### Roger Fletcher FRS (University of Dundee and University of Edinburgh)

#### A new low-rank quasi-Newton update scheme for NLP

*Monday 12 December 2005 at 15.30, JCMB 6206*

##### Abstract

A new quasi-Newton scheme for updating a low-rank positive
semi-definite Hessian approximation is described, primarily for use
in sequential quadratic programming methods for nonlinear programming.
Where possible the symmetric rank one update formula is used, but
when this is not possible a new rank two update is used, which is not in
the Broyden family, although invariance under linear transformations
of the variables is preserved. The representation provides a limited memory
capability, and there is an ordering scheme which enables 'old' information
to be deleted when the memory is full. Hereditary and conjugacy properties
are preserved to the maximum extent when minimizing a quadratic function
subject to linear constraints. Practical experience is described on small
(and some larger) CUTE test problems, and is reasonably encouraging.

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