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Tensor Z-eigenvalue complementarity problems

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  • Meilan Zeng

    (Hubei Engineering University)

Abstract

This paper studies tensor Z-eigenvalue complementarity problems. We formulate the tensor Z-eigenvalue complementarity problem as constrained polynomial optimization, and propose a semidefinite relaxation algorithm for solving the complementarity Z-eigenvalues of tensors. For every tensor that has finitely many complementarity Z-eigenvalues, we can compute all of them and show that our algorithm has the asymptotic and finite convergence. Numerical experiments indicate the efficiency of the proposed method.

Suggested Citation

  • Meilan Zeng, 2021. "Tensor Z-eigenvalue complementarity problems," Computational Optimization and Applications, Springer, vol. 78(2), pages 559-573, March.
    • Handle: RePEc:spr:coopap:v:78:y:2021:i:2:d:10.1007_s10589-020-00248-1
    DOI: 10.1007/s10589-020-00248-1
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    References listed on IDEAS

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    1. Jiawang Nie & Xinzhen Zhang, 2018. "Real eigenvalues of nonsymmetric tensors," Computational Optimization and Applications, Springer, vol. 70(1), pages 1-32, May.
    2. Shenglong Hu & Liqun Qi, 2012. "Algebraic connectivity of an even uniform hypergraph," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 564-579, November.
    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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