Representations of non-negative polynomials via KKT ideals
Volume 102 / 2011
Annales Polonici Mathematici 102 (2011), 101-109
MSC: 11E25, 13P25, 14P10, 90C22.
DOI: 10.4064/ap102-2-1
Abstract
This paper studies the representation of a non-negative polynomial $f$ on a non-compact semi-algebraic set $K$ modulo its KKT (Karush–Kuhn–Tucker) ideal. Under the assumption that $f$ satisfies the boundary Hessian conditions (BHC) at each zero of $f$ in $K$, we show that $f$ can be represented as a sum of squares (SOS) of real polynomials modulo its KKT ideal if $f\ge 0$ on $K$.
