IJPAM: Volume 28, No. 2 (2006)


Issam A.R. Moghrabi
Department of Computer Science
Faculty of Science
Beirut Arab University
P.O. Box 11-5020, Beirut, LEBANON
e-mail: i_moghrabi@yahoo.com

Abstract.We present in this work a new perspective on the derivation of quasi-Newton algorithms for unconstrained optimization. The new algorithms are intended as an improvement on the multi-step methods presented by the author in previous work. The parameterization of the polynomials take into account the spacing between the points in the gradient space as well as exploiting the function values readily available from the previous $m+1$ iterations in an $m$-multi-step method. This employment of function values is done through utilizing such values in a nononlinear power model. Numerical results suggest that the new method improves over other existing ones that belong to the same class.

Received: December 21, 2005

AMS Subject Classification: 65K10

Key Words and Phrases: unconstrained optimization, quasi-Newton methods, multi-step methods

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 28
Issue: 2