Computational Optimization and Applications

, Volume 70, Issue 2, pp 419–441 | Cite as

Completely positive tensor recovery with minimal nuclear value

  • Anwa Zhou
  • Jinyan Fan


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.


Completely positive tensor Tensor recovery The CP-nuclear values Moment problem Semidefinite program 

Mathematics Subject Classification

15A69 65K05 90C22 90C30 



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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsShanghai UniversityShanghaiPeople’s Republic of China
  2. 2.School of Mathematical SciencesShanghai Jiao Tong UniversityShanghaiPeople’s Republic of China

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