International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 12583, 8 pages
doi:10.1155/IJMMS/2006/12583
Extra multistep BFGS updates in quasi-Newton methods
Department of Computer Science, Faculty of Science, Beirut Arab University, Beirut 115020, Lebanon
Received 5 December 2005; Revised 7 March 2006; Accepted 25 April 2006
Copyright © 2006 Issam A. R. Moghrabi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
This note focuses on developing quasi-Newton methods
that combine m+1
multistep and single-step updates on a
single iteration for the sake of constructing the new
approximation to the Hessian matrix to be used on the next
iteration in computing the search direction. The approach
considered here exploits the merits of the multistep methods and
those of El-Baali (1999) to create a hybrid technique.
Our numerical results are encouraging and reveal that our proposed
approach is promising. The new methods compete well with
El-Baali's extra update algorithms (1999).