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.