Copositivity for a Class of Fourth-Order Symmetric Tensors Given by Scalar Dark Matter

Yisheng Song () and Xudong Li ()
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Yisheng Song: Chongqing Normal University
Xudong Li: Henan Normal University

Journal of Optimization Theory and Applications, 2022, vol. 195, issue 1, No 15, 334-346

Abstract: Abstract The mathematical model of general scalar potentials may be written as a fourth-order symmetric tensor with a particular structure in particle physics. In this paper, we mainly discuss the copositivity of a class of tensors defined by the scalar dark matter with the Higgs doublet and an inert doublet and a complex singlet. With the help of its structure, we obtain the necessary and sufficient conditions, which attains the analytic conditions required by the physical problems. At the same time, this work presents how to determine a unique solution of the tensor complementarity problem with a parameter.

Keywords: Copositivity; Fourth-order tensors; Homogeneous polynomial; Tensor complementarity problem; 90C23; 15A63; 81T32; 70S20; 15A72; 47H09; 15A48; 47H07 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-022-02086-z

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