BilevelJuMP.jl

BilevelJuMP.jl is a JuMP extension for modeling and solving bilevel optimization problems.

License

BilevelJuMP.jl is licensed under the MIT license.

Documentation

You can find the documentation at https://joaquimg.github.io/BilevelJuMP.jl/stable/.

Help

If you need help, please open a GitHub issue.

Example

Install

import PkgPkg.add("BilevelJuMP")Pkg.add("HiGHS")

Run

using BilevelJuMP, HiGHSmodel = BilevelModel(    HiGHS.Optimizer,    mode = BilevelJuMP.FortunyAmatMcCarlMode(primal_big_M = 100, dual_big_M = 100))@variable(Lower(model), x)@variable(Upper(model), y)@objective(Upper(model), Min, 3x + y)@constraints(Upper(model), begin    x <= 5    y <= 8    y >= 0end)@objective(Lower(model), Min, -x)@constraints(Lower(model), begin     x +  y <= 8    4x +  y >= 8    2x +  y <= 13    2x - 7y <= 0end)optimize!(model)objective_value(model) # = 3 * (3.5 * 8/15) + 8/15 # = 6.13...value(x) # = 3.5 * 8/15 # = 1.86...value(y) # = 8/15 # = 0.53...

Citing BilevelJuMP

If you use BilevelJuMP.jl, we ask that you please cite the following paper:

@article{diasgarcia2023bileveljump,
    title = {{BilevelJuMP.jl}: {M}odeling and {S}olving {B}ilevel {O}ptimization {P}roblems in {J}ulia},
    author = {{Dias Garcia}, Joaquim and Bodin, Guilherme and Street, Alexandre},
    journal = {INFORMS Journal on Computing},
    doi = {https://doi.org/10.1287/ijoc.2022.0135},
    pages = {1-9},
    year = {2023}
}

Here is an earlier preprint.