IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v78y2021i2d10.1007_s10589-020-00248-1.html
   My bibliography  Save this article

Tensor Z-eigenvalue complementarity problems

Author

Listed:
  • Meilan Zeng

    (Hubei Engineering University)

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.

Suggested Citation

  • Meilan Zeng, 2021. "Tensor Z-eigenvalue complementarity problems," Computational Optimization and Applications, Springer, vol. 78(2), pages 559-573, March.
    • Handle: RePEc:spr:coopap:v:78:y:2021:i:2:d:10.1007_s10589-020-00248-1
    DOI: 10.1007/s10589-020-00248-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-020-00248-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-020-00248-1?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. Laurent, M., 2009. "Sums of squares, moment matrices and optimization over polynomials," Other publications TiSEM 9fef820b-69d2-43f2-a501-e, Tilburg University, School of Economics and Management.
    2. Shenglong Hu & Liqun Qi, 2012. "Algebraic connectivity of an even uniform hypergraph," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 564-579, November.
    3. Jiawang Nie & Xinzhen Zhang, 2018. "Real eigenvalues of nonsymmetric tensors," Computational Optimization and Applications, Springer, vol. 70(1), pages 1-32, May.
    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. 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.
    2. Shenglong Hu & Guoyin Li & Liqun Qi, 2016. "A Tensor Analogy of Yuan’s Theorem of the Alternative and Polynomial Optimization with Sign structure," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 446-474, February.
    3. Lulu Cheng & Xinzhen Zhang & Guyan Ni, 2021. "A semidefinite relaxation method for second-order cone tensor eigenvalue complementarity problems," Journal of Global Optimization, Springer, vol. 79(3), pages 715-732, March.
    4. Tian Liu & Chaoyi Wang & Ke Xu, 2015. "Large hypertree width for sparse random hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 531-540, April.
    5. Laurent, Monique & Vargas, Luis Felipe, 2022. "Finite convergence of sum-of-squares hierarchies for the stability number of a graph," Other publications TiSEM 3998b864-7504-4cf4-bc1d-f, Tilburg University, School of Economics and Management.
    6. Laurent, M. & Rostalski, P., 2012. "The approach of moments for polynomial equations," Other publications TiSEM f08f3cd2-b83e-4bf1-9322-a, Tilburg University, School of Economics and Management.
    7. Tomohiko Mizutani & Makoto Yamashita, 2013. "Correlative sparsity structures and semidefinite relaxations for concave cost transportation problems with change of variables," Journal of Global Optimization, Springer, vol. 56(3), pages 1073-1100, July.
    8. Fook Wai Kong & Polyxeni-Margarita Kleniati & Berç Rustem, 2012. "Computation of Correlated Equilibrium with Global-Optimal Expected Social Welfare," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 237-261, April.
    9. Sandra S. Y. Tan & Antonios Varvitsiotis & Vincent Y. F. Tan, 2021. "Analysis of Optimization Algorithms via Sum-of-Squares," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 56-81, July.
    10. Hao Hu & Renata Sotirov, 2021. "The linearization problem of a binary quadratic problem and its applications," Annals of Operations Research, Springer, vol. 307(1), pages 229-249, December.
    11. P. M. Kleniati & P. Parpas & B. Rustem, 2010. "Decomposition-based Method for Sparse Semidefinite Relaxations of Polynomial Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 289-310, May.
    12. T. D. Chuong & V. Jeyakumar & G. Li, 2019. "A new bounded degree hierarchy with SOCP relaxations for global polynomial optimization and conic convex semi-algebraic programs," Journal of Global Optimization, Springer, vol. 75(4), pages 885-919, December.
    13. O. P. Ferreira & S. Z. Németh, 2019. "On the spherical convexity of quadratic functions," Journal of Global Optimization, Springer, vol. 73(3), pages 537-545, March.
    14. Papp, Dávid & Regős, Krisztina & Domokos, Gábor & Bozóki, Sándor, 2023. "The smallest mono-unstable convex polyhedron with point masses has 8 faces and 11 vertices," European Journal of Operational Research, Elsevier, vol. 310(2), pages 511-517.
    15. Jiawang Nie & Suhan Zhong, 2023. "Loss functions for finite sets," Computational Optimization and Applications, Springer, vol. 84(2), pages 421-447, March.
    16. Ruixue Zhao & Jinyan Fan, 2020. "Higher-degree tensor eigenvalue complementarity problems," Computational Optimization and Applications, Springer, vol. 75(3), pages 799-816, April.
    17. Sönke Behrends & Anita Schöbel, 2020. "Generating Valid Linear Inequalities for Nonlinear Programs via Sums of Squares," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 911-935, September.
    18. Jinyan Fan & Anwa Zhou, 2017. "A semidefinite algorithm for completely positive tensor decomposition," Computational Optimization and Applications, Springer, vol. 66(2), pages 267-283, March.
    19. V. Jeyakumar & G. Li & S. Srisatkunarajah, 2014. "Global optimality principles for polynomial optimization over box or bivalent constraints by separable polynomial approximations," Journal of Global Optimization, Springer, vol. 58(1), pages 31-50, January.
    20. Feng Guo & Li Wang & Guangming Zhou, 2014. "Minimizing rational functions by exact Jacobian SDP relaxation applicable to finite singularities," Journal of Global Optimization, Springer, vol. 58(2), pages 261-284, February.

    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:spr:coopap:v:78:y:2021:i:2:d:10.1007_s10589-020-00248-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.