Constraint associated with a variable set

[odow]

Reported by @lopenguin at https://discourse.julialang.org/t/dual-to-psd-constraint-in-jump/126352

If I have

using JuMP
model = Model()
@variable(model, A[1:2, 1:2] >= 0, PSD)
@variable(model, B[1:2, 1:2] in HermitianPSDCone())
@variable(model, C[1:3] in SecondOrderCone())

it's not at all trivial to get the constraint reference so I can query the dual.

One suggested workaround might be:

using JuMP
model = Model()
@variable(model, A[1:2, 1:2] >= 0, Symmetric)
@constraint(model, A_ref, A in PSDCone())
@variable(model, B[1:2, 1:2], Hermitian)
@constraint(model, B_ref, B in HermitianPSDCone())
@variable(model, C[1:3])
@constraint(model, C_ref, C in SecondOrderCone())

For scalar variables, we have:

model = Model()
@variable(model, x >= 0, Int)
LowerBoundRef(x)
IntegerRef(x)

So perhaps we need something similar.

[odow]

The underlying issue is that we aren't doing anything with the ConstraintIndex returned here:

JuMP.jl/src/variables.jl

Line 1971 in bea72a0

x, _ = MOI.add_constrained_variable(moi_backend, set)

JuMP.jl/src/variables.jl

Line 1989 in bea72a0

x, _ = MOI.add_constrained_variable(moi_backend, set)

JuMP.jl/src/variables.jl

Line 2165 in bea72a0

var_index, con_index = MOI.add_constrained_variable(moi_backend, set)

JuMP.jl/src/variables.jl

Line 2248 in bea72a0

var_indices, con_index = MOI.add_constrained_variables(moi_backend, set)

[odow]

ConstrainedVariableRef
ConstrainedInSetRef
InSetConstraintRef
SetRef
VariableSetRef
VariableInSetRef **
ConstraintAtCreationRef
ConstrainedOnCreationRef
CreationConstraintRef

[odow]

We discussed this on today's call, and agreed that we need a dictionary in model to map between variables and their corresponding set.

We did not agree on a name for the ref. Conclusion is that I should prototype the PR with documentation etc, and we can decide then.