#416 - Conversion from Zonotope to HPolytope

[schillic]

Closes #416.

[mforets]

This efficient conversion is a great feature to have, i look forward to reviewing it.

[schillic]

I think it is far from efficient, but the problem is just hard.

[schillic]

I realized that I added the convert method. What I wanted to add was the constraints_list method 😢

[schillic]

I just renamed the variable name for StrictlyIncreasingIndices from ip to sii (I think I first had a different name for the type and then forgot to adapt the variable name).

[mforets]

I realized that I added the convert method. What I wanted to add was the constraints_list method

i think that the convert(HPolytope, ::Zonotope) method should be added as well, because it is a pity that it falls back to the dual representation given that constraints_list can make use of this PR.

EDIT:

Actually, convert methods for HPolytope and HPolyhedron are very different:

# uses dual rep
function convert(::Type{HPolytope}, P::AbstractPolytope)
    return convert(HPolytope, convert(VPolytope, P))
end

# may or may not use dual rep depending on the implementation of constraints_list
function convert(::Type{HPolyhedron}, P::AbstractPolytope)
    return HPolyhedron(constraints_list(P))
end

Let me note that this would also make sense:

function convert(::Type{HPolytope}, P::AbstractPolytope)
    return HPolytope(constraints_list(P))
end

I don't know for sure which implementation we should pick. Maybe it is better to have both implementations available through a kwarg. (I tend to think that the implem that calls the constraints_list should be the default one).

Since this is a bit out of the scope of a Zonotpe -> HPolytope conversion, i suggest that we tackle this is a separate issue. I've created #1017.

[mforets]

I finished reviewing it all, well done! 👏
It won't be hard to re-use this code with parallelotopes.

As suggested below, while we are at this let's fix the case m=n before merging. I also left three ideas to make it faster.

[schillic]

i think that the convert(HPolytope, ::Zonotope) method should be added as well, because it is a pity that it falls back to the dual representation given that constraints_list can make use of this PR.

No need for that. In #932 we want to use constraints_list by default.