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A hierarchy of semidefinite relaxations for completely positive tensor optimization problems

Author

Listed:
  • Anwa Zhou

    (Shanghai University)

  • Jinyan Fan

    (Shanghai Jiao Tong University)

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.

Suggested Citation

  • Anwa Zhou & Jinyan Fan, 2019. "A hierarchy of semidefinite relaxations for completely positive tensor optimization problems," Journal of Global Optimization, Springer, vol. 75(2), pages 417-437, October.
    • Handle: RePEc:spr:jglopt:v:75:y:2019:i:2:d:10.1007_s10898-019-00751-8
    DOI: 10.1007/s10898-019-00751-8
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    References listed on IDEAS

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    1. Xiaolong Kuang & Luis F. Zuluaga, 2018. "Completely positive and completely positive semidefinite tensor relaxations for polynomial optimization," Journal of Global Optimization, Springer, vol. 70(3), pages 551-577, March.
    2. Laurent, M., 2009. "Sums of squares, moment matrices and optimization over polynomials," Other publications TiSEM 9fef820b-69d2-43f2-a501-e, Tilburg University, School of Economics and Management.
    3. Peter Dickinson & Luuk Gijben, 2014. "On the computational complexity of membership problems for the completely positive cone and its dual," Computational Optimization and Applications, Springer, vol. 57(2), pages 403-415, March.
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