia
Format:	Thesis
Language:	English
Published:	2019
Subjects:	Equations Analytical methods used in the solution of physical problems Algorithms
Online Access:	https://ir.uitm.edu.my/id/eprint/39809/1/39809.pdf
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id	my-uitm-ir.39809
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spelling	my-uitm-ir.398092020-12-24T06:02:03Z Comparisons between Newton and Quasi-Newton method in solving unconstrained optimization problems / Naznin Faiqa Khirul Fozi & Hanis Sofia Mohd Rodi 2019-07 Khirul Fozi, Naznin Faiqa Mohd Rodi, Hanis Sofia Equations Mathematical statistics. Probabilities Analytical methods used in the solution of physical problems Algorithms Newton and Quasi-Newton methods are widely used in solving unconstrained optimization problems. The solution to optimization problems are known as local optimum solutions and global minimum solutions. For Newton method, if the initial points are far from the solution points, it may fail to converge. As an alternative, two Quasi-Newton methods which are Davidon-Fletcher-Powell (DFP) and Broyden- Fletcher-Goldfarb-Shanno (BFGS) methods were developed to overcome this problem. In this research, a comparison was made between Newton and Quasi-Newton method to determine the best method in solving unconstrained optimization problems. These methods were tested using six test functions with different initial points and their performance were compared based on the number of iterations, CPU time, and accuracy. This research also discussed about the convergence rate, global convergence and local convergence of the three methods. From numerical results, it has been shown that BFGS method is better compared to the other methods. 2019-07 Thesis https://ir.uitm.edu.my/id/eprint/39809/ https://ir.uitm.edu.my/id/eprint/39809/1/39809.pdf text en public degree Universiti Teknologi MARA Faculty of Computer and Mathematical Sciences Jusoh, Ibrahim
institution	Universiti Teknologi MARA
collection	UiTM Institutional Repository
language	English
advisor	Jusoh, Ibrahim
topic	Equations Equations Analytical methods used in the solution of physical problems Algorithms
spellingShingle	Equations Equations Analytical methods used in the solution of physical problems Algorithms Khirul Fozi, Naznin Faiqa Mohd Rodi, Hanis Sofia Comparisons between Newton and Quasi-Newton method in solving unconstrained optimization problems / Naznin Faiqa Khirul Fozi & Hanis Sofia Mohd Rodi
description	Newton and Quasi-Newton methods are widely used in solving unconstrained optimization problems. The solution to optimization problems are known as local optimum solutions and global minimum solutions. For Newton method, if the initial points are far from the solution points, it may fail to converge. As an alternative, two Quasi-Newton methods which are Davidon-Fletcher-Powell (DFP) and Broyden- Fletcher-Goldfarb-Shanno (BFGS) methods were developed to overcome this problem. In this research, a comparison was made between Newton and Quasi-Newton method to determine the best method in solving unconstrained optimization problems. These methods were tested using six test functions with different initial points and their performance were compared based on the number of iterations, CPU time, and accuracy. This research also discussed about the convergence rate, global convergence and local convergence of the three methods. From numerical results, it has been shown that BFGS method is better compared to the other methods.
format	Thesis
qualification_level	Bachelor degree
author	Khirul Fozi, Naznin Faiqa Mohd Rodi, Hanis Sofia
author_facet	Khirul Fozi, Naznin Faiqa Mohd Rodi, Hanis Sofia
author_sort	Khirul Fozi, Naznin Faiqa
title	Comparisons between Newton and Quasi-Newton method in solving unconstrained optimization problems / Naznin Faiqa Khirul Fozi & Hanis Sofia Mohd Rodi
title_short	Comparisons between Newton and Quasi-Newton method in solving unconstrained optimization problems / Naznin Faiqa Khirul Fozi & Hanis Sofia Mohd Rodi
title_full	Comparisons between Newton and Quasi-Newton method in solving unconstrained optimization problems / Naznin Faiqa Khirul Fozi & Hanis Sofia Mohd Rodi
title_fullStr	Comparisons between Newton and Quasi-Newton method in solving unconstrained optimization problems / Naznin Faiqa Khirul Fozi & Hanis Sofia Mohd Rodi
title_full_unstemmed	Comparisons between Newton and Quasi-Newton method in solving unconstrained optimization problems / Naznin Faiqa Khirul Fozi & Hanis Sofia Mohd Rodi
title_sort	comparisons between newton and quasi-newton method in solving unconstrained optimization problems / naznin faiqa khirul fozi & hanis sofia mohd rodi
granting_institution	Universiti Teknologi MARA
granting_department	Faculty of Computer and Mathematical Sciences
publishDate	2019
url	https://ir.uitm.edu.my/id/eprint/39809/1/39809.pdf
_version_	1783734543251931136

Comparisons between Newton and Quasi-Newton method in solving unconstrained optimization problems / Naznin Faiqa Khirul Fozi & Hanis Sofia Mohd Rodi

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