#605 - Function for checking boundedness

[schillic]

Closes #605.

This PR adds isbounded(::Set).
There is a default implementation (that uses isbounded_unit_dims), but only the implementations of ExponentialProjectionMap, HPolyhedron, Intersection(Array), and LinearMap may fall back to that default if some sufficient/necessary checks fail. For the other set types, the check is trivial (or recursive for operations).

Some tests do not work before merging #940, so they currently throw an error. Whatever gets merged last has to update those tests.

@mforets: Can you please check the implementations for LinearMap, ExponentialMap, and ExponentialProjectionMap if they are correct or if they can be improved?

[mforets]

May i suggest to rename isbounded_unit_dims -> isbounded_unit_dimensions ?

(Comparing to constrained_dimensions.)

[mforets]

LGTM 👏 👏 👏

[schillic]

Do you agree that for ExponentialMap the condition isbounded(em.X) is sufficient and necessary?
If X is unbounded in only one dimension, can it happen that a matrix exponential is zero in that dimension? I was thinking that in 1D this cannot happen (e^x > 0 for all x), but I am lost in higher dimensions.

[mforets]

Do you agree that for ExponentialMap the condition isbounded(em.X) is sufficient and necessary?

Yes, it follows from the invertibility of M := exp(A) for any matrix A, see the properties of the matrix exponential.

Indeed, suppose by contradiction that the set Y = MX is bounded but the set X is unbounded. Then there exists a sequence of elements of X, x^j for j=1,2,... such that ||x^j|| -> oo. Let y^j = Mx^j for all j. Then since M is invertible, x^j = inv(M) * y^j and thus ||x^j|| <= ||inv(M)|| ||y^j||, and the right-hand side is bounded by hypothesis, thus the sequence ||x^j|| is bounded, a contradiction.

We can use this condition in LinearMap and ExponentialProjectionMap as well.