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A semidefinite algorithm for completely positive tensor decomposition

Author

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  • Jinyan Fan

    (Shanghai Jiao Tong University)

  • Anwa Zhou

    (Shanghai University)

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.

Suggested Citation

  • Jinyan Fan & Anwa Zhou, 2017. "A semidefinite algorithm for completely positive tensor decomposition," Computational Optimization and Applications, Springer, vol. 66(2), pages 267-283, March.
    • Handle: RePEc:spr:coopap:v:66:y:2017:i:2:d:10.1007_s10589-016-9870-9
    DOI: 10.1007/s10589-016-9870-9
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    References listed on IDEAS

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    1. Laurent, M., 2009. "Sums of squares, moment matrices and optimization over polynomials," Other publications TiSEM 9fef820b-69d2-43f2-a501-e, Tilburg University, School of Economics and Management.
    2. Anwa Zhou & Jinyan Fan, 2015. "Interiors of completely positive cones," Journal of Global Optimization, Springer, vol. 63(4), pages 653-675, December.
    3. Peter Dickinson & Luuk Gijben, 2014. "On the computational complexity of membership problems for the completely positive cone and its dual," Computational Optimization and Applications, Springer, vol. 57(2), pages 403-415, March.
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    Cited by:

    1. Jinyan Fan & Jiawang Nie & Anwa Zhou, 2019. "Completely Positive Binary Tensors," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 1087-1100, August.
    2. Anwa Zhou & Jinyan Fan, 2018. "Completely positive tensor recovery with minimal nuclear value," Computational Optimization and Applications, Springer, vol. 70(2), pages 419-441, June.

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