Every convex homogeneous polynomial (or form) is nonnegative. Blekherman has shown that there exist forms are not sums of squares via a nonconstructive argument. We provide an explicit example form degree four in 272 variables sum squares. The related to the Cauchy-Schwarz inequality over octonions. proof uses symmetry reduction together with fact (due Blekherman) even degree, near-constant on ...

Semidefinite programs (SDPs) are standard convex problems that frequently found in control and optimization applications. Interior-point methods can solve SDPs polynomial time up to arbitrary accuracy, but scale poorly as the size of matrix variables number constraints increases. To improve scalability, be approximated with lower upper bounds through use structured subsets (e.g., diagonally-dom...