add_constrained_variable(s) can break for CachingOptimizer if an optimizer has been attached

[martinbiel]

If a CachingOptimizer has an attached optimizer, and add_constrained_variable(opt, set) is called, it defaults to the fallback

function add_constrained_variable(model::ModelLike, set::AbstractScalarSet)
    variable = add_variable(model)
    constraint = add_constraint(model, SingleVariable(variable), set)
    return variable, constraint
end

in variables.jl. If the attached optimizer only supports the set through add_constrained_variable, then this errors. Here is a MWE:

using MathOptInterface
const MOI = MathOptInterface
const MOIU = MOI.Utilities

struct DummySet <: MOI.AbstractScalarSet end

MOI.supports_add_constrained_variable(::MOIU.MockOptimizer, ::Type{DummySet}) = true
function MOI.add_constrained_variable(::MOIU.MockOptimizer, ::DummySet)
    # Dummy support
    return MOI.VariableIndex(1), MOI.ConstraintIndex{MOI.SingleVariable, DummySet}(1)
end

cache = MOIU.UniversalFallback(MOIU.Model{Float64}())
m = MOIU.CachingOptimizer(cache, MOIU.MANUAL)
s = MOIU.MockOptimizer(MOIU.Model{Float64}(), supports_names=false)
MOIU.reset_optimizer(m, s)
# Catched by universal fallback
MOI.add_constrained_variable(m, DummySet())
# Properly calls add_constrained_variable during copy
MOIU.attach_optimizer(m)
# Adding constrained var after optimizer has been attached
# errors even though optimizer supports the dummy set
if MOI.supports_add_constrained_variable(m.optimizer, DummySet)
    MOI.add_constrained_variable(m, DummySet())
end

ERROR: MathOptInterface.UnsupportedConstraint{MathOptInterface.SingleVariable,DummySet}: `MathOptInterface.SingleVariable`-in-`DummySet` constraint is not supported by the model.
Stacktrace:
 [1] add_constraint(::MathOptInterface.Utilities.Model{Float64}, ::MathOptInterface.SingleVariable, ::DummySet) at /home/mbiel/.julia/dev/MathOptInterface/src/Utilities/model.jl:539
 [2] add_constraint(::MathOptInterface.Utilities.MockOptimizer{MathOptInterface.Utilities.Model{Float64}}, ::MathOptInterface.SingleVariable, ::DummySet) at /home/mbiel/.julia/dev/MathOptInterface/src/Utilities/mockoptimizer.jl:113
 [3] add_constraint(::MathOptInterface.Utilities.CachingOptimizer{MathOptInterface.AbstractOptimizer,MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}, ::MathOptInterface.SingleVariable, ::DummySet) at /home/mbiel/.julia/dev/MathOptInterface/src/Utilities/cachingoptimizer.jl:262
 [4] add_constrained_variable(::MathOptInterface.Utilities.CachingOptimizer{MathOptInterface.AbstractOptimizer,MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}, ::DummySet) at /home/mbiel/.julia/dev/MathOptInterface/src/variables.jl:88

A more relevant example would be a custom set that requires a variable bridge and must be added through add_constrained_variable. The problem holds for vector sets as well.

A suggested fix is to implement add_constrained_variable(s) for CachingOptimizer in the same way as add_variable and add_constraint.