The convergence rate of the moment-SOS hierarchy on a compact semi-algebraic set is O(1/r^L), where L is the Lojasiewicz exponent of the set's defining polynomials.
On the effective Putinar 's Positivstellensatz and moment approximation
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On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences
The convergence rate of the moment-SOS hierarchy on a compact semi-algebraic set is O(1/r^L), where L is the Lojasiewicz exponent of the set's defining polynomials.