Bridges fail test_model_LowerBoundAlreadySet test

[odow]

julia> using GLPK

julia> GLPK.MOI.Test.test_model_LowerBoundAlreadySet(
           GLPK.Optimizer(), MOI.Test.Config()
       )

julia> GLPK.MOI.Test.test_model_LowerBoundAlreadySet(
           MOI.Bridges.full_bridge_optimizer(GLPK.Optimizer(), Float64), 
           MOI.Test.Config(),
       )
Test Failed at /Users/oscar/.julia/dev/MathOptInterface/src/Test/test_model.jl:815
  Expression: MOI.add_constraint(model, f, set2)
    Expected: MathOptInterface.LowerBoundAlreadySet{MathOptInterface.Semicontinuous{Float64}, MathOptInterface.GreaterThan{Float64}}(MathOptInterface.VariableIndex(1))
  No exception thrown
ERROR: There was an error during testing

Same happens with test_model_UpperBoundAlreadySet, but I assume it's the same problem.

[blegat]

I can reproduce it without GLPK like so:

model = MOI.Utilities.Model{Float64}()
bridged = MOI.Bridges.Constraint.SemiToBinary{Float64}(model)
MOI.Test.test_model_LowerBoundAlreadySet(bridged, MOI.Test.Config())

The issue is that the bridge creates affine constraints:

MathOptInterface.jl/src/Bridges/Constraint/semi_to_binary.jl

Lines 48 to 56 in e51754f

	# var - LB * bin >= 0
	lb = MOIU.operate(*, T, -s.lower, MOI.SingleVariable(binary))
	lb = MOIU.operate!(+, T, lb, f)
	lb_ci = MOI.add_constraint(model, lb, MOI.GreaterThan{T}(zero(T)))
	# var - UB * bin <= 0
	ub = MOIU.operate(*, T, -s.upper, MOI.SingleVariable(binary))
	ub = MOIU.operate!(+, T, ub, f)
	ub_ci = MOI.add_constraint(model, ub, MOI.LessThan{T}(zero(T)))

Therefore, the inner model does not see it as variable bound and do not see any double lower bound.
One way to fix it would be #1097
So the bridge would say that it is watching this variable so that when a new bound is set, it gets notified and can throw an error.

[blegat]

It's still failing for some solvers, see, e.g., https://github.com/blegat/ICCOPT_SummerSchool_2022/blob/main/SimpleConicADMM/test/MOI_wrapper.jl.
We could fix it now with final_touch but we might want to first discuss variable bounds.
We start by reopening this issue though.

[odow]

I still think the fix for this issue is #1879.

[blegat]

Not sure since there is no ZeroOne in test_model_LowerBoundAlreadySet. We might need it for ScalarFunctionizeBridge as well.