**Tuesday, 13:15 - 13:40 h, Room: H 2036**

**Luis Zuluaga**

Positive polynomials on unbounded domains

**Coauthors: Javier F. Peña, Juan C. Vera**

**Abstract:**

Certificates of non-negativity are fundamental tools in optimization. A "certificate'' is generally understood as an expression that makes the non-negativity of the function in question evident. Recently, sum-of-squares certificates of non-negativity for polynomials have been used to obtain powerful numerical techniques for solving polynomial optimization problems; in particular, for mixed integer programs, and non-convex binary programs. We present a new certificate of non-negativity for polynomials over the intersection of a closed set *S* and the zero set of a given polynomial *h(x)*. The certificate is written in terms of the set of non-negative polynomials over *S* and the ideal generated by *h(x)*. Our certificate of non-negativity yields a copositive programming reformulation for a very general class of polynomial optimization problems.

Talk 1 of the invited session Tue.2.H 2036

**"Advances in convex optimization"** [...]

Cluster 4

**"Conic programming"** [...]