A hierarchy of semidefinite relaxations for completely positive tensor optimization problems

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

Journal of Global Optimization, 2019, vol. 75, issue 2, No 6, 417-437

Abstract: 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.

Keywords: CP tensor program; Best CP tensor approximation; Linear optimization with moments; Nonnegative decomposition; Semidefinite program; Primary: 15A69; 44A60; 90C22; 90C26 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10898-019-00751-8

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