On homogeneous and self-dual algorithms for the linear complementarity problem

We present some generalizations of a homogeneous and self-dual linear programming (LP) algorithm to solving the monotone linear complementarity problem (LPC). Again, while it achieves the best known interior-point iteration complexity, the algorithm does not need to use any ‘big-M’ number, and it detects LCP infeasibility by generating a certificate. To our knowledge, this is the first interior-point and infeasible-starting algorithm for the LCP with these desired features.