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^Ty

subject to Ax + By + Cz = q and (x, y, z) ≥ 0.

We show that the algorithm is a fully polynomial-time approximation scheme (FPTAS) for computing an ε-approximate stationary point of the GLCP. Note that there are some GLCPs in which every stationary point is a solution (x^Ty = 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.