Bilinear optimality constraints for the cone of positive polynomials

Noyan, Nilay and Papp, David and Rudolf, Gabor and Alizadeh, Farid (2008) Bilinear optimality constraints for the cone of positive polynomials. (Submitted)

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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.

Item Type:Article
ID Code:9658
Deposited By:Nilay Noyan
Deposited On:15 Dec 2008 16:10
Last Modified:03 Dec 2009 12:41

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