The global linear convergence of a noninterior path-following algorithm for linear complementarity problems

A noninterior path-following algorithm is proposed for the linear complemen tarity problem. The method employs smoothing techniques introduced by Kanzo w. If the LCP is P-0 + R-0 and satisfies a nondegeneracy condition due to F ukushima, Luo, and Pang, then the algorithm is globally linearly convergent . As with interior point path-following methods, the convergence theory rel ies on the notion of a neighborhood for the central path. However, the choi ce of neighborhood differs significantly from that which appears in the int erior point literature. Numerical experiments are presented that illustrate the significance of the neighborhood concept for this class of methods.