# BilevelJuMP.jl: Modeling and Solving Bilevel Optimization in Julia

arXiv: https://arxiv.org/abs/2205.02307 · HTML: https://mlsanity.com/paper/2205.02307/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2022.

## Built on by (most cited first, 1 of 1)

- [Evaluation of Electricity Market Clearing Mechanisms via Reinforcement Learning: Prices, Remuneration and Competitive Dynamics](https://mlsanity.com/paper/2602.01392/) (2026)

## Abstract (arXiv)

In this paper we present BilevelJuMP, a new Julia package to support bilevel optimization within the JuMP framework. The package is a Julia library that enables the user to describe both upper and lower-level optimization problems using the JuMP algebraic syntax. Due to the generality and flexibility our library inherits from JuMP's syntax, our package allows users to model bilevel optimization problems with conic constraints in the lower level and all JuMP supported constraints in the upper level (Conic, Quadratic, Non-Linear, Integer, etc.). Moreover, the user-defined problem can be subsequently solved by various techniques relying on mathematical program with equilibrium constraints (MPEC) reformulations. Manipulations on the original problem data are possible due to MathOptInterface.jl's structures and Dualization.jl features. Hence, the proposed package allows quickly model, deploy, and thereby experiment bilevel models based on off-the-shelf mixed integer linear programming and nonlinear solvers.