- On hyperbolicity cones associated with elementary symmetric polynomials Yuriy Zinchenko(zinchenmcmaster.ca) Abstract: Elementary symmetric polynomials can be thought of as derivative polynomials of $E_n(x)=\prod_{i=1,\ldots,n} x_i$. Their associated hyperbolicity cones give a natural sequence of relaxations for $\Re^n_+$. 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 $E_{n-1}(x)=\sum_{1 \leq i \leq n} \prod_{j \neq i} x_j$ together with its self-concordant barrier functional. Keywords: hyperbolic polynomials; hyperbolicity cones; elementary symmetric polynomials; positive semi-definite representability Category 1: Linear, Cone and Semidefinite Programming (Other ) Citation: Download: [PDF]Entry Submitted: 09/04/2007Entry Accepted: 09/04/2007Entry Last Modified: 09/04/2007Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.