The linear complementarity problem is to find vector $z$ in $\mathrm{IR}^{n}$
satisfying $z^{T}(Mz+q)=0$, $Mz+q\geqslant0,$ $z\geqslant0$, where $M$ as a
matrix and $q$ as a vector, are given data; this problem becomes in present the
subject of much important research because it arises in many areas and it
includes important fields, we cite for example the linear and nonlinear
programming, the convex quadratic programming and the variational inequalities
problems, ...