A globally convergent algorithm for MPCC

We propose a penalty formulation based on the new regularization scheme for mathematical programs with complementarity constraints (MPCCs). We present an active set method which solves a sequence of penalty-regularized problems. We study global convergence properties of the method under the MPCC-linear independence constraint qualification. In particular, any accumulation point of the generated iterates is a strong stationary point if the penalty parameter is bounded. Otherwise, the convergence to points having a certain stationarity property is established. A strategy for updating the penalty parameter is proposed and numerical results on a collection of test problems are reported.