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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 $E_{n1}(x)=\sum_{1 \leq i \leq n} \prod_{j \neq i} x_j$ together with its selfconcordant barrier functional. Keywords: hyperbolic polynomials; hyperbolicity cones; elementary symmetric polynomials; positive semidefinite representability Category 1: Linear, Cone and Semidefinite Programming (Other ) Citation: Download: [PDF] Entry Submitted: 09/04/2007 Modify/Update this entry  
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