Bilinear optimality constraints for the cone of positive polynomials

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.

Available Versions of this Item

• Bilinear optimality constraints for the cone of positive polynomials. (deposited 15 Dec 2008 16:10) [Currently Displayed]
  • Bilinearity rank of the cone of positive polynomials and related cones. (deposited 03 Dec 2009 12:41)
    • Bilinearity rank of the cone of positive polynomials and related cones. (deposited 13 Oct 2010 10:17)
      • Bilinear optimality constraints for the cone of positive polynomials. (deposited 20 Oct 2011 14:33)