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International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 12583, 8 pages

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 Hindawi Publishing Corporation. 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.


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).