Completely positive tensor recovery with minimal nuclear value

Anwa Zhou () and Jinyan Fan ()
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Anwa Zhou: Shanghai University
Jinyan Fan: Shanghai Jiao Tong University

Computational Optimization and Applications, 2018, vol. 70, issue 2, No 4, 419-441

Abstract: 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.

Keywords: Completely positive tensor; Tensor recovery; The CP-nuclear values; Moment problem; Semidefinite program; 15A69; 65K05; 90C22; 90C30 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10589-018-0003-5

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