Unbounded convex hull is possible?

Question

I'm reading this lecture note for additional study.(https://people.orie.cornell.edu/dpw/orie6300/fall2008/Lectures/lec05.pdf)

For Q the convex hull of a finite number of vectors v1, v2, . . . , vk, Q is a polytope. An unbounded polyhedra is not a polytope

Think of unbounded polyhedra.

The convex hull should be also unbounded? (Since the polyhedra is also a convex?)

Or in this case does it means that the convex hull doesn't exists?

Answer 1

Assume everything is finite dimensional. Looking at the lecture note, your question is probably related to the Weyl-Minkowski theorem for the representation of a polyhedron. Namely, if the polyhedron is closed and bounded, then it is the convex hull of its extreme points. If the polyhedron is unbounded, then it is the Minkowski sum of the convex hull of its extreme points and conic hull of its extreme rays. See this What is Weyl-Minkowski theorem?