Discrete Transforms, Semidefinite Programming, and Sum-of-Squares Representations of Nonnegative Polynomials

Abstract. We present a new semidefinite programming formulation of sum-of-squares representations of nonnegative polynomials, cosine polynomials and trigonometric polynomials of one variable. The parametrization is based on discrete transforms (specifically, the discrete Fourier, cosine and polynomial transforms) and has a simple structure that can be exploited by straightforward modifications of standard interior-point algorithms.