Jacobian Smoothing Methods for General Nonlinear Complementarity Problems

We present a new algorithm for the solution of general (not necessarily monotone) complementarity problems. The algorithm is based on a reformulation of the complementar-ity 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 com-plementarity problems. Extensive numerical results indicate that the new algorithm works very well. In particular, it can solve all complementarity problems from the MCPLIB and GAMSLIB libraries.