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Quasi-Newton (Variable Metric) Methods

Quasi-Newton methods attempt to generate an estimate of the inverse of the Hessian matrix . This is then used to determine the next iteration point.

The gradient in the region around a is given by

At the minima the gradient is zero

thus the best next direction step is given by

The BFGS (`Broyden-Fletcher-Goldfarb-Shanno') algorithm is based on this technique [6].

Bob Fisher
Fri Mar 28 14:12:50 GMT 1997