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Completely positive tensor recovery with minimal nuclear value

Author

Listed:
  • Anwa Zhou

    (Shanghai University)

  • Jinyan Fan

    (Shanghai Jiao Tong University)

Abstract

In this paper, we introduce the CP-nuclear value of a completely positive (CP) tensor and study its properties. A semidefinite relaxation algorithm is proposed for solving the minimal CP-nuclear-value tensor recovery. If a partial tensor is CP-recoverable, the algorithm can give a CP tensor recovery with the minimal CP-nuclear value, as well as a CP-nuclear decomposition of the recovered CP tensor. If it is not CP-recoverable, the algorithm can always give a certificate for that, when it is regular. Some numerical experiments are also presented.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:70:y:2018:i:2:d:10.1007_s10589-018-0003-5
    DOI: 10.1007/s10589-018-0003-5
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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. 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.
    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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