## View abstract

### Session II.6 - Computational Algebraic Geometry

Saturday, June 17, 14:30 ~ 15:00

## The SONC Cone: Primal and Dual Perspectives

### Timo de Wolff

#### TU Braunschweig, Germany   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak6577b0d4aaa2120f4633754222c08774').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy6577b0d4aaa2120f4633754222c08774 = 't.d&#101;-w&#111;lff' + '&#64;'; addy6577b0d4aaa2120f4633754222c08774 = addy6577b0d4aaa2120f4633754222c08774 + 't&#117;-br&#97;&#117;nschw&#101;&#105;g' + '&#46;' + 'd&#101;'; var addy_text6577b0d4aaa2120f4633754222c08774 = 't.d&#101;-w&#111;lff' + '&#64;' + 't&#117;-br&#97;&#117;nschw&#101;&#105;g' + '&#46;' + 'd&#101;';document.getElementById('cloak6577b0d4aaa2120f4633754222c08774').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy6577b0d4aaa2120f4633754222c08774 + '\'>'+addy_text6577b0d4aaa2120f4633754222c08774+'<\/a>';

Solving polynomial optimization problems requires to certify nonnegativity of multivariate, real polynomials. A classical way to do this are sums of squares (SOS). An alternative way are sums of nonnegative circuit polynomials (SONC), which I introduced joint with Iliman in 2014 building on work by Reznick. For a fixed support, SONCs form a convex cone, which has the same dimension as the corresponding nonnegativity cone. Moreover, motivated from a dualization process, one can obtain a particular (strict but full-dimensional) subcone of the SONC cone - the DSONC cone - leading to certificates which have, despite being weaker than SONC, the benefit to be obtainable via linear programming. In this talk I will speak about the SONC cone and its DSONC subcone. It is based on ArXiv 2204.03918.

Joint work with Janin Heuer (TU Braunschweig).