## Abstract

For a proper cone K ⊂ Rn and its dual cone K the complementary slackness condition
xT s = 0 defines an n-dimensional manifold C(K) in the space { (x, s) | x ∈ K, s ∈ K }. When
K is a symmetric cone, this manifold can be described by a set of n bilinear equalities. This
fact proves to be very useful when optimizing over such cones, therefore it is natural to look
for similar optimality constraints for non-symmetric cones. In this paper we examine the cone
of positive polynomials P2n+1 and its dual, the moment cone M2n+1. We show that there are
exactly 4 linearly independent bilinear identities which hold for all (x, s) ∈ C(K), regardless
of the dimension of the cones.