Let K be a closed convex cone that intersects the nonnegative orthant at 0, that is, K n+ = {0}. Then there exists a

Let K be a closed convex cone that intersects the nonnegative orthant at 0, that is, K ∩ ℜn+ = {0}. Then there exists a hyperplane with positive normal p > 0 (i.e., pi > 0 for every i) such that pTx ≤ 0 for every x ∈ K.