  In this paper, we first propose a new Levenberg-Marquardt method for solving
constrained (and not necessarily square) nonlinear systems. Basically, the
method combines the unconstrained Levenberg-Marquardt method with a type of
feasible inexact projection. The local convergence of the new method as well as
results on its rate are established by using an error bound condition, which is
weaker than the standard full-rank assumption. We further present and analyze a
global version of the first method by means of a nonmonotone line search
technique. Finally, numerical experiments illustrating the practical advantages
of the proposed schemes are reported.
