IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v61y2015i4p627-641.html
   My bibliography  Save this article

A quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map

Author

Listed:
  • Qin Ni
  • Liqun Qi

Abstract

In this paper we propose a quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map where the Newton method is used to solve an equivalent system of nonlinear equations. The semi-symmetric tensor is introduced to reveal the relation between homogeneous polynomial map and its associated semi-symmetric tensor. Based on this relation a globally and quadratically convergent algorithm is established where the line search is inserted. Some numerical results of this method are reported. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:61:y:2015:i:4:p:627-641
    DOI: 10.1007/s10898-014-0209-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-014-0209-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-014-0209-8?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. Shenglong Hu & Liqun Qi, 2012. "Algebraic connectivity of an even uniform hypergraph," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 564-579, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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. Lixing Han, 2019. "A Continuation Method for Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 949-963, March.
    3. 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).
    4. Gaohang Yu & Zefeng Yu & Yi Xu & Yisheng Song & Yi Zhou, 2016. "An adaptive gradient method for computing generalized tensor eigenpairs," Computational Optimization and Applications, Springer, vol. 65(3), pages 781-797, December.
    5. 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.

    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. 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.
    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. Yisheng Song & Liqun Qi, 2015. "Properties of Some Classes of Structured Tensors," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 854-873, June.
    4. Meilan Zeng, 2021. "Tensor Z-eigenvalue complementarity problems," Computational Optimization and Applications, Springer, vol. 78(2), pages 559-573, March.
    5. Yuning Yang & Qingzhi Yang & Liqun Qi, 2014. "Properties and methods for finding the best rank-one approximation to higher-order tensors," Computational Optimization and Applications, Springer, vol. 58(1), pages 105-132, May.

    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:jglopt:v:61:y:2015:i:4:p:627-641. 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.