Copositivity Detection of Tensors: Theory and Algorithm

Haibin Chen (), Zheng-Hai Huang () and Liqun Qi ()
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Haibin Chen: Qufu Normal University
Zheng-Hai Huang: Tianjin University
Liqun Qi: The Hong Kong Polytechnic University

Journal of Optimization Theory and Applications, 2017, vol. 174, issue 3, No 8, 746-761

Abstract: Abstract A symmetric tensor is called copositive if it generates a multivariate form taking nonnegative values over the nonnegative orthant. Copositive tensors have found important applications in polynomial optimization, tensor complementarity problems and vacuum stability of a general scalar potential. In this paper, we consider copositivity detection of tensors from both theoretical and computational points of view. After giving several necessary conditions for copositive tensors, we propose several new criteria for copositive tensors based on the representation of the multivariate form in barycentric coordinates with respect to the standard simplex and simplicial partitions. It is verified that, as the partition gets finer and finer, the concerned conditions eventually capture all strictly copositive tensors. Based on the obtained theoretical results with the help of simplicial partitions, we propose a numerical method to judge whether a tensor is copositive or not. The preliminary numerical results confirm our theoretical findings.

Keywords: Symmetric tensor; Strictly copositive tensor; Positive semi-definiteness; Simplicial partition; 65H17; 15A18; 90C30 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-017-1131-2

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