[RFC] Cut interface

[blegat]

An AbstractNode must implements getoptimalitycut and getfeasibilitycut.

• getoptimalitycut must returns a MinFunCut (do you prefer UBFunCut ?) (θ ≦ ⟨a, x⟩ + β) or a MaxFunCut (do you prefer LBFunCut ?) (θ ≧ ⟨a, x⟩ + β).
• getfeasibilitycut must returns a LBCut (⟨a, x⟩ ≧ β) or a UBCut (⟨a, x⟩ ≦ β). The 4 cut types will be defined in CutPruners. What do you think ?

[odow]

Why not parameterise the cuts by :lb or :ub?

[blegat]

We could have something like that too but having different types can be helpful when we want to do multiple dispatch. We could also have Cut{Fun, LB} where Fun and LB are boolean

[frapac]

I think these notations make already sense with those used in CutPruners.jl: https://github.com/JuliaPolyhedra/CutPruners.jl/blob/master/src/abstract.jl#L17