Stable reduced Hessian updates for indefinite quadratic programming

Stable techniques are considered for updating the reduced Hessian matrix that arises in a null{space active set method for Quadratic Programming when the Hessian matrix itself may be indeenite. A scheme for deening and updating the null-space basis matrix is described which is adequately stable and allows advantage to be taken of sparsity. A new canonical form for the reduced Hessian matrix is proposed that can be updated in a numerically stable way. Some consequences for the choice of minor iteration search direction are described.