MathOptComplements.jl
MathOptComplements.jl is a JuMP extension for reformulating complementarity constraints.
License
MathOptComplements.jl is licensed under the MIT License.
Getting help
If you need help, please ask a question on the JuMP community forum.
If you have a reproducible example of a bug, please open a GitHub issue.
Installation
Install MathOptComplements using Pkg.add:
import Pkg
Pkg.add(; url = "https://github.com/jump-dev/MathOptComplements.jl")
Use with JuMP
Use MathOptComplements.jl with JuMP as follows:
using JuMP
import Ipopt
import MathOptComplements
model = Model(() -> MathOptComplements.Optimizer(Ipopt.Optimizer()))
set_attribute(
model,
MathOptComplements.DefaultComplementarityReformulation(),
MathOptComplements.ScholtesRelaxation(0.0),
)
@variable(model, z[1:2])
set_lower_bound(z[2], 0)
@objective(model, Min, (z[1] - 1)^2 + z[2]^2)
@constraint(model, z[2] - z[1] ⟂ z[2])
optimize!(model)
If you use Ipopt, we recommend setting the following options to improve the performance:
set_attribute(model, "mu_strategy", "adaptive")
set_attribute(model, "bound_push", 1e-1)
set_attribute(model, "bound_relax_factor", 0.0)
Supported reformulations
You can change the reformulation by using the optimizer attribute
MathOptComplements.DefaultComplementarityReformulation. The following values
are supported. Check their docstrings for details.
MathOptComplements.ScholtesRelaxation(tau)(default)MathOptComplements.FischerBurmeisterRelaxation(tau)MathOptComplements.LiuFukushimaRelaxation(tau)MathOptComplements.KanzowSchwarzRelaxation(tau)
Most reformulations are not equivalent to the original problem, which is why they are not activated by default. This arXiv paper has a recent benchmark comparing the different reformulations on MacMPEC.
Funding
We acknowledge support from the Fondation Mathématiques Jacques Hadamard which has funded the PGMO-IROE project “A new optimization suite for large-scale market equilibrium”.