Low-Rank Univariate Sum of Squares Has No Spurious Local Minima

Benoît Legat, Chenyang Yuan, Pablo A. Parrilo

We study the problem of decomposing a polynomial $p$ into a sum of $r$ squares by minimizing a quadratically penalized objective $f_p(\mathbf{u}) = \left\lVert \sum_{i=1}^r u_i^2 -…