If I have a inequality constrained system:
w = Mz + q <= 0, z<=0, z^T w = 0
that for some given properties M and q has multiple solutions, is there any way of determining which of the LCP solutions (w,z) Lemke's algorithm will find? As there are no means of providing an initial guess, I assume the algorithm will find the nonlinear solution (w,z) that is closest to the linear solution (w,0). But how would I determine what can be considered "close"?