题目：          Nonnegative polynomials and circuit polynomials

报告人：      王杰（北京大学）

时间地点：  2019.02.27  14:00pm  N219

摘要：          The concept of sums of nonnegative circuit polynomials (SONC) was introduced as a new certificate of nonnegativity of polynomials, which was proved to be efficient in many cases. It is natural to ask which types of nonnegative polynomials admit SONC decompositions and how big the gap between the PSD cone and the SONC cone is. In this talk, we will consider these questions. Moreover, we clarify an important fact that every SONC polynomial decomposes into a sum of nonnegative circuit polynomials with the same support, which reveals the advantage of SONC decompositions for certifying nonnegativity of sparse polynomials compared with the classical SOS decompositions.