A simple implementation of the Benders decomposition method with JuMP.

A good start with this package is the corresponding blog post. The implementation is far from smart since it uses the matrix form of the subproblem.

SimpleBenders.jl assumes a problem of the form:

min f(y) + <c, x>
s.t.
G(x) ∈ S
A x + D y ≥ b
x ≥ 0

The projected-out sub-problem requires data stored in a dedicated structure:

struct SubProblemData
    b::Vector{Float64}
    D::Matrix{Float64}
    A::Matrix{Float64}
    c::Vector{Float64}
end

The different bindings correspond to the problem presented above. Users can build their upper-level model m with the y variables, and define the objective on the main variables: f(y). The main function, benders_optimize! can be called with:

benders_optimize!(m::Model, y::Vector{VariableRef}, sd::SubProblemData, sp_optimizer, f)

Which will solve the problem using Benders decomposition.