Introduction to Mathematical Programming with Equilibrium Constraints (MPECs) and Bilevel Optimization
Optimization and Control
2026-05-04 v1
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.
Cite
@article{arxiv.2605.00386,
title = {Introduction to Mathematical Programming with Equilibrium Constraints (MPECs) and Bilevel Optimization},
author = {Louis Shuo Wang},
journal= {arXiv preprint arXiv:2605.00386},
year = {2026}
}