How to change the variable bound from an interval to its lower and upper bound in JuMP?

Question

When I read a model from a ".mps" file using "read_from_file" in JuMP and print it, I find that many bounds are written in the interval format like "x \in [0, 1]". I want to change an interval to a lower bound and an upper bound like "x >= 0, x <= 1" but when I use the function "lower_bound", it tells me "x does not have a lower bound". Why would this happen? How can I do the transformation?

Answer 1

You can use:

julia> using JuMP

julia> function change_interval_to_bounds(model::JuMP.Model)
           for c_index in all_constraints(model, VariableRef, MOI.Interval{Float64})
               constraint = constraint_object(c_index)
               delete(model, c_index)
               set_lower_bound(constraint.func, constraint.set.lower)
               set_upper_bound(constraint.func, constraint.set.upper)
           end
           return
       end
change_interval_to_bounds (generic function with 1 method)

julia> model = Model();

julia> @variable(model, x in MOI.Interval(0.0, 1.0));

julia> print(model)
Feasibility
Subject to
 x ∈ [0, 1]

julia> change_interval_to_bounds(model)

julia> print(model)
Feasibility
Subject to
 x ≥ 0
 x ≤ 1

We don't have built-in support for this because we assume that models read from file should stay as they are. (And it's only a few lines to implement manually.)

When you create a model using @variable(model, l <= x <= u) we add two separate constraints instead of a single Interval constraint because people want to change bounds, etc.