`primal_feasibility_report` fails with indicator constraints in `distance_to_set`

[MagicMuscleMan]

I am not sure whether this is a JuMP.jl problem calling the wrong method or a MathOptInterface.jl problem missing the correct method. I guess the latter one, so I report it here.

I want to find the constraint which violates a solution which should be valid according to what I want, but seems to be invalid according to what I have written. However, it crashes. I boiled it down to this:

julia> using JuMP

julia> model = Model();

julia> @variable(model, b, Bin);

julia> @variable(model, x);

julia> @constraint(model, b --> {x >= 0});

julia> primal_feasibility_report(model, Dict(x => 1.0, b => 1.0), atol=10^-9)
ERROR: distance_to_set using the distance metric MathOptInterface.Utilities.ProjectionUpperBoundDistance() for set type MathOptInterface.Indicator{MathOptInterface.ACTIVATE_ON_ONE, MathOptInterface.GreaterThan{Float64}} has not been implemented yet.
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:44
  [2] distance_to_set(d::MathOptInterface.Utilities.ProjectionUpperBoundDistance, ::Vector{…}, set::MathOptInterface.Indicator{…})
    @ MathOptInterface.Utilities ~/.julia/packages/MathOptInterface/03Qtw/src/Utilities/distance_to_set.jl:75
  [3] distance_to_set(point::Vector{…}, set::MathOptInterface.Indicator{…})
    @ MathOptInterface.Utilities ~/.julia/packages/MathOptInterface/03Qtw/src/Utilities/distance_to_set.jl:71
  [4] _distance_to_set(point::Vector{…}, set::MathOptInterface.Indicator{…}, ::Type)
    @ JuMP ~/.julia/packages/JuMP/7eD71/src/feasibility_checker.jl:214
  [5] _add_infeasible_constraints(model::Model, ::Type{…}, ::Type{…}, violated_constraints::Dict{…}, point_f::Function, atol::Float64)
    @ JuMP ~/.julia/packages/JuMP/7eD71/src/feasibility_checker.jl:143
  [6] primal_feasibility_report(point::Function, model::Model; atol::Float64, skip_missing::Bool)
    @ JuMP ~/.julia/packages/JuMP/7eD71/src/feasibility_checker.jl:107
  [7] primal_feasibility_report
    @ ~/.julia/packages/JuMP/7eD71/src/feasibility_checker.jl:99 [inlined]
  [8] #primal_feasibility_report#114
    @ ~/.julia/packages/JuMP/7eD71/src/feasibility_checker.jl:58 [inlined]
  [9] top-level scope
    @ REPL[6]:1
 [10] top-level scope
    @ REPL:1
Some type information was truncated. Use `show(err)` to see complete types.

[odow]

This is the right place. I guess I need to be more e thorough at defining all the distance metrics now that sets like indicator are being more widely used!

[MagicMuscleMan]

I wondered whether we can dispatch on MathOptInterface.Indicator and if the indicator constraint is satisfied call distance_to_set with the inner set, i.e. GreaterThan in the above example.
But if the indicator constraint is not active we'd need to return 0.0.

[MagicMuscleMan]

This seems to work for the above use case:

function distance_to_set(d::AbstractDistance, x, set::MOI.Indicator{MOI.ACTIVATE_ON_ONE, T}) where T
    indicator = first(x)
    iszero(indicator) && return 0.0
    isone(indicator) && return distance_to_set(d, last(x), set.set)
    lazy"Indicator variable $x is neither zero nor one." |> MethodError |> throw
end

Open questions:

• Does the tolerance need to be accounted for when testing for zero or one?
• Can the indicator constraint have any other values than the exact ones?
• Will x always contain exactly two values with the first one being the indicator?
• Is x indexable or only iterable in general?

[MagicMuscleMan]

And accordingly:

function distance_to_set(d::AbstractDistance, x, set::MOI.Indicator{MOI.ACTIVATE_ON_ZERO, T}) where T
    indicator = first(x)
    isone(indicator) && return 0.0
    iszero(indicator) && return distance_to_set(d, last(x), set.set)
    lazy"Indicator variable $x is neither zero nor one." |> MethodError |> throw
end

[odow]

See #2923 for the indicator case, and #2924 for a list of sets without a distance.