We consider the unconstrained optimization of multivariate trigonometric polynomials by sum-of-squares hierarchy lower bounds. first show a convergence rate for relaxation with degree without any assumption on polynomial to minimize. Second, when has finite number global minimizers invertible Hessians at these minimizers, we an exponential explicit constants. Our results also apply minimizing r...

Representation of a given nonnegative multivariate polynomial in terms of a sum of squares of polynomials has become an essential subject in recent developments of sums of squares optimization and SDP (semidefinite programming) relaxation of polynomial optimization problems. We disscuss effective methods to obtain a simpler representation of a “sparse” polynomial as a sum of squares of sparse p...