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Test of copositive tensors

  • * Corresponding author: Xinzhen Zhang

    * Corresponding author: Xinzhen Zhang 
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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  • 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.

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


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