Add bridge to that converts upper/lower constraints to interval constraints

[freemin7]

It is much simpler to implement a solver interface that just handles interval constraints.
However currently such a solver wouldn't be able to handle one sided constraints due to a lack of a bridge converting them to interval constraints.

Another issue that pops up his that in what interval x <= 6 should be expressed as. The obvious solution -Inf <= x <= 6 only works floating point numbers, Inf does not exist for integers or Fraction types (as @blegat pointed out in the Gitter). In this case it should be possible to pass some lower/upper bound as parameter for the bridge which should be used instead of -Inf and Inf.

Bounding Inf to a finite value is also a thing i've seen on NLP solvers which work with floating points exclusively.

[odow]

It's also not obvious what should happen if multiple bound constraints get added.

model = Optimizer()
x = MOI.add_variable(model)
MOI.add_constraint(model, x, MOI.LessThan(1.0))
MOI.add_constraint(model, x, MOI.GreaterThan(1.0))  # But an interval bound already exists!

[blegat]

The bridge would only support floating point numbers so if integer or rational are use, the bridge will simply not be used. I don't like introducing arbitrarily large values, this can lead to subtle bugs. It can be done at the level of solver wrappers but I'd rather not do it at the level of MOI.
For SingleVariable bounds, I would say the error is expected. The user should set an Interval constraint instead. As JuMP is not doing it, it should start doing it.
Another approach would be to transform the second add_constraint with set(..., MOI.Interval(1.0, 1.0)) inside the bridge with something like #1097
Anyway, this does not prevent us from using it for ScalarAffineFunction and ScalarQuadraticFunction.

[shadiakiki1986]

@blegat I started a draft PR #1195 for this. Could you take a quick look and tell me if I'm on the right track? I tried to use your comment above as well as gitter chat on November 6, 2020 8:59 PM

[shadiakiki1986]

@freemin7 with the pr merged, you might want to test your issue again on master