How the Grinch solved MPECs - Mathematical Programs with Equilibrium Constraints
by
Sven Leyffer
University of Dundee

Equilibrium constraints in the form of complementarity conditions, and more generally variational inequalities, often appear as constraints in optimization problems, leading to MPECs (Mathematical Programs with Equilibrium Constraints). The talk starts by reviewing some new applications of this modeling tool.

Over recent years, it has been argued that equilibrium constraints cannot be solved satisfactorily with standard techniques for Nonlinear Programming (NLP). Both numerical and theoretical evidence has been advanced which support this view.

We re-examine this assertion and present some startling numerical evidence which suggests that certain NLP solvers can solve MPECs robustly and efficiently. We conclude by giving some theoretical justification for the success of NLP methods.

Mathematical Programs with Equilibrium Constraints

Date received: March 30, 2001