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An Improvement of Computing Newton’s Direction for Finding Unconstrained Minimizer for Large-Scale Problems with an Arrowhead Hessian Matrix

In large-scale problems, classical Newton’s method requires solving a large linear system of equations resulting from determining the Newton direction. This process often related as a very complicated process, and it requires a lot of computation (either in time calculation or memory requirement per...

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Main Authors: Khadizah Ghazali, Jumat Sulaiman, Yosza Dasril, Darmesah Gabda
Format: Conference or Workshop Item
Language:English
Published: 2020
Online Access:https://eprints.ums.edu.my/id/eprint/25538/1/An%20Improvement%20of%20Computing%20Newton%E2%80%99s%20Direction%20for%20Finding%20Unconstrained%20Minimizer.pdf
https://eprints.ums.edu.my/id/eprint/25538/
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spelling my.ums.eprints.255382020-07-01T03:47:10Z https://eprints.ums.edu.my/id/eprint/25538/ An Improvement of Computing Newton’s Direction for Finding Unconstrained Minimizer for Large-Scale Problems with an Arrowhead Hessian Matrix Khadizah Ghazali Jumat Sulaiman Yosza Dasril Darmesah Gabda In large-scale problems, classical Newton’s method requires solving a large linear system of equations resulting from determining the Newton direction. This process often related as a very complicated process, and it requires a lot of computation (either in time calculation or memory requirement per iteration). Thus to avoid this problem, we proposed an improved way to calculate the Newton direction using an Accelerated Overrelaxation (AOR) point iterative method with two different parameters. To check the performance of our proposed Newton’s direction, we used the Newton method with AOR iteration for solving unconstrained optimization problems with its Hessian is in arrowhead form and compared it with a combination of the Newton method with Gauss-Seidel (GS) iteration and the Newton method with Successive Over Relaxation (SOR) iteration. Finally, comparison results show that our proposed technique is significantly more efficient and more reliable than reference methods. 2020 Conference or Workshop Item PeerReviewed text en https://eprints.ums.edu.my/id/eprint/25538/1/An%20Improvement%20of%20Computing%20Newton%E2%80%99s%20Direction%20for%20Finding%20Unconstrained%20Minimizer.pdf Khadizah Ghazali and Jumat Sulaiman and Yosza Dasril and Darmesah Gabda (2020) An Improvement of Computing Newton’s Direction for Finding Unconstrained Minimizer for Large-Scale Problems with an Arrowhead Hessian Matrix. In: Computational Science and Technology.
institution Universiti Malaysia Sabah
building UMS Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Sabah
content_source UMS Institutional Repository
url_provider http://eprints.ums.edu.my/
language English
description In large-scale problems, classical Newton’s method requires solving a large linear system of equations resulting from determining the Newton direction. This process often related as a very complicated process, and it requires a lot of computation (either in time calculation or memory requirement per iteration). Thus to avoid this problem, we proposed an improved way to calculate the Newton direction using an Accelerated Overrelaxation (AOR) point iterative method with two different parameters. To check the performance of our proposed Newton’s direction, we used the Newton method with AOR iteration for solving unconstrained optimization problems with its Hessian is in arrowhead form and compared it with a combination of the Newton method with Gauss-Seidel (GS) iteration and the Newton method with Successive Over Relaxation (SOR) iteration. Finally, comparison results show that our proposed technique is significantly more efficient and more reliable than reference methods.
format Conference or Workshop Item
author Khadizah Ghazali
Jumat Sulaiman
Yosza Dasril
Darmesah Gabda
spellingShingle Khadizah Ghazali
Jumat Sulaiman
Yosza Dasril
Darmesah Gabda
An Improvement of Computing Newton’s Direction for Finding Unconstrained Minimizer for Large-Scale Problems with an Arrowhead Hessian Matrix
author_facet Khadizah Ghazali
Jumat Sulaiman
Yosza Dasril
Darmesah Gabda
author_sort Khadizah Ghazali
title An Improvement of Computing Newton’s Direction for Finding Unconstrained Minimizer for Large-Scale Problems with an Arrowhead Hessian Matrix
title_short An Improvement of Computing Newton’s Direction for Finding Unconstrained Minimizer for Large-Scale Problems with an Arrowhead Hessian Matrix
title_full An Improvement of Computing Newton’s Direction for Finding Unconstrained Minimizer for Large-Scale Problems with an Arrowhead Hessian Matrix
title_fullStr An Improvement of Computing Newton’s Direction for Finding Unconstrained Minimizer for Large-Scale Problems with an Arrowhead Hessian Matrix
title_full_unstemmed An Improvement of Computing Newton’s Direction for Finding Unconstrained Minimizer for Large-Scale Problems with an Arrowhead Hessian Matrix
title_sort improvement of computing newton’s direction for finding unconstrained minimizer for large-scale problems with an arrowhead hessian matrix
publishDate 2020
url https://eprints.ums.edu.my/id/eprint/25538/1/An%20Improvement%20of%20Computing%20Newton%E2%80%99s%20Direction%20for%20Finding%20Unconstrained%20Minimizer.pdf
https://eprints.ums.edu.my/id/eprint/25538/
_version_ 1760230381389348864
score 13.211869

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