A convex polynomial that is not sos-convex

Amir Ali Ahmadi, Pablo A. Parrilo

A multivariate polynomial $p(x)=p(x_1,...,x_n)$ is sos-convex if its Hessian $H(x)$ can be factored as $H(x)=M^T(x)M(x)$ with a possibly nonsquare polynomial matrix $M(x)$. It is…