IDEAS home Printed from https://ideas.repec.org/p/cor/louvco/1997049.html
   My bibliography  Save this paper

Structure of non-negative polynomials and optimization problems

Author

Listed:
  • NESTEROV, Yurii

    (Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Louvain la Neuve, Belgium)

Abstract

In this paper we give an explicit description of the cone of univariate non-negative polynomials in terms of the cone of positive semidefinite matrices. As a consequence of that result, we get a description of the cones of polynomials, which are non-negative on a ray and on an interval, and the description of non-negative trigonometric polynomials. We present some extension of these results on multi-dimensional case.

Suggested Citation

  • NESTEROV, Yurii, 1997. "Structure of non-negative polynomials and optimization problems," LIDAM Discussion Papers CORE 1997049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1997049
    as

    Download full text from publisher

    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp1997.html
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Ho-Yin Mak & Ying Rong & Jiawei Zhang, 2015. "Appointment Scheduling with Limited Distributional Information," Management Science, INFORMS, vol. 61(2), pages 316-334, February.
    2. Ioana Popescu, 2005. "A Semidefinite Programming Approach to Optimal-Moment Bounds for Convex Classes of Distributions," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 632-657, August.
    3. Teles, João P. & Castro, Pedro M. & Matos, Henrique A., 2013. "Univariate parameterization for global optimization of mixed-integer polynomial problems," European Journal of Operational Research, Elsevier, vol. 229(3), pages 613-625.
    4. van Eekelen, Wouter, 2023. "Distributionally robust views on queues and related stochastic models," Other publications TiSEM 9b99fc05-9d68-48eb-ae8c-9, Tilburg University, School of Economics and Management.
    5. Xiaolong Kuang & Luis F. Zuluaga, 2018. "Completely positive and completely positive semidefinite tensor relaxations for polynomial optimization," Journal of Global Optimization, Springer, vol. 70(3), pages 551-577, March.

    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:cor:louvco:1997049. 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: Alain GILLIS (email available below). General contact details of provider: https://edirc.repec.org/data/coreebe.html .

    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.