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A hierarchy of semidefinite relaxations for completely positive tensor optimization problems

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Abstract

In this paper, we study the completely positive (CP) tensor program, which is a linear optimization problem with the cone of CP tensors and some linear constraints. We reformulate it as a linear program over the cone of moments, then construct a hierarchy of semidefinite relaxations for solving it. We also discuss how to find a best CP approximation of a given tensor. Numerical experiments are presented to show the efficiency of the proposed methods.

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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, and MOE-LSC, 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 Jinyan Fan.

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Anwa Zhou was partially supported by the NSFC Grant 11701356, the National Postdoctoral Program for Innovative Talents Grant BX201600097 and Project Funded by China Postdoctoral Science Foundation Grant 2016M601562. Jinyan Fan was partially supported by the NSFC Grant 11571234.

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Zhou, A., Fan, J. A hierarchy of semidefinite relaxations for completely positive tensor optimization problems. J Glob Optim 75, 417–437 (2019). https://doi.org/10.1007/s10898-019-00751-8

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