IJPAM: Volume 18, No. 3 (2005)

A QUADRATIC TERMINATION QUASI-NEWTON
ALGORITHM WITHOUT EXACT LINEAR SEARCHES

Issam A.R. Moghrabi
Department of Computer Science
Faculty of Science
Beirut Arab University
P.O. Box 11-5020, Beirut, LEBANON
e-mail: imoghrabi@bau.edu.lb


Abstract.A new Quasi-Newton for unconstrained optimization that obtains the minimum for a quadratic function in a finite number of iterations is derived in this paper. The number of steps to obtain the minimum does not exceed the dimension of the problem being solved. The new algorithm competes favorably with Dixon's method [6], as our numerical results indicate. The algorithm presented here does not require any extra storage as in the case of Dixon's technique where an additional $O(n)$ storage is retained and updated at each iteration.

Received: October 18, 2004

AMS Subject Classification: 65K10

Key Words and Phrases: nonlinear programming, unconstrained optimization, quasi-Newton methods

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 18
Issue: 3