#### Conference abstracts

Session A2 - Computational Algebraic Geometry

July 11, 18:00 ~ 18:25 - Room B5

## A Positivstellensatz for Sums of Nonnegative Circuit Polynomials

### Timo de Wolff

### TU Berlin, Germany - dewolff@math.tu-berlin.de

In 2014, Iliman and I introduced an entirely new nonnegativity certificate based on sums of nonnegative circuit polynomials (SONC), which are independent of sums of squares. We successfully applied SONCs to global nonnegativity problems.

In 2016, Dressler, Iliman, and I proved a Positivstellensatz for SONCs, which provides a converging hierarchy of lower bounds for constrained polynomial optimization problems. These bounds can be computed efficiently via relative entropy programming.

In this talk, I will give an overview about sums of nonnegative circuit polynomials, introduce our Positivstellensatz, and if time permits, briefly explain the connection to relative entropy programming.

Joint work with Mareike Dressler (Goethe University Frankfurt), Sadik Iliman.