A Multidimensional Filter Algorithm for Nonlinear Equations and
                        Nonlinear Least-Squares

               Nick Gould, S. Leyffer and Ph. L. Toint

                            Report 03/15

We introduce a new algorithm for the solution of systems of nonlinear
equations and nonlinear least-squares problems that attempts to combine the
efficiency of filter techniques and the robustness of trust-region methods.
The algorithm is shown, under reasonable assumptions, to globally converge to
zeros of the system, or to first-order stationary points of the Euclidean norm
of its residual. Preliminary numerical experience is presented that shows
substantial gains in efficiency over the traditional monotone trust-region
approach.