Rounding sum-of-squares relaxations

Abstract

We present a general approach to rounding semidefinite programming relaxations obtained by the Sum-of-Squares method (Lasserre hierarchy). Our approach is based on using the connection between these relaxations and the Sum-of-Squares proof system to transform a combining algorithm---an algorithm that maps a distribution over solutions into a (possibly weaker) solution---into a rounding algorithm that maps a solution of the relaxation to a solution of the original problem