Convex Optimization · Problem 2.35

Convex functions — Boyd & Vandenberghe

Mathematics — Optimization · copositive-matrices

Problem

Copositive matrices. A matrix

X \in \mathbf{S}^n

is called copositive if

z^T X z \geq 0

for all

z \succeq 0

. Verify that the set of copositive matrices is a proper cone. Find its dual cone.