Title: From coefficients to samples: a new approach to SOS optimization Speaker: Pablo A. Parrilo (ETH Zurich) We introduce a new methodology for the numerical solution of semidefinite relaxations arising from the sum of squares (SOS) decomposition of multivariate polynomials. The method is based on a novel SOS representation, where polynomials are represented by a finite set of values at discrete sampling points, complemented by an orthogonalization technique. The methods have very appealing theoretical and numerical properties; the associated semidefinite programs are better conditioned, and have a rank one property that enables a fast computation of search directions in interior point methods. The results are illustrated with examples, and numerical results for a preliminary implementation. Joint work with Johan Löfberg (ETH Zurich)