Nonlinear programming without a penalty function or a filter

                      N. I. M. Gould and Ph. L. Toint

             Report 07/02                      23 April 2007


A new method is introduced for solving equality constrained nonlinear
optimization problems.  This method does not use a penalty function, nor a
barrier or a filter, and yet can be proved to be globally convergent to
first-order stationary points. It uses different trust-regions to cope with
the nonlinearities of the objective function and the constraints, and allows
inexact SQP steps that do not lie exactly in the nullspace of the local
Jacobian. Preliminary numerical experiments on CUTEr problems indicate that
the method performs well.