Jacobian Smoothing Methods for General Nonlinear Complementarity Problems

Abstract

We present a new algorithm for the solution of general (not necessarily monotone) complementarity problems. The algorithm is based on a reformulation of the complementarity problem as a nonsmooth system of equations by using the Fischer-Burmeister function. We use an idea by Chen, Qi and Sun and apply a Jacobian smoothing method (which is a mixture between nonsmooth Newton and smoothing methods) in order to solve this system. In contrast to Chen, Qi and Sun, however, our method can be applied to general complementarity problems. Extensive numerical results indicate that the new algorithm worlds very well. In particular, it can solve all complementarity problems from the MCPLIB and GAMSLIB libraries.