[feature] JuMP: Support accessing the attribute MathOptInterface.ConstraintDual(1)

[oyamad]

Is it possible to get the dual solution from a JuMP model constructed from a polyhedron?

using Polyhedra
using JuMP
using Clp
using LinearAlgebra

hrep = HalfSpace([-1, 0], 0) ∩ HalfSpace([0, -1], 0) ∩ HalfSpace([1, 1], 1)
model = Model(with_optimizer(Clp.Optimizer, LogLevel=0))
@variable(model, x[1:2])
con = @constraint(model, x in hrep)
@objective(model, Max, dot([1, 0], x))
optimize!(model)
value.(x)

2-element Array{Float64,1}:
  1.0
 -0.0

But dual and shadow_price do not work:

dual(con)

ArgumentError: Constraint bridge of type `Polyhedra.PolyhedraToLPBridge{Float64,MathOptInterface.ScalarAffineFunction{Float64}}` does not support accessing the attribute `MathOptInterface.ConstraintDual(1)`.

...

shadow_price(con)

The shadow price is not defined or not implemented for this type of constraint.

...

[blegat]

Not yet. We need to figure out what it would be.
It could be a struct providing a mapping between H-Rep indices and the dual of the corresponding constraint