4 papers
Stubborn Polynomials
Lorenzo Baldi, Grigoriy Blekherman, Khazhgali Kozhasov +3
The relationship between nonnegative polynomials and sums of squares is a classical topic in real algebraic geometry. We study \emph{stubborn polynomials} on a real variety …
Certificates for nonnegativity of multivariate integer polynomials under perturbations
MatÃas R Bender, Khazhgali Kozhasov, Elias Tsigaridas +1
We develop a general and unconditional framework for certifying the global nonnegativity of multivariate integer polynomials; based on rewriting them as sum of squares modulo their…
On the minimal algebraic complexity of the rank-one approximation problem for general inner products
Khazhgali Kozhasov, Alan Muniz, Yang Qi +1
We study the algebraic complexity of Euclidean distance minimization from a generic tensor to a variety of rank-one tensors. The Euclidean Distance (ED) degree of the Segre-Verones…
On odd powers of nonnegative polynomials that are not sums of squares
Grigoriy Blekherman, Khazhgali Kozhasov, Bruce Reznick
We initiate a systematic study of nonnegative polynomials such that is not a sum of squares for any odd , calling such \emph{stubborn}. We develop a new inva…