IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v82y2022i1d10.1007_s10589-022-00360-4.html
   My bibliography  Save this article

Parametric shape optimization using the support function

Author

Listed:
  • Pedro R. S. Antunes

    (Universidade Aberta
    Group of Mathematical Physics, Faculdade de Ciências da Universidade de Lisboa)

  • Beniamin Bogosel

    (École Polytechnique)

Abstract

The optimization of shape functionals under convexity, diameter or constant width constraints shows numerical challenges. The support function can be used in order to approximate solutions to such problems by finite dimensional optimization problems under various constraints. We propose a numerical framework in dimensions two and three and we present applications from the field of convex geometry. We consider the optimization of functionals depending on the volume, perimeter and Dirichlet Laplace eigenvalues under the aforementioned constraints. In particular we confirm numerically Meissner’s conjecture, regarding three dimensional bodies of constant width with minimal volume.

Suggested Citation

  • Pedro R. S. Antunes & Beniamin Bogosel, 2022. "Parametric shape optimization using the support function," Computational Optimization and Applications, Springer, vol. 82(1), pages 107-138, May.
    • Handle: RePEc:spr:coopap:v:82:y:2022:i:1:d:10.1007_s10589-022-00360-4
    DOI: 10.1007/s10589-022-00360-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-022-00360-4
    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/s10589-022-00360-4?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. Shengfeng Zhu, 2018. "Effective Shape Optimization of Laplace Eigenvalue Problems Using Domain Expressions of Eulerian Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 17-34, January.
    2. Pedro R. S. Antunes & Pedro Freitas, 2012. "Numerical Optimization of Low Eigenvalues of the Dirichlet and Neumann Laplacians," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 235-257, July.
    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. Torra, Vicenç, 2023. "The transport problem for non-additive measures," European Journal of Operational Research, Elsevier, vol. 311(2), pages 679-689.

    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. Meizhi Qian & Shengfeng Zhu, 2022. "A level set method for Laplacian eigenvalue optimization subject to geometric constraints," Computational Optimization and Applications, Springer, vol. 82(2), pages 499-524, June.
    2. Shengfeng Zhu, 2018. "Effective Shape Optimization of Laplace Eigenvalue Problems Using Domain Expressions of Eulerian Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 17-34, January.

    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:82:y:2022:i:1:d:10.1007_s10589-022-00360-4. 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.