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Higher-degree tensor eigenvalue complementarity problems

Author

Listed:
  • Ruixue Zhao

    (Shanghai Jiao Tong University)

  • Jinyan Fan

    (Shanghai Jiao Tong University)

Abstract

In this paper, we study the higher-degree tensor eigenvalue complementarity problem (HDTEiCP). We give an upper bound for the number of the higher-degree complementarity eigenvalues for the generic HDTEiCP. A semidefinite relaxation algorithm is proposed for computing all the higher-degree complementarity eigenvalues sequentially, as well as the corresponding eigenvectors, and the convergence of the algorithm is discussed. Some numerical results are also given.

Suggested Citation

  • Ruixue Zhao & Jinyan Fan, 2020. "Higher-degree tensor eigenvalue complementarity problems," Computational Optimization and Applications, Springer, vol. 75(3), pages 799-816, April.
    • Handle: RePEc:spr:coopap:v:75:y:2020:i:3:d:10.1007_s10589-019-00159-w
    DOI: 10.1007/s10589-019-00159-w
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    References listed on IDEAS

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    1. Chen Ling & Hongjin He & Liqun Qi, 2016. "On the cone eigenvalue complementarity problem for higher-order tensors," Computational Optimization and Applications, Springer, vol. 63(1), pages 143-168, January.
    2. 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.
    3. Chen Ling & Hongjin He & Liqun Qi, 2016. "Higher-degree eigenvalue complementarity problems for tensors," Computational Optimization and Applications, Springer, vol. 64(1), pages 149-176, May.
    4. Laurent, M., 2009. "Sums of squares, moment matrices and optimization over polynomials," Other publications TiSEM 9fef820b-69d2-43f2-a501-e, Tilburg University, School of Economics and Management.
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