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

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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.

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Acknowledgements

Xinzhen Zhang was partially supported by the National Natural Science Foundation of China (Grant Nos. 11871369 and 12071343). Guyan Ni was partially supported by the National Natural Science Foundation of China (Grant No. 11871472).

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Authors and Affiliations

  1. School of Mathematics, Tianjin University, Tianjin, 300354, China

    Lulu Cheng & Xinzhen Zhang

  2. Department of Mathematics, National University of Defense Technology, Changsha, Hunan, China

    Guyan Ni

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  1. Lulu Cheng
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  2. Xinzhen Zhang
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  3. Guyan Ni
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Correspondence to Xinzhen Zhang.

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Cheng, L., Zhang, X. & Ni, G. A semidefinite relaxation method for second-order cone tensor eigenvalue complementarity problems. J Glob Optim 79, 715–732 (2021). https://doi.org/10.1007/s10898-020-00954-4

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