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A Modified Spectral Gradient Method for Solving Non Linear System

The objective of this project is to modify the spectral gradient method in solving the nonlinear systems. The multiple damping spectral gradient method with line search has been proposed for making improvements to the slow convergence issues. It operates separately on the gradient vector norm and th...

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Main Author: Koay, Yeong Lin
Format: Final Year Project / Dissertation / Thesis
Published: 2020
Subjects:
QA Mathematics
Online Access:http://eprints.utar.edu.my/4200/1/1701678_KOAY_YEONG_LIN.pdf
http://eprints.utar.edu.my/4200/
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spelling my-utar-eprints.42002021-08-09T11:46:00Z A Modified Spectral Gradient Method for Solving Non Linear System Koay, Yeong Lin QA Mathematics The objective of this project is to modify the spectral gradient method in solving the nonlinear systems. The multiple damping spectral gradient method with line search has been proposed for making improvements to the slow convergence issues. It operates separately on the gradient vector norm and the objective function at the same time and can be considered as an alternative for solving large-scale optimization problems. The results show that the spectral gradient method provides the best performance in solving the optimization problems, compared to the steepest descent method and conjugate gradient method, under the backtracking line search with Armijo condition (BTA). The main difference between these methods is the calculation of direction vector, dk. Besides, there is a relationship between solving a series of nonlinear equations and finding the optimal solutions to the problems. Most of the methods used for solving nonlinear systems are optimization-based methods. Therefore, the spectral gradient method with the BTA line search technique has been modified in order to solve solving the nonlinear systems. The efficiency of the modified spectral gradient method is tested by comparing the number of iterations, the number of function call and the computational time, with the BFGS method, steepest descent method and conjugate gradient method. The step length of these methods is selected by using the modified BTA line search technique. Finally, the modified spectral gradient method shows a better performance compared to the steepest descent method and the conjugate gradient method. The modified method gives more stable results compared to the BFGS method because numerous papers from different researchers have suggested that the BFGS method is not an appropriate method in solving the large-scale problems. Furthermore, the SG method is popular due to the fact that less storage is needed for the calculation. The modified SG method can be used in solving some nonlinear application problems. Thus, the modified spectral gradient method can be considered as an alternative method for solving nonlinear systems. The improvements in the amount of tested problem, line search strategy and search direction are recommended, in order to increase the efficiency of the modified method. 2020 Final Year Project / Dissertation / Thesis NonPeerReviewed application/pdf http://eprints.utar.edu.my/4200/1/1701678_KOAY_YEONG_LIN.pdf Koay, Yeong Lin (2020) A Modified Spectral Gradient Method for Solving Non Linear System. Final Year Project, UTAR. http://eprints.utar.edu.my/4200/
institution Universiti Tunku Abdul Rahman
building UTAR Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Tunku Abdul Rahman
content_source UTAR Institutional Repository
url_provider http://eprints.utar.edu.my
topic QA Mathematics
spellingShingle QA Mathematics
Koay, Yeong Lin
A Modified Spectral Gradient Method for Solving Non Linear System
description The objective of this project is to modify the spectral gradient method in solving the nonlinear systems. The multiple damping spectral gradient method with line search has been proposed for making improvements to the slow convergence issues. It operates separately on the gradient vector norm and the objective function at the same time and can be considered as an alternative for solving large-scale optimization problems. The results show that the spectral gradient method provides the best performance in solving the optimization problems, compared to the steepest descent method and conjugate gradient method, under the backtracking line search with Armijo condition (BTA). The main difference between these methods is the calculation of direction vector, dk. Besides, there is a relationship between solving a series of nonlinear equations and finding the optimal solutions to the problems. Most of the methods used for solving nonlinear systems are optimization-based methods. Therefore, the spectral gradient method with the BTA line search technique has been modified in order to solve solving the nonlinear systems. The efficiency of the modified spectral gradient method is tested by comparing the number of iterations, the number of function call and the computational time, with the BFGS method, steepest descent method and conjugate gradient method. The step length of these methods is selected by using the modified BTA line search technique. Finally, the modified spectral gradient method shows a better performance compared to the steepest descent method and the conjugate gradient method. The modified method gives more stable results compared to the BFGS method because numerous papers from different researchers have suggested that the BFGS method is not an appropriate method in solving the large-scale problems. Furthermore, the SG method is popular due to the fact that less storage is needed for the calculation. The modified SG method can be used in solving some nonlinear application problems. Thus, the modified spectral gradient method can be considered as an alternative method for solving nonlinear systems. The improvements in the amount of tested problem, line search strategy and search direction are recommended, in order to increase the efficiency of the modified method.
format Final Year Project / Dissertation / Thesis
author Koay, Yeong Lin
author_facet Koay, Yeong Lin
author_sort Koay, Yeong Lin
title A Modified Spectral Gradient Method for Solving Non Linear System
title_short A Modified Spectral Gradient Method for Solving Non Linear System
title_full A Modified Spectral Gradient Method for Solving Non Linear System
title_fullStr A Modified Spectral Gradient Method for Solving Non Linear System
title_full_unstemmed A Modified Spectral Gradient Method for Solving Non Linear System
title_sort modified spectral gradient method for solving non linear system
publishDate 2020
url http://eprints.utar.edu.my/4200/1/1701678_KOAY_YEONG_LIN.pdf
http://eprints.utar.edu.my/4200/
_version_ 1709672663889215488
score 13.211869

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