Khadizah Ghazali and Jumat Sulaiman and Yosza Dasril and Darmesah Gabda (2020) An alternative approach for finding Newton's direction in solving largescale unconstrained optimization for problems with an arrowhead Hessian matrix. Mathematics and Statistics, 8 (2A). 40 46. ISSN 23322071
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Abstract
In this paper, we proposed an alternative way to find the Newton direction in solving largescale unconstrained optimization problems where the Hessian of the Newton direction is an arrowhead matrix. The alternative approach is a twopoint Explicit Group GaussSeidel (2EGGS) block iterative method. To check the validity of our proposed Newton’s direction, we combined the Newton method with 2EGGS iteration for solving unconstrained optimization problems and compared it with a combination of the Newton method with GaussSeidel (GS) point iteration and the Newton method with Jacobi point iteration. The numerical experiments are carried out using three different artificial test problems with its Hessian in the form of an arrowhead matrix. In conclusion, the numerical results showed that our proposed method is more superior than the reference method in term of the number of inner iterations and the execution time.
Item Type:  Article 

Keyword:  Newton Method , Explicit Group Iteration , Unconstrained Optimization Problems , LargeScale Optimization , Arrowhead Matrix 
Subjects:  Q Science > QC Physics 
Department:  FACULTY > Faculty of Science and Natural Resources 
Depositing User:  NORAINI LABUK  
Date Deposited:  25 Jun 2021 19:53 
Last Modified:  25 Jun 2021 19:53 
URI:  https://eprints.ums.edu.my/id/eprint/27442 
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