  In this paper a special semi-smooth equation associated to the second order
cone is studied. It is shown that, under mild assumptions, the semi-smooth
Newton method applied to this equation is well-defined and the generated
sequence is globally and Q-linearly convergent to a solution. As an
application, the obtained results are used to study the linear second order
cone complementarity problem, with special emphasis on the particular case of
positive definite matrices. Moreover, some computational experiments designed
to investigate the practical viability of the method are presented.
