SOS-convexity
A multivariate polynomial is SOS-convex (or sum of squares convex) if its Hessian matrix H can be factored as H(x) = ST(x)S(x) where S is a matrix (possibly rectangular) which entries are polynomials in x.[1] In other words, the Hessian matrix is a SOS matrix polynomial.
This article may be too technical for most readers to understand. (July 2020) |
An equivalent definition is that the form defined as g(x,y) = yTH(x)y is a sum of squares of forms.[2]