Fails to optimize expressions containing a sup/inf on an interval valued function.

[freemin7]

y = Interval(-0.1,0.1)
k(x) = ( ((x+y)- 2)^6 + 0.2 ) * (log(1+(x+y)^2))
global_min, minimisers = minimise(x -> sup(k(x)), -0.2..3)

results in:

ERROR: MethodError: no method matching sup(::Float64)
Closest candidates are:
  sup(::Interval) at C:\Users\freemint\.julia\packages\IntervalArithmetic\UR6Qe\src\intervals\arithmetic.jl:306
  sup(::DecoratedInterval{T}) where T at C:\Users\freemint\.julia\packages\IntervalArithmetic\UR6Qe\src\decorations\functions.jl:54
Stacktrace:
 [1] minimise(f::var"#1#2", X::Interval{Float64}; structure::Type{HeapedVector}, tol::Float64)
   @ IntervalOptimisation C:\Users\freemint\.julia\packages\IntervalOptimisation\deTUP\src\optimise.jl:40
 [2] minimise(f::Function, X::Interval{Float64})
   @ IntervalOptimisation C:\Users\freemint\.julia\packages\IntervalOptimisation\deTUP\src\optimise.jl:22
 [3] top-level scope
   @ REPL[5]:1

However:

julia> sup(x::Real) = x
sup (generic function with 3 methods)

julia> inf(x::Real) = x
inf (generic function with 3 methods)

does not fix it and raises a new issue which suggests that there might be something else going on.

ERROR: ArgumentError: reducing over an empty collection is not allowed
Stacktrace:
  [1] _empty_reduce_error()
    @ Base .\reduce.jl:299
  [2] reduce_empty(op::Function, #unused#::Type{Real})
    @ Base .\reduce.jl:309
  [3] mapreduce_empty(#unused#::typeof(identity), op::Function, T::Type)
    @ Base .\reduce.jl:343
  [4] reduce_empty(op::Base.MappingRF{typeof(identity), typeof(min)}, #unused#::Type{Real})
    @ Base .\reduce.jl:329
  [5] reduce_empty_iter
    @ .\reduce.jl:355 [inlined]
  [6] mapreduce_empty_iter(f::Function, op::Function, itr::Vector{Real}, ItrEltype::Base.HasEltype)
    @ Base .\reduce.jl:351
  [7] _mapreduce(f::typeof(identity), op::typeof(min), #unused#::IndexLinear, A::Vector{Real})
    @ Base .\reduce.jl:400
  [8] _mapreduce_dim
    @ .\reducedim.jl:318 [inlined]
  [9] #mapreduce#672
    @ .\reducedim.jl:310 [inlined]
 [10] mapreduce
    @ .\reducedim.jl:310 [inlined]
 [11] #_minimum#694
    @ .\reducedim.jl:878 [inlined]
 [12] _minimum
    @ .\reducedim.jl:878 [inlined]
 [13] #_minimum#693
    @ .\reducedim.jl:877 [inlined]
 [14] _minimum
    @ .\reducedim.jl:877 [inlined]
 [15] #minimum#691
    @ .\reducedim.jl:873 [inlined]
 [16] minimum(a::Vector{Real})
    @ Base .\reducedim.jl:873
 [17] minimise(f::var"#3#4", X::Interval{Float64}; structure::Type{HeapedVector}, tol::Float64)
    @ IntervalOptimisation C:\Users\freemint\.julia\packages\IntervalOptimisation\deTUP\src\optimise.jl:60
 [18] minimise(f::Function, X::Interval{Float64})
    @ IntervalOptimisation C:\Users\freemint\.julia\packages\IntervalOptimisation\deTUP\src\optimise.jl:22
 [19] top-level scope
    @ REPL[11]:1

[freemin7]

@Suavesito-Olimpiada could you see if that issue vanishes on your fix for #62 ?

[Suavesito-Olimpiada]

No, it does not work. But... if you change your algorithm to this t works

k(x, y) = (((x+y) - 2)^6 + 0.2) * log(1 + (x+y)^2)
global_min, minimisers = minimise(x -> k(x[1], x[2]), (-0.2..3) × (-0.1..0.1))

[freemin7]

@Suavesito-Olimpiada Thanks for trying it out.
You are solving an entirely different problem in your suggestions. I want something along the lines of min_x max_y f(x,y) not min_{x,y} f(x,y).

[Suavesito-Olimpiada]

Ok, now I see what you're trying to do. I don't know is this kind of algorithms are really suited for finding minmax of functions. Maybe this is a theoretical difficulty.