  We herein propose a variant of the projected inexact Levenberg--Marquardt
method (ILMM) for solving constrained nonsmooth equations. Since the orthogonal
projection onto the feasible set may be computationally expensive, we propose a
local ILMM with feasible inexact projections. By using assumption of
semi-smoothness and an error bound condition which is weaker than the standard
full rank assumption, we establish its convergence results, including results
on its rate. Finally, some computacional results are reported in order to
illustrate the advantages of the new schemes.
