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A semidefinite algorithm for completely positive tensor decomposition

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Abstract

A symmetric tensor, which has a symmetric nonnegative decomposition, is called a completely positive tensor. In this paper, we characterize the completely positive tensor as a truncated moment sequence, and transform the problem of checking whether a tensor is completely positive to checking whether its corresponding truncated moment sequence admits a representing measure, then present a semidefinite algorithm to solve it. If a tensor is not completely positive, a certificate for it can be obtained; if it is completely positive, a nonnegative decomposition can be obtained.

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Acknowledgments

The first author was supported in part by NSFC Grant 11571234. The second author was supported in part by CPSF Grant BX201600097.

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Correspondence to Jinyan Fan.

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Fan, J., Zhou, A. A semidefinite algorithm for completely positive tensor decomposition. Comput Optim Appl 66, 267–283 (2017). https://doi.org/10.1007/s10589-016-9870-9

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  • DOI: https://doi.org/10.1007/s10589-016-9870-9

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