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Higher-degree tensor eigenvalue complementarity problems

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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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanghai Jiao Tong University, 200240, Shanghai, China

    Ruixue Zhao

  2. School of Mathematical Sciences, and Key Lab of Scientific and Engineering Computing (Ministry of Education), Shanghai Jiao Tong University, 200240, Shanghai, China

    Jinyan Fan

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  1. Ruixue Zhao
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  2. Jinyan Fan
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Correspondence to Jinyan Fan.

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The authors are supported by Chinese NSF Grants 11571234 and 11971309.

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Zhao, R., Fan, J. Higher-degree tensor eigenvalue complementarity problems. Comput Optim Appl 75, 799–816 (2020). https://doi.org/10.1007/s10589-019-00159-w

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  • DOI: https://doi.org/10.1007/s10589-019-00159-w

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