IDEAS home Printed from https://ideas.repec.org/h/spr/lnechp/978-3-540-28258-7_14.html
   My bibliography  Save this book chapter

Sufficiency Conditions for Infinite Horizon Optimal Control Problems

In: Recent Advances in Optimization

Author

Listed:
  • Sabine Pickenhain

    (Brandenburg University of Technology Cottbus)

  • Valeriya Lykina

    (Brandenburg University of Technology Cottbus)

Abstract

Summary In this paper we formulate and use the duality concept of Klötzler (1977) for infinite horizon optimal control problems. The main idea is choosing weighted Sobolev and weighted Lp spaces as the state and control spaces, respectively. Different criteria of optimality are known for specific problems, e.g. the overtaking criterion of von Weizsäcker (1965), the catching up criterion of Gale (1967) and the sporadically catching up criterion of Halkin (1974). Corresponding to these criteria we develop the duality theory and prove sufficient conditions for local optimality. Here we use some remarkable properties of weighted spaces. An example is presented where the solution is obtained in the framework of these weighted spaces, but which does not belong to standard Sobolev spaces.

Suggested Citation

  • Sabine Pickenhain & Valeriya Lykina, 2006. "Sufficiency Conditions for Infinite Horizon Optimal Control Problems," Lecture Notes in Economics and Mathematical Systems, in: Alberto Seeger (ed.), Recent Advances in Optimization, pages 217-232, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-28258-7_14
    DOI: 10.1007/3-540-28258-0_14
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

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


    Cited by:

    1. Valeriya Lykina, 2016. "An Existence Theorem for a Class of Infinite Horizon Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 50-73, April.
    2. A. J. Zaslavski, 2010. "Stability of a Turnpike Phenomenon for a Discrete-Time Optimal Control System," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 597-612, June.

    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:spr:lnechp:978-3-540-28258-7_14. 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.