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The generalized problem of moments is a conic linear optimization problemover the convex cone of positive Borel measures with given support. It has alarge variety of applications, including global optimization of polynomials andrational functions, options pricing in finance, constructing quadrature schemesfor numerical integration, and distributionally robust optimization. A usualsolution approach, due to J.B. Lasserre, is to approximate the convex cone ofpositive Borel measures by finite dimensional outer and inner conicapproximations. We will review some results on these approximations, with aspecial focus on the convergence rate of the hierarchies of upper and lowerbounds for the general problem of moments that are obtained from these innerand outer approximations.

A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis