[Bridges] map_set is the wrong way round

[odow]

I have been trying to write better tests for Variable.SetMapBridge in #2664, and I got hopelessly confused. But, I think I found the culprit:

In Constraint.SetMapBridge, map_set is the forward user-space -> bridged-space:

MathOptInterface.jl/src/Bridges/Constraint/bridges/RSOCtoSOCBridge.jl

Lines 46 to 51 in 3bbca2a

	function MOI.Bridges.map_set(
	::Type{<:RSOCtoSOCBridge},
	set::MOI.RotatedSecondOrderCone,
	)
	return MOI.SecondOrderCone(MOI.dimension(set))
	end

In Variable.SetMapbridge, map_set is the backward bridged-space -> user-space:

MathOptInterface.jl/src/Bridges/Variable/bridges/RSOCtoSOCBridge.jl

Lines 38 to 43 in 3bbca2a

	function MOI.Bridges.map_set(
	::Type{<:RSOCtoSOCBridge},
	set::MOI.SecondOrderCone,
	)
	return MOI.RotatedSecondOrderCone(MOI.dimension(set))
	end

@blegat is this intentional? Can I fix this? Or are there other packages using this?

[odow]

I see plenty of Constraint.SetMapBridge in the wild, but I don't see any Variable.SetMapBridge: https://juliahub.com/ui/Search?type=code&q=SetMapBridge

[blegat]

Yes it's intentional (explained in my thesis). The idea is than when you have a map S = A*T then you can define a constraint bridge mapping constraints in T to constraints in S and variable bridges mapping variables in S to variables in T. So the map does not go in the same direction for variable and constraint bridges

[odow]

What about the functions? Nothing seems very consistent, and it doesn't help that everything is symmetric etc. So as long as you use inverse_map_ and map_ it looks like it works.

[odow]

For example, when getting the ConstraintPrimal we use map_function

MathOptInterface.jl/src/Bridges/Variable/set_map.jl

Lines 147 to 154 in 93694da

	function MOI.get(
	model::MOI.ModelLike,
	attr::MOI.ConstraintPrimal,
	bridge::SetMapBridge,
	)
	value = MOI.get(model, attr, bridge.constraint)
	return MOI.Bridges.map_function(bridge, value)
	end

but for getting the ConstraintDual we use inverse_adjoint_map_function:

MathOptInterface.jl/src/Bridges/Variable/set_map.jl

Lines 156 to 163 in 93694da

	function MOI.get(
	model::MOI.ModelLike,
	attr::MOI.ConstraintDual,
	bridge::SetMapBridge,
	)
	value = MOI.get(model, attr, bridge.constraint)
	return MOI.Bridges.inverse_adjoint_map_function(typeof(bridge), value)
	end

[odow]

Closing. I'll add comments to #2664