The Global Linear Convergence of a Noninterior Path-Following Algorithm for Linear Complementarity Problems

A non{interior path following algorithm is proposed for the linear complementarity problem. The method employs smoothing techniques introduced by Kanzow. If the LCP is P 0 +R 0 and satisses a non{degeneracy condition due to Fukushima, Luo, and Pang, then the algorithm is globally linearly convergent. As with interior point path following methods, the convergence theory relies on the notion of a neighborhood for the central path. However, the choice of neighborhood diiers signiicantly from that which appears in the interior point literature. Numerical experiments are presented that illustrate the signiicance of the neighborhood concept for this class of methods.