Test of copositive tensors

Li Li; Xinzhen Zhang; Zheng-Hai Huang; Liqun Qi

doi:10.3934/jimo.2018075

Article Contents

2019, Volume 15, Issue 2: 881-891. Doi: 10.3934/jimo.2018075

This issue Previous Article An integrated Principal Component Analysis and multi-objective mathematical programming approach to agile supply chain network design under uncertainty Next Article A semidefinite relaxation algorithm for checking completely positive separable matrices

Test of copositive tensors

a.
School of Mathematics, Tianjin University, 135 Yaguan Road, Tianjin 300350, China
b.
Department of Mathematics, Taiyuan Normal University, 319 University Street, Jinzhong, Shanxi 030619, China
c.
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

* Corresponding author: Xinzhen Zhang
* Corresponding author: Xinzhen Zhang

Received: May 31, 2017

Revised: December 31, 2017

Early access: June 2018

Published: January 2019

The second author is supported by the National Natural Science Foundation of China(Grant No. 11471242). The third author is supported by the National Natural Science Foundation of China(Grant No.11431002) and the fourth author is supported by the Hong Kong Research Grant Council (Grant No. PolyU 501913, 15302114, 15300715 and 15301716).

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Abstract

In this paper, an SDP relaxation algorithm is proposed to test the copositivity of higher order tensors. By solving finitely many SDP relaxations, the proposed algorithm can determine the copositivity of higher order tensors. Furthermore, for any copositive but not strictly copositive tensor, the algorithm can also check it exactly. Some numerical results are reported to show the efficiency of the proposed algorithm.

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Mathematics Subject Classification: 15A72, 65H20, 90C22, 90C59.

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