An improvement of BFGS by applying n-th section method for solving unconstrained optimization / Nurul Atikah Mohamed Ramli

Optimization is one of mathematics field that greatly developed when Quasi-newton method was presented to solve the unconstrained optimization problem. An iterative method is used to solve the problem by finding the value of search direction, dk and step size, ak. There are different methods that ca...

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Main Author:	Mohamed Ramli, Nurul Atikah
Format:	Thesis
Language:	English
Published:	2019
Subjects:	Operative surgery Technique of surgical operations
Online Access:	https://ir.uitm.edu.my/id/eprint/79308/1/79308.pdf
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spelling	my-uitm-ir.793082023-09-08T03:46:58Z An improvement of BFGS by applying n-th section method for solving unconstrained optimization / Nurul Atikah Mohamed Ramli 2019 Mohamed Ramli, Nurul Atikah Operative surgery. Technique of surgical operations Optimization is one of mathematics field that greatly developed when Quasi-newton method was presented to solve the unconstrained optimization problem. An iterative method is used to solve the problem by finding the value of search direction, dk and step size, ak. There are different methods that can be an option to solve the dk and ak in optimization problem to get the best results in term of number of iterations and CPU time. Thus, in this research, an improvement of one of the Quasi-newton method which is Broyden-Fletcher-Goldfarb-Shanno (BFGS) method has been done by employing new inexact line search method. From the previous researches, there are a few of inexact line search method that have been introduced such as Goldstein, Armijo and Wolfe line search. However, these line searches are complicated and its complexity will burden the CPU time even though the number of iteration is reduced in BFGS method. The improvement is finding the step size ak to solve the problem by employing a new inexact line search method. This new inexact line search is known as M-th section method. The n-th section method is the modification of the original bisection method. As in bisection method, this simple n-th section method divides each interval section with an even number of interval which is greater than two. Thus, n-th section method in this project is fourth and sixth section method. This new proposed algorithm is compared with the original bisection and newton method in terms of number of iteration and CPU time. Numerical results are obtained based on eight test functions with two different tolerances. This research shows that the proposed algorithm is efficient when compared to bisection and newton method as inexact line search method. Besides, this proposed algorithm has achieved the global solution and possessed sufficient descent condition. The result is analysed based on number of iterations and CPU times. It is concluded that the n-th section method which is the sixth section method is the best method that can be used as the inexact line search in BFGS to lower the number of iterations and solve most of the problems. 2019 Thesis https://ir.uitm.edu.my/id/eprint/79308/ https://ir.uitm.edu.my/id/eprint/79308/1/79308.pdf text en public masters Universiti Teknologi MARA (UiTM) Faculty of Computer and Mathematical Sciences Jusoh, Ibrahim
institution	Universiti Teknologi MARA
collection	UiTM Institutional Repository
language	English
advisor	Jusoh, Ibrahim
topic	Operative surgery Technique of surgical operations
spellingShingle	Operative surgery Technique of surgical operations Mohamed Ramli, Nurul Atikah An improvement of BFGS by applying n-th section method for solving unconstrained optimization / Nurul Atikah Mohamed Ramli
description	Optimization is one of mathematics field that greatly developed when Quasi-newton method was presented to solve the unconstrained optimization problem. An iterative method is used to solve the problem by finding the value of search direction, dk and step size, ak. There are different methods that can be an option to solve the dk and ak in optimization problem to get the best results in term of number of iterations and CPU time. Thus, in this research, an improvement of one of the Quasi-newton method which is Broyden-Fletcher-Goldfarb-Shanno (BFGS) method has been done by employing new inexact line search method. From the previous researches, there are a few of inexact line search method that have been introduced such as Goldstein, Armijo and Wolfe line search. However, these line searches are complicated and its complexity will burden the CPU time even though the number of iteration is reduced in BFGS method. The improvement is finding the step size ak to solve the problem by employing a new inexact line search method. This new inexact line search is known as M-th section method. The n-th section method is the modification of the original bisection method. As in bisection method, this simple n-th section method divides each interval section with an even number of interval which is greater than two. Thus, n-th section method in this project is fourth and sixth section method. This new proposed algorithm is compared with the original bisection and newton method in terms of number of iteration and CPU time. Numerical results are obtained based on eight test functions with two different tolerances. This research shows that the proposed algorithm is efficient when compared to bisection and newton method as inexact line search method. Besides, this proposed algorithm has achieved the global solution and possessed sufficient descent condition. The result is analysed based on number of iterations and CPU times. It is concluded that the n-th section method which is the sixth section method is the best method that can be used as the inexact line search in BFGS to lower the number of iterations and solve most of the problems.
format	Thesis
qualification_level	Master's degree
author	Mohamed Ramli, Nurul Atikah
author_facet	Mohamed Ramli, Nurul Atikah
author_sort	Mohamed Ramli, Nurul Atikah
title	An improvement of BFGS by applying n-th section method for solving unconstrained optimization / Nurul Atikah Mohamed Ramli
title_short	An improvement of BFGS by applying n-th section method for solving unconstrained optimization / Nurul Atikah Mohamed Ramli
title_full	An improvement of BFGS by applying n-th section method for solving unconstrained optimization / Nurul Atikah Mohamed Ramli
title_fullStr	An improvement of BFGS by applying n-th section method for solving unconstrained optimization / Nurul Atikah Mohamed Ramli
title_full_unstemmed	An improvement of BFGS by applying n-th section method for solving unconstrained optimization / Nurul Atikah Mohamed Ramli
title_sort	improvement of bfgs by applying n-th section method for solving unconstrained optimization / nurul atikah mohamed ramli
granting_institution	Universiti Teknologi MARA (UiTM)
granting_department	Faculty of Computer and Mathematical Sciences
publishDate	2019
url	https://ir.uitm.edu.my/id/eprint/79308/1/79308.pdf
_version_	1783736270383480832

An improvement of BFGS by applying n-th section method for solving unconstrained optimization / Nurul Atikah Mohamed Ramli

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