Cover Image

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...

Full description

Saved in:
Bibliographic Details
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
Programming. Rule-based programming. Backtrack programming
Online Access:http://ir.uitm.edu.my/id/eprint/38918/1/38918.pdf
http://ir.uitm.edu.my/id/eprint/38918/
Tags: Add Tag
No Tags, Be the first to tag this record!
id my.uitm.ir.38918
record_format eprints
spelling my.uitm.ir.389182020-12-09T03:39:37Z http://ir.uitm.edu.my/id/eprint/38918/ 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 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 NonPeerReviewed text en http://ir.uitm.edu.my/id/eprint/38918/1/38918.pdf Ismail, Nur Intan Syahirah and Aziz, Nur Atikah (2019) 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. Degree thesis, Universiti Teknologi MARA.
institution Universiti Teknologi Mara
building Tun Abdul Razak Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Mara
content_source UiTM Institutional Repository
url_provider http://ir.uitm.edu.my/
language English
topic Mathematical statistics. Probabilities
Analytical methods used in the solution of physical problems
Programming. Rule-based programming. Backtrack programming
spellingShingle Mathematical statistics. Probabilities
Analytical methods used in the solution of physical problems
Programming. Rule-based programming. Backtrack programming
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
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
publishDate 2019
url http://ir.uitm.edu.my/id/eprint/38918/1/38918.pdf
http://ir.uitm.edu.my/id/eprint/38918/
_version_ 1685651616844218368
score 13.211869

Similar Items