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April  2019, 15(2): 881-891. doi: 10.3934/jimo.2018075

## 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

Received  June 2017 Revised  January 2018 Published  June 2018

Fund Project: 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).

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.

Citation: Li Li, Xinzhen Zhang, Zheng-Hai Huang, Liqun Qi. Test of copositive tensors. Journal of Industrial & Management Optimization, 2019, 15 (2) : 881-891. doi: 10.3934/jimo.2018075
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