Convex Optimization · Problem 2.39

Convex functions — Boyd & Vandenberghe

Mathematics — Optimization · separation-of-cones

Problem

Separation of cones. Let

K

and

\tilde{K}

be two convex cones whose interiors are nonempty and disjoint. Show that there is a nonzero

y

such that

y \in K^*

-y \in \tilde{K}^*