The investigation of gradient method namely Steepest Descent and extending of Barzilai Borwein for solving unconstrained optimization problem / Nur Intan Syahirah Ismail & Nur Atikah Aziz

Steepest Descent is one of the pioneers method in solving optimization problem since it is globally convergence. Even though it is globally convergence, the convergence rate is still slow. Thus, in this project we focusing more on SD method and its modification, to get the better convergence rate. T...

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Main Authors:	Ismail, Nur Intan Syahirah, Aziz, Nur Atikah
Format:	Thesis
Language:	English
Published:	2019
Subjects:	Mathematical statistics Probabilities Analytical methods used in the solution of physical problems
Online Access:	https://ir.uitm.edu.my/id/eprint/38918/1/38918.pdf
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id	my-uitm-ir.38918
record_format	uketd_dc
spelling	my-uitm-ir.389182020-12-09T03:39:37Z The investigation of gradient method namely Steepest Descent and extending of Barzilai Borwein for solving unconstrained optimization problem / Nur Intan Syahirah Ismail & Nur Atikah Aziz 2019-07 Ismail, Nur Intan Syahirah Aziz, Nur Atikah Mathematical statistics. Probabilities Analytical methods used in the solution of physical problems Programming. Rule-based programming. Backtrack programming Steepest Descent is one of the pioneers method in solving optimization problem since it is globally convergence. Even though it is globally convergence, the convergence rate is still slow. Thus, in this project we focusing more on SD method and its modification, to get the better convergence rate. This research is to investigate the behavior of gradient method namely Steepest Descent (SD), Barzilai Borwein 1(BB1), Barzilai Borwein 2(BB2) and Jaafar Mohamed (JM). This project is to analyse the performance of this four-method based on CPU time and number of iterations, and to show their global convergence. Eight test functions with several initial points from four geometrical quadrants has been chosen to test on SD, BB1, BB2 and JM method. The collected data is determined based on the number of iteration and CPU time by using exact line search. The results also show that all the methods possess global convergence. In order to analyse the best method geometrically, the performance profile by Dolan and Moore is used. Based on this performance profile, the best method will be determined. Lastly, numerical result will be generated from this research as a numerical prove to all the behaviour of the methods listed above. 2019-07 Thesis https://ir.uitm.edu.my/id/eprint/38918/ https://ir.uitm.edu.my/id/eprint/38918/1/38918.pdf text en public degree Universiti Teknologi MARA Faculty of Computer & Mathematical Sciences Jusoh, Ibrahim Mohd Ali, Mohd Rivaie
institution	Universiti Teknologi MARA
collection	UiTM Institutional Repository
language	English
advisor	Jusoh, Ibrahim Mohd Ali, Mohd Rivaie
topic	Mathematical statistics Probabilities Analytical methods used in the solution of physical problems Mathematical statistics Probabilities
spellingShingle	Mathematical statistics Probabilities Analytical methods used in the solution of physical problems Mathematical statistics Probabilities Ismail, Nur Intan Syahirah Aziz, Nur Atikah The investigation of gradient method namely Steepest Descent and extending of Barzilai Borwein for solving unconstrained optimization problem / Nur Intan Syahirah Ismail & Nur Atikah Aziz
description	Steepest Descent is one of the pioneers method in solving optimization problem since it is globally convergence. Even though it is globally convergence, the convergence rate is still slow. Thus, in this project we focusing more on SD method and its modification, to get the better convergence rate. This research is to investigate the behavior of gradient method namely Steepest Descent (SD), Barzilai Borwein 1(BB1), Barzilai Borwein 2(BB2) and Jaafar Mohamed (JM). This project is to analyse the performance of this four-method based on CPU time and number of iterations, and to show their global convergence. Eight test functions with several initial points from four geometrical quadrants has been chosen to test on SD, BB1, BB2 and JM method. The collected data is determined based on the number of iteration and CPU time by using exact line search. The results also show that all the methods possess global convergence. In order to analyse the best method geometrically, the performance profile by Dolan and Moore is used. Based on this performance profile, the best method will be determined. Lastly, numerical result will be generated from this research as a numerical prove to all the behaviour of the methods listed above.
format	Thesis
qualification_level	Bachelor degree
author	Ismail, Nur Intan Syahirah Aziz, Nur Atikah
author_facet	Ismail, Nur Intan Syahirah Aziz, Nur Atikah
author_sort	Ismail, Nur Intan Syahirah
title	The investigation of gradient method namely Steepest Descent and extending of Barzilai Borwein for solving unconstrained optimization problem / Nur Intan Syahirah Ismail & Nur Atikah Aziz
title_short	The investigation of gradient method namely Steepest Descent and extending of Barzilai Borwein for solving unconstrained optimization problem / Nur Intan Syahirah Ismail & Nur Atikah Aziz
title_full	The investigation of gradient method namely Steepest Descent and extending of Barzilai Borwein for solving unconstrained optimization problem / Nur Intan Syahirah Ismail & Nur Atikah Aziz
title_fullStr	The investigation of gradient method namely Steepest Descent and extending of Barzilai Borwein for solving unconstrained optimization problem / Nur Intan Syahirah Ismail & Nur Atikah Aziz
title_full_unstemmed	The investigation of gradient method namely Steepest Descent and extending of Barzilai Borwein for solving unconstrained optimization problem / Nur Intan Syahirah Ismail & Nur Atikah Aziz
title_sort	investigation of gradient method namely steepest descent and extending of barzilai borwein for solving unconstrained optimization problem / nur intan syahirah ismail & nur atikah aziz
granting_institution	Universiti Teknologi MARA
granting_department	Faculty of Computer & Mathematical Sciences
publishDate	2019
url	https://ir.uitm.edu.my/id/eprint/38918/1/38918.pdf
_version_	1783734491102052352

The investigation of gradient method namely Steepest Descent and extending of Barzilai Borwein for solving unconstrained optimization problem / Nur Intan Syahirah Ismail & Nur Atikah Aziz

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