Approximation Hierarchies for the Copositive Tensor Cone and Their Application to the Polynomial Optimization over the Simplex

Muhammad Faisal Iqbal, Faizan Ahmed*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
64 Downloads (Pure)

Abstract

In this paper, we discuss the cone of copositive tensors and its approximation. We describe some basic properties of copositive tensors and positive semidefinite tensors. Specifically, we show that a non-positive tensor (or Z-tensor) is copositive if and only if it is positive semidefinite. We also describe cone hierarchies that approximate the copositive cone. These hierarchies are based on the sum of squares conditions and the non-negativity of polynomial coefficients. We provide a compact representation for the approximation based on the non-negativity of polynomial coefficients. As an immediate consequence of this representation, we show that the approximation based on the non-negativity of polynomial coefficients is polyhedral. Furthermore, these hierarchies are used to provide approximation results for optimizing a (homogeneous) polynomial over the simplex.

Original languageEnglish
Article number1683
Number of pages17
JournalMathematics
Volume10
Issue number10
DOIs
Publication statusPublished - 14 May 2022

Keywords

  • approximation hierarchies
  • copositive tensor
  • polynomial optimization
  • positive semidefinite tensor
  • simplex
  • sum of squares

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