IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v64y2016i3p451-468.html
   My bibliography  Save this article

A new semi-smooth Newton multigrid method for control-constrained semi-linear elliptic PDE problems

Author

Listed:
  • Jun Liu
  • Mingqing Xiao

Abstract

In this paper a new multigrid algorithm is proposed to accelerate the convergence of the semi-smooth Newton method that is applied to the first order necessary optimality systems arising from a class of semi-linear control-constrained elliptic optimal control problems. Under admissible assumptions on the nonlinearity, the discretized Jacobian matrix is proved to have an uniformly bounded inverse with respect to mesh size. Different from current available approaches, a new numerical implementation that leads to a robust multigrid solver is employed to coarsen the grid operator. Numerical simulations are provided to illustrate the efficiency of the proposed method, which shows to be computationally more efficient than the full-approximation-storage multigrid in current literature. In particular, our proposed approach achieves a mesh-independent convergence and its performance is highly robust with respect to the regularization parameter. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • Jun Liu & Mingqing Xiao, 2016. "A new semi-smooth Newton multigrid method for control-constrained semi-linear elliptic PDE problems," Journal of Global Optimization, Springer, vol. 64(3), pages 451-468, March.
    • Handle: RePEc:spr:jglopt:v:64:y:2016:i:3:p:451-468
    DOI: 10.1007/s10898-014-0206-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-014-0206-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-014-0206-y?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.

    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:64:y:2016:i:3:p:451-468. 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: 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.