We consider a mathematical program with
complementarity constraints (MPCC). Our purpose is to develop
methods that enable us to compute a solution or a point with some
kind of stationarity to MPCC by solving a finite number of
nonlinear programs. To this end, we first introduce an active set
identification technique. Then, by applying this technique to a
smoothing continuation method presented by Fukushima and Pang
(1999), we propose a hybrid method for solving MPCC. Under
reasonable assumptions, the hybrid algorithm is shown to possess a
finite termination property. Numerical experience shows that the
proposed approach is quite effective.