ABSTRACT: 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 has 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.

INTRODUCTION

Nonlinear complementarity problems arise in many economic applications, most notably in the applied general equilibrium area. The past decade has seen an enormous increase in our ability to solve large-scale complementarity problems, due not only to the phenomenal increase in computer speed, but also to advances made in algorithms and software for complementarity problems. This paper attempts to review some of those advances and revisits some older techniques for the purpose of solving optimization problems with complementarity constraints, typically termed mathematical programs with equilibrium constraints (MPECs) in the literature.

Three advances in the past two decades have increased the capability of modelers to solve large-scale complementarity problems.