An interior point method for mathematical programs with equilibrium constraints

We discuss an interior point method for the computation of a stationary point of a mathematical program with equilibrium constraints (MPEC). The method can be initiated at a fairly arbitrary vector. In general, each iteration of the method consists of computing a search direction followed by a step size calculation. The search direction is computed by solving a perturbed Newton equation that is derived from the family of interior point methods for constrained equations; the step size is determined by an Armijo line search applied to a penalized objective function of the MPEC. A subsequential convergence result is established under a strict complementarity assumption.