IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v423y2022ics0096300321009498.html
   My bibliography  Save this article

An SDP relaxation method for perron pairs of a nonnegative tensor

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321009498
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126866?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mingyuan Cao & Qingdao Huang & Chaoqian Li & Yueting Yang, 2020. "A Subspace Modified Broyden–Fletcher–Goldfarb–Shanno Method for $$\mathcal {B}$$B-eigenvalues of Symmetric Tensors," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 419-432, February.
    2. Xiao Wang & Xinzhen Zhang & Guangming Zhou, 2020. "SDP relaxation algorithms for $$\mathbf {P}(\mathbf {P}_0)$$P(P0)-tensor detection," Computational Optimization and Applications, Springer, vol. 75(3), pages 739-752, April.
    3. Riccardo De Blasis & Giovanni Batista Masala & Filippo Petroni, 2021. "A Multivariate High-Order Markov Model for the Income Estimation of a Wind Farm," Energies, MDPI, vol. 14(2), pages 1-16, January.
    4. Arapis, Anastasios N. & Makri, Frosso S. & Psillakis, Zaharias M., 2016. "On the length and the position of the minimum sequence containing all runs of ones in a Markovian binary sequence," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 45-54.
    5. Kharin, Yuriy & Voloshko, Valeriy, 2021. "Robust estimation for Binomial conditionally nonlinear autoregressive time series based on multivariate conditional frequencies," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    6. Nikolaos Stavropoulos & Alexandra Papadopoulou & Pavlos Kolias, 2021. "Evaluating the Efficiency of Off-Ball Screens in Elite Basketball Teams via Second-Order Markov Modelling," Mathematics, MDPI, vol. 9(16), pages 1-13, August.
    7. P.-C. G. Vassiliou & T. P. Moysiadis, 2010. "$\boldsymbol{\mathcal{G}-}$ Inhomogeneous Markov Systems of High Order," Methodology and Computing in Applied Probability, Springer, vol. 12(2), pages 271-292, June.
    8. Liying Kang & Wei Zhang & Erfang Shan, 2021. "The spectral radius and domination number in linear uniform hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 42(3), pages 581-592, October.
    9. Meilan Zeng, 2021. "Tensor Z-eigenvalue complementarity problems," Computational Optimization and Applications, Springer, vol. 78(2), pages 559-573, March.
    10. Alla Kammerdiner & Alexander Veremyev & Eduardo Pasiliao, 2017. "On Laplacian spectra of parametric families of closely connected networks with application to cooperative control," Journal of Global Optimization, Springer, vol. 67(1), pages 187-205, January.
    11. Fokianos, Konstantinos & Fried, Roland & Kharin, Yuriy & Voloshko, Valeriy, 2022. "Statistical analysis of multivariate discrete-valued time series," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    12. Ioannis Kontoyiannis & Lambros Mertzanis & Athina Panotopoulou & Ioannis Papageorgiou & Maria Skoularidou, 2022. "Bayesian context trees: Modelling and exact inference for discrete time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1287-1323, September.
    13. Lulu Cheng & Xinzhen Zhang, 2020. "A semidefinite relaxation method for second-order cone polynomial complementarity problems," Computational Optimization and Applications, Springer, vol. 75(3), pages 629-647, April.
    14. Honghai Li & Jia-Yu Shao & Liqun Qi, 2016. "The extremal spectral radii of $$k$$ k -uniform supertrees," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 741-764, October.
    15. Wai Ki Ching & Eric S. Fung & Michael K. Ng, 2004. "Higher‐order Markov chain models for categorical data sequences," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(4), pages 557-574, June.
    16. Francesco Bartolucci & Alessio Farcomeni, 2010. "A note on the mixture transition distribution and hidden Markov models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 132-138, March.
    17. Shouqiang Du & Liyuan Cui & Yuanyuan Chen & Yimin Wei, 2022. "Stochastic Tensor Complementarity Problem with Discrete Distribution," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 912-929, March.
    18. G. H. Shirdel & A. Mortezaee & E. Golpar-raboky, 2021. "$${\mathcal {C}}^k_{m,s}$$ C m , s k as a k-uniform hypergraph and some its properties," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(1), pages 297-303, March.
    19. James, Marilyn, 1999. "Towards an integrated needs and outcome framework," Health Policy, Elsevier, vol. 46(3), pages 165-177, March.
    20. Bruno Damásio & João Nicolau, 2020. "Time Inhomogeneous Multivariate Markov Chains: Detecting and Testing Multiple Structural Breaks Occurring at Unknown," Working Papers REM 2020/0136, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:423:y:2022:i:c:s0096300321009498. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.