Utilities.Model does not support complex number types

[odow]

julia> MOI.Utilities.Model{Complex{Float64}}()
ERROR: MethodError: Cannot `convert` an object of type 
  Nothing to an object of type 
  Union{}
Closest candidates are:
  convert(::Type{Union{}}, ::Any) at essentials.jl:203
  convert(::Type{T}, ::Any) where T<:VecElement at baseext.jl:8
  convert(::Type{var"#s814"} where var"#s814"<:LinearAlgebra.Hermitian, ::Union{LinearAlgebra.Hermitian, LinearAlgebra.Symmetric}) at /Users/julia/buildbot/worker/package_macos64/build/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/symmetric.jl:194
  ...
Stacktrace:
 [1] convert(#unused#::Type{Union{}}, x::Nothing)
   @ Base ./essentials.jl:203
 [2] MathOptInterface.Utilities.ModelFunctionConstraints{ComplexF64}()
   @ MathOptInterface.Utilities ~/.julia/dev/MathOptInterface/src/Utilities/struct_of_constraints.jl:378
 [3] MathOptInterface.Utilities.Model{ComplexF64}()
   @ MathOptInterface.Utilities ~/.julia/dev/MathOptInterface/src/Utilities/model.jl:736
 [4] top-level scope
   @ REPL[24]:1

[odow]

Oooof. This is a tricky one.

The issue is that some of the sets have restrictions on type parameters:

julia> MOI.PowerCone{ComplexF64}
ERROR: TypeError: in PowerCone, in T, expected T<:Real, got Type{ComplexF64}
Stacktrace:
 [1] top-level scope
   @ REPL[59]:1

which causes some weird errors, but effectively we can't support ComplexF64 in Model.

[odow]

Closing this for now since there's no simple solution and we can work-around it with a UniversalFallback. We can come back to it if it pops up again.

Edit: Actually one solution might be adding ScalarAffineFunction{Complex{T}} and EqualTo{Complex{T}} as functions and sets, but that isn't a general solution.