IDEAS home Printed from https://ideas.repec.org/a/hin/jnlmpe/6107517.html
   My bibliography  Save this article

Solvability of Two Classes of Tensor Complementarity Problems

Author

Listed:
  • Yang Xu
  • Weizhe Gu
  • He Huang

Abstract

In this paper, we first introduce a class of tensors, called positive semidefinite plus tensors on a closed cone, and discuss its simple properties; and then, we focus on investigating properties of solution sets of two classes of tensor complementarity problems. We study the solvability of a generalized tensor complementarity problem with a - strictly copositive tensor and a positive semidefinite plus tensor on a closed cone and show that the solution set of such a complementarity problem is bounded. Moreover, we prove that a related conic tensor complementarity problem is solvable if the involved tensor is positive semidefinite on a closed convex cone and is uniquely solvable if the involved tensor is strictly positive semidefinite on a closed convex cone. As an application, we also investigate a static traffic equilibrium problem which is reformulated as a concerned complementarity problem. A specific example is also given.

Suggested Citation

  • Yang Xu & Weizhe Gu & He Huang, 2019. "Solvability of Two Classes of Tensor Complementarity Problems," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-8, March.
    • Handle: RePEc:hin:jnlmpe:6107517
    DOI: 10.1155/2019/6107517
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/MPE/2019/6107517.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/MPE/2019/6107517.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/6107517?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
    ---><---

    Citations

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


    Cited by:

    1. Tran Nghi & Nguyen Nang Tam, 2020. "A Frank–Wolfe-Type Theorem for Cubic Programs and Solvability for Quadratic Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 448-468, November.
    2. Tong-tong Shang & Jing Yang & Guo-ji Tang, 2022. "Generalized Polynomial Complementarity Problems over a Polyhedral Cone," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 443-483, February.

    More about this item

    Statistics

    Access and download statistics

    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:hin:jnlmpe:6107517. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.