A moment-SOS semidefinite hierarchy computes best W2 and TV mixture approximations over semi-algebraic parameter sets and can recover the mixture order from a rank condition.
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Mixtures Closest to a Given Measure: A Semidefinite Programming Approach
A moment-SOS semidefinite hierarchy computes best W2 and TV mixture approximations over semi-algebraic parameter sets and can recover the mixture order from a rank condition.