Introduction to Mathematical Programming with Equilibrium Constraints (MPECs) and Bilevel Optimization

TL;DR

This paper introduces mathematical programs with equilibrium constraints (MPECs), explaining their formulations, applications, and existence theory, emphasizing their structure as optimization problems constrained by equilibrium models.

Contribution

It provides a comprehensive overview of MPECs, including formulations, applications, and foundational existence results, serving as an introductory resource.

Findings

MPECs are optimization problems with feasible sets defined by equilibrium models.

Equivalent formulations of equilibrium constraints are presented.

Basic existence theory for optimal solutions of MPECs is summarized.

Abstract

Our aim is to explain mathematical programs with equilibrium constraints (MPECs), motivate them through applications, present the main equivalent formulations of equilibrium constraints, and summarize the basic existence theory for optimal solutions. The central message is that an MPEC is an optimization problem whose feasible set is partly defined by another optimization, variational inequality, complementarity system, or equilibrium model.