Add method to MOI.add_constrained_variable

[joehuchette]

While doing some benchmarking, I noticed that calling MOI.add_constrained_variable(::Gurobi.Optimizer, set::Gurobi._SCALAR_SET) was spending roughly the same amount of time in GRBaddvar as it was in setting the bound attributes. This seemed a bit wasteful, so I added a new method that lives here that sets the bounds directly in GRBaddvar.

I'm a bit uncertain how to update lower_bound_if_bounded and upper_bound_if_bounded. The comments for _VariableInfo suggest that these fields should be NaN if and only if a variable has no bound constraints on it. That will never be the case in this method, so therefore I should set both bound values, even to +/-Inf for one-sided bounds. However, after looking through the rest of the file I'm not certain that this is the behavior actually implemented in, e.g.,

MOI.set(::Optimizer, ::MOI.ConstraintSet, ::MOI.ConstraintIndex{MOI.SingleVariable, S}, s::S) where {S <: Gurobi._SCALAR_SETS}

So, guidance would be appreciated on what I should do there.

[odow]

The whole _bound_if_bounded thing was a hack to work around SecondOrderCones, because when adding a SOC, we might change the bound of the epigraph variable to 0, so it's not sufficient to just query Gurobi's internal value of the bound.

A better way, going forward, would be to add an additional linear constraint that t >= 0, instead of modifying the bounds, but I don't have the time to implement.

I this method tested/used by JuMP?

[joehuchette]

Not by JuMP, I'm calling it directly in Cerberus. I'm not sure if this is being tested in MOI.Tests. Should I add a unit test in this repo?

[joehuchette]

[odow]

A unit test would be good, if you have time.

[blegat]

Maybe also add a comment explaining why Gurobi.jl defines this method (as you explain in the first comment of thi PR)

[joehuchette]