  In this paper a special piecewise linear system is studied. It is shown that,
under a mild assumption, the semi-smooth Newton method applied to this system
is well defined and the method generates a sequence that converges linearly to
a solution. Besides, we also show that the generated sequence is bounded, for
any starting point, and a formula for any accumulation point of this sequence
is presented. As an application, we study the convex quadratic programming
problem under positive constraints. The numerical results suggest that the
semi-smooth Newton method achieves accurate solutions to large scale problems
in few iterations.
