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

A noninterior path-following algorithm is proposed for the linear complementarity problem. The method employs smoothing techniques introduced by Kanzow. If the LCP is P₀ + R₀ and satisfies a nondegeneracy 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 differs significantly from that which appears in the interior point literature. Numerical experiments are presented that illustrate the significance of the neighborhood concept for this class of methods.