In this paper we consider the question of solving equilibrium problems---formulated as complementarity problems and, more generally, mathematical programs with equilibrium constraints (MPEC's)---as nonlinear programs, using an interior-point approach. These problems pose theoretical difficulties for nonlinear solvers, including interior-point methods. We examine the use of penalty methods to get around these difficulties, present an example from game theory where this makes a difference in practice, and provide substantial numerical results. We go on to show that penalty methods can resolve some problems that interior-point algorithms encounter in general.
Technical Report ORFE-03-02, Department of Operations Research and Financial Engineering, Princeton University, Princeton NJ, 08544, October 2003.