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A semidefinite relaxation method for second-order cone tensor eigenvalue complementarity problems

Author

Listed:
  • Lulu Cheng

    (Tianjin University)

  • Xinzhen Zhang

    (Tianjin University)

  • Guyan Ni

    (National University of Defense Technology)

Abstract

This paper discusses second-order cone tensor eigenvalue complementarity problem. We reformulate second-order cone tensor eigenvalue complementarity problem as two constrained polynomial optimizations. For these two reformulated optimizations, Lasserre-type semidefinite relaxation methods are proposed to compute all second-order cone tensor complementarity eigenpairs. The proposed algorithms terminate when there are finitely many second-order cone complementarity eigenvalues. Numerical examples are reported to show the efficiency of the proposed algorithms.

Suggested Citation

  • Lulu Cheng & Xinzhen Zhang & Guyan Ni, 2021. "A semidefinite relaxation method for second-order cone tensor eigenvalue complementarity problems," Journal of Global Optimization, Springer, vol. 79(3), pages 715-732, March.
    • Handle: RePEc:spr:jglopt:v:79:y:2021:i:3:d:10.1007_s10898-020-00954-4
    DOI: 10.1007/s10898-020-00954-4
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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. Jiawang Nie & Xinzhen Zhang, 2018. "Real eigenvalues of nonsymmetric tensors," Computational Optimization and Applications, Springer, vol. 70(1), pages 1-32, May.
    3. 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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