A semidefinite relaxation algorithm for checking completely positive separable matrices
Anwa Zhou Jinyan Fan
Journal of Industrial & Management Optimization 2019, 15(2): 893-908 doi: 10.3934/jimo.2018076

A symmetric matrix $A$ is completely positive (CP) if there exists an entrywise nonnegative matrix $V$ such that $A = VV ^T$. A real symmetric matrix is called completely positive separable (CPS) if it can be written as a sum of rank-1 Kronecker products of completely positive matrices. This paper studies the CPS problem. A criterion is given to determine whether a given matrix is CPS, and a specific CPS decomposition is constructed if the matrix is CPS.

keywords: Completely positive matrices completely positive separability moment problems semidefinite algorithm

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