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Completely positive tensor recovery with minimal nuclear value

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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.

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Acknowledgements

The authors thank the associate editor and anonymous referees for their valuable comments and suggestions. Anwa Zhou is partially supported by the NSFC Grant 11701356, National Postdoctoral Program for Innovative Talents Grant BX201600097 and China Postdoctoral Science Foundation Grant 2016M601562. Jinyan Fan is partially supported by the NSFC Grant 11571234.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Anwa Zhou

  2. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Jinyan Fan

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  1. Anwa Zhou
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  2. Jinyan Fan
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Correspondence to Anwa Zhou.

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Zhou, A., Fan, J. Completely positive tensor recovery with minimal nuclear value. Comput Optim Appl 70, 419–441 (2018). https://doi.org/10.1007/s10589-018-0003-5

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