Convergence rates of moment-sum-of-squares hierarchies for volume   approximation of semialgebraic sets
  Moment-sum-of-squares hierarchies of semidefinite programs can be used to approximate the volume of a given compact basic semialgebraic set K. The idea consists of approximating from above the indicator function of K with a sequence of polynomials of increasing degree d, so that the integrals of these polynomials generate a convergence sequence of upper bounds on the volume of K. We show that the asymptotic rate of this convergence is at least O(1/ log log d). 
Milan Korda, Didier Henrion (LAAS-MAC, CTU)
math.OC