For generically generated moment matrices with O(n^d) atoms, the minimal face of the pseudo-moment cone is simplicial, enabling an efficient Carathéodory-type atomic decomposition algorithm.
Tssos: A moment-sos hierarchy that exploits term sparsity.SIAM Journal on Optimization, 31(1):30–58
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Simplicial Regularizability of the Pseudo-Moment Cone and Carath\'eodory-Type Atomic Decomposition of Moment Matrices
For generically generated moment matrices with O(n^d) atoms, the minimal face of the pseudo-moment cone is simplicial, enabling an efficient Carathéodory-type atomic decomposition algorithm.