On Modified DFP Update for Unconstrained Optimization
American Journal of Applied Mathematics
Volume 5, Issue 1, February 2017, Pages: 19-30
Received: Dec. 25, 2016; Accepted: Jan. 9, 2017; Published: Feb. 6, 2017
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Authors
Saad Shakir Mahmood, Department of Mathematics, College of Education, Almustansiryah University, Baghdad, Iraq
Samira Hassan Shnywer, Department of Mathematics, College of Education, Almustansiryah University, Baghdad, Iraq
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Abstract
In this paper, we propose a new modify of DFP update with a new extended quasi-Newton condition for unconstrained optimization problem so called update. This update is based on a new Zhang Xu condition we show that update preserves the value of determinant of the next Hessian matrix equal to the value of determinant of current Hessian matrix theoretically and practically. Global convergence of the modify is established. Local and super linearly convergence are obtained for the proposed method. Numerical results are given to compare a performance of the modify method with the standard DFP method on same function is selected.
Keywords
Quasi-Newton Equation, the DFP Updating Formula, Global Convergence and Super Linearly Convergence
To cite this article
Saad Shakir Mahmood, Samira Hassan Shnywer, On Modified DFP Update for Unconstrained Optimization, American Journal of Applied Mathematics. Vol. 5, No. 1, 2017, pp. 19-30. doi: 10.11648/j.ajam.20170501.13
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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