On hyperbolicity cones associated with elementary symmetric polynomials

Elementary symmetric polynomials can be thought of as derivative polynomials of En(x) = i=1,...,n xi. Their associated hyperbolicity cones give a natural sequence of relaxations for Rn +. We establish a recursive structure for these cones, namely, that the coordinate projections of these cones are themselves hyperbolicity cones associated with elementary symmetric polynomials. As a consequence of this recursion, we give an alternative characterization of these cones, and give an algebraic characterization for one particular dual cone associated with En-1(x) = 1in j=i xj together with its self-concordant barrier functional.

• Type: Journal
• Year: 2008
• Where: OL
• Authors: Yuriy Zinchenko
• Keywords: Cones, Elementary Symmetric Polynomials, Hyperbolicity Cones, OL 2008