Frank-Wolfe theorem: why the polyhedral set must be convex?

55 Views Asked by At

The theorem states that a lower bounded quadratic function attains its infimum on a convex polyhedral set. My question is why does the set must be convex?

I've been trying to understand the analytical proof from Blum and Oettli and I can't see where the convexity is involved.

Thank you!