Some pivot schemes for the linear complementarity problem

We are concerned with solutions to the LCP: $$ \begin{gathered} w = q + {\rm M}z; w, z \geqslant 0; w_i z_i = 0; i = 1, 2. \ldots , n \hfill \\ (M is n by n; q a column). \hfill \\ \end{gathered} $$