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

Author

Listed:
  • Yisheng Song

    (Chongqing Normal University)

  • Xudong Li

    (Henan Normal University)

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.

Suggested Citation

  • Yisheng Song & Xudong Li, 2022. "Copositivity for a Class of Fourth-Order Symmetric Tensors Given by Scalar Dark Matter," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 334-346, October.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:1:d:10.1007_s10957-022-02086-z
    DOI: 10.1007/s10957-022-02086-z
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    References listed on IDEAS

    as
    1. Yisheng Song & Wei Mei, 2018. "Structural Properties of Tensors and Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 289-305, February.
    2. Yisheng Song & Gaohang Yu, 2016. "Properties of Solution Set of Tensor Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 85-96, July.
    3. Zheng-Hai Huang & Liqun Qi, 2017. "Formulating an n-person noncooperative game as a tensor complementarity problem," Computational Optimization and Applications, Springer, vol. 66(3), pages 557-576, April.
    4. Haibin Chen & Zheng-Hai Huang & Liqun Qi, 2018. "Copositive tensor detection and its applications in physics and hypergraphs," Computational Optimization and Applications, Springer, vol. 69(1), pages 133-158, January.
    5. Yisheng Song & Liqun Qi, 2016. "Eigenvalue analysis of constrained minimization problem for homogeneous polynomial," Journal of Global Optimization, Springer, vol. 64(3), pages 563-575, March.
    6. Yisheng Song & Liqun Qi, 2016. "Tensor Complementarity Problem and Semi-positive Tensors," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1069-1078, June.
    7. Yang Guo & Shaofang Hong, 2021. "A Novel Necessary and Sufficient Condition for the Positivity of a Binary Quartic Form," Journal of Mathematics, Hindawi, vol. 2021, pages 1-7, November.
    8. Haibin Chen & Zheng-Hai Huang & Liqun Qi, 2017. "Copositivity Detection of Tensors: Theory and Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 746-761, September.
    9. Xue-Li Bai & Zheng-Hai Huang & Yong Wang, 2016. "Global Uniqueness and Solvability for Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 72-84, July.
    10. Yisheng Song & Liqun Qi, 2015. "Properties of Some Classes of Structured Tensors," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 854-873, June.
    11. Maolin Che & Liqun Qi & Yimin Wei, 2016. "Positive-Definite Tensors to Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 475-487, February.
    Full references (including those not matched with items on IDEAS)

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