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Tensor Z-eigenvalue complementarity problems

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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.

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Acknowledgements

The author is very grateful to School of Mathematical Sciences, Shanghai Jiao Tong University for its support and help. The author would like to thank the associate editor and two anonymous referees for their constructive comments and suggestions.

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  1. School of Mathematics and Statistics, Hubei Engineering University, Xiaogan, Hubei, 432000, China

    Meilan Zeng

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  1. Meilan Zeng
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Correspondence to Meilan Zeng.

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This work was supported by the Science and Technology Foundation of the Department of Education of Hubei Province (B2020151) and the University-Industry Collaborative Education Program (201901032002).

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Zeng, M. Tensor Z-eigenvalue complementarity problems. Comput Optim Appl 78, 559–573 (2021). https://doi.org/10.1007/s10589-020-00248-1

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