**Time**: Refreshments at 1:30PM, Talk at 2:00pm

**Title**: Preconditioning by limited memory quasi-Newton methods

**Abstract**: We will discuss ideas from existing paper by Fletcher and extending it to different set of problems of slowly varying systems. The quasi-Newton scheme updates a low rank positive semi-definite Hessian approximation which is used 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.