IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v94y1997i2d10.1023_a1022616327742.html
   My bibliography  Save this article

An Optimal Control Problem for Flows with Discontinuities

Author

Listed:
  • E. M. Cliff

    (Virginia Polytechnic Institute and State University)

  • M. Heinkenschloss

    (Rice University)

  • A. R. Shenoy

    (Virginia Polytechnic Institute and State University)

Abstract

In this paper, we study a design problem for a duct flow with a shock. The presence of the shock causes numerical difficulties. Good shock-capturing schemes with low continuity properties often cannot be combined successfully with efficient optimization methods requiring smooth functions. A remedy studied in this paper is to introduce the shock location as an explicit variable. This allows one to fit the shock and yields a problem with sufficiently smooth functions. We prove the existence of optimal solutions, Fréchet differentiability, and the existence of Lagrange multipliers. In the second part, we introduce and investigate the discrete problem and study the relations between the optimality conditions for the infinite-dimensional problem and the discretized one. This reveals important information for the numerical solution of the problem. Numerical examples are given to demonstrate the theoretical findings.

Suggested Citation

  • E. M. Cliff & M. Heinkenschloss & A. R. Shenoy, 1997. "An Optimal Control Problem for Flows with Discontinuities," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 273-309, August.
  • Handle: RePEc:spr:joptap:v:94:y:1997:i:2:d:10.1023_a:1022616327742
    DOI: 10.1023/A:1022616327742
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1022616327742
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1023/A:1022616327742?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.

    Citations

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


    Cited by:

    1. Vicente, Luis N., 2002. "Local analysis of a new multipliers method," European Journal of Operational Research, Elsevier, vol. 143(2), pages 432-451, December.
    2. Alina Chertock & Michael Herty & Alexander Kurganov, 2014. "An Eulerian–Lagrangian method for optimization problems governed by multidimensional nonlinear hyperbolic PDEs," Computational Optimization and Applications, Springer, vol. 59(3), pages 689-724, December.
    3. Fang, Jianshu & Hai, Wenhua & Chong, Guishu & Xie, Qiongtao, 2005. "Chaotic Josephson effects in two-coupled Bose–Einstein condensates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(1), pages 133-142.

    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:joptap:v:94:y:1997:i:2:d:10.1023_a:1022616327742. 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.