[FileFormats] read double-sided variable bounds separately

[odow]

Closes #2547

[sstroemer]

Sorry if this is too nit-picky, but: Could creating the "helper" Interval set be an overhead for large files?

Something like this would be possible here (but makes it more convoluted):

if isfinite(data.col_lower[i])
    MOI.add_constraint(model, x, MOI.GreaterThan(data.col_lower[i]::Float64))
end

if isfinite(data.col_upper[i])
    MOI.add_constraint(model, x, MOI.LessThan(data.col_upper[i]::Float64))
end

This would also handle two edge cases differently:

1. If data.col_lower[i] > data.col_upper[i], it adds the bounds keeping the model infeasible (bounds_to_set would currently remove the bounds and create a free variable)
2. If data.col_lower[i] == data.col_upper[i], it sticks to adding bounds, and does not convert those into a single equality

(1.) is maybe not really important, but (2.) could lead to similar problems as the initial version:

• I create a variable that somewhere along the way gets equal bounds, then
• write that to a file, read it back in, and
• the bounds are gone, has_*_bound will return false, and I can't change the bounds anymore.

Further, this also impacts how fix(x, value; force=false) behaves. With bounds it errors, with the EqualTo it overwrites.

[odow]

Could creating the "helper" Interval set be an overhead for large files?

Nope. It's a struct that is on the stack.

Something like this would be possible here

bounds_to_set already does this 😄 it will return an Interval only if both sides are finite.

the bounds are gone, has_*_bound will return false, and I can't change the bounds anymore.

You'd need to unfix(x); set_lower_bound(x, lb).

The issue is that JuMP doesn't offer a nice way to interact with interval bounds.

I agree that lower/upper/fixed bounds are more convoluted than a plain lower/upper bound. You'll need to write some JuMP code to deal with the different situations.