A FULLY POLYNOMIAL-TIME APPROXIMATION ALGORITHM FOR COMPUTING A STATIONARY POINT OF THE GENERAL LINEAR COMPLEMENTARITY-PROBLEM

We apply a potential reduction algorithm to solve the general linear complementarity problem (GLCP) minimize x(T)y subject to Ax + By + Cz = q and (x, y, z) greater-than-or-equal-to 0. We show that the algorithm is a fully polynomial-time approximation scheme (FPTAS) for computing an epsilon-approximate stationary point of the GLCP. Note that there are some GLCPs in which every stationary point is a solution (x(T)y = 0). These include the LCPs with row sufficient matrices. We also show that the algorithm is a polynomial-time algorithm for a special class of GLCPs.