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An SDP relaxation method for perron pairs of a nonnegative tensor

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  • Li, Li
  • Yan, Xihong
  • Zhang, Xinzhen

Abstract

In this paper, we focus on Perron pairs of a nonnegative tensor, which have wide applications in many areas, such as higher order Markov chains and hypergraph theory. We first propose a SemiDefinite Programming (SDP) relaxation algorithm to directly compute all Perron eigenvectors of a nonnegative tensor with finite Perron eigenvectors, where all Perron eigenvectors associated with monotonous Perron eigenvalues are generated by solving finite SDP problems. Then, the convergence of the proposed algorithm is proved. Finally, numerical experiments illustrate the efficiency of the proposed algorithm.

Suggested Citation

  • Li, Li & Yan, Xihong & Zhang, Xinzhen, 2022. "An SDP relaxation method for perron pairs of a nonnegative tensor," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    • Handle: RePEc:eee:apmaco:v:423:y:2022:i:c:s0096300321009498
    DOI: 10.1016/j.amc.2021.126866
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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. Qin Ni & Liqun Qi, 2015. "A quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map," Journal of Global Optimization, Springer, vol. 61(4), pages 627-641, April.
    3. Adrian Raftery & Simon Tavaré, 1994. "Estimation and Modelling Repeated Patterns in High Order Markov Chains with the Mixture Transition Distribution Model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(1), pages 179-199, March.
    4. Shenglong Hu & Liqun Qi, 2015. "The Laplacian of a uniform hypergraph," Journal of Combinatorial Optimization, Springer, vol. 29(2), pages 331-366, February.
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