From the introduction: The equilibrium constraints in MPEC problems are usually modeled by a set of parametric variational inequalities or complementarity constraints. Although a powerful theory has been developed for variational inequalities, the parameterized setting in MPEC problems make these problems very difficult to solve. There have been different approaches to deal with this problem such as general penalization techniques, heuristics, and continuation methods.
In this paper we focus on transforming an MPEC problem into a regular nonlinear programming problem (NLP). From a practitioner’s point of view, this is quite valuable since the transformed problems can be directly solved by various optimization packages. In order to transform an MPEC problem into a nonlinear optimization problem, we use continuation methods. The idea of continuation methods is based on solving a sequence of perturbed problems. The main tool in modeling the perturbed problems is a specific smoothing function, which is used to approximate the difficult equilibrium constraints.
The contribution of this paper is two-fold: First, we try to exploit the application of an alternative smoothing function within continuation methods. The proposed smoothing function not only shows a good performance but also provides a flexible way of modeling a more general type of MPEC problem. Second, we work on a set of test problems collected from the literature. These problems are remodeled by the proposed smoothing function and then solved with a publicly available solver. Again for a practitioner, it is very valuable to be able to use a software package, since it provides a fast and efficient way for dealing with MPEC problems.