Jacobian smoothing methods for nonlinear complementarity problems

We present a new algorithm for the solution of general (not necessarily mon otone) 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 ap ply a Jacobian smoothing method (which combines nonsmooth Newton and smooth ing methods) to solve this system. In contrast to that of Chen, Qi, and Sun , however, our method is at least well defined for general complementarity problems. Extensive numerical results indicate that the new algorithm works very well. In particular, it can solve all nonlinear complementarity probl ems from the MCPLIB and GAMSLIB libraries.