Mathematical Programs with Equilibrium Constraints: Automatic Reformulation and Solution via Constrained Optimization

Constrained optimization has been extensively used to solve many large scale deterministic problems arising in economics, including, for example, square systems of equations and nonlinear programs. A separate set of models have been generated more recently, using complementarity to model various phenomena, particularly in general equilibria. The unifying framework of mathematical programs with equilibrium constraints (MPEC) has been postulated for problems that combine facets of optimization and complementarity. This paper briefly reviews some methods available to solve these problems and describes a new suite of tools for working with MPEC models. Computational results demonstrating the potential of this tool are given that automatically construct and solve a variety of different nonlinear programming reformulations of MPEC problems. This material is based on research partially supported by the National Science Foundation Grant CCR-9972372, the Air Force Office of Scientific Research Grant F49620-011-0040, Microsoft Corporation and the Guggenheim Foundation Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, OX1 3QD Permanent address: Computer Sciences Department, University of Wisconsin, 1210 West Dayton Street, Madison, Wisconsin 53706, USA GAMS Development Corporation, 1217 Potomac Street, N.W., Washington, D.C. 20007