  The generalized problem of moments is a conic linear optimization problem
over the convex cone of positive Borel measures with given support. It has a
large variety of applications, including global optimization of polynomials and
rational functions, options pricing in finance, constructing quadrature schemes
for numerical integration, and distributionally robust optimization. A usual
solution approach, due to J.B. Lasserre, is to approximate the convex cone of
positive Borel measures by finite dimensional outer and inner conic
approximations. We will review some results on these approximations, with a
special focus on the convergence rate of the hierarchies of upper and lower
bounds for the general problem of moments that are obtained from these inner
and outer approximations.
