IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v56y2013i4p1361-1373.html
   My bibliography  Save this article

An adaptive domain decomposition method for the Hamilton–Jacobi–Bellman equation

Author

Listed:
  • H. Alwardi
  • S. Wang
  • L. Jennings

Abstract

In this paper, we propose an efficient algorithm for a Hamilton–Jacobi–Bellman equation governing a class of optimal feedback control and stochastic control problems. This algorithm is based on a non-overlapping domain decomposition method and an adaptive least-squares collocation radial basis function discretization with a novel matrix inversion technique. To demonstrate the efficiency of this method, numerical experiments on test problems with up to three states and two control variables have been performed. The numerical results show that the proposed algorithm is highly parallelizable and its computational cost decreases exponentially as the number of sub-domains increases. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • H. Alwardi & S. Wang & L. Jennings, 2013. "An adaptive domain decomposition method for the Hamilton–Jacobi–Bellman equation," Journal of Global Optimization, Springer, vol. 56(4), pages 1361-1373, August.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:4:p:1361-1373
    DOI: 10.1007/s10898-012-9850-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-012-9850-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-012-9850-2?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. Pereyra, V. & Scherer, G., 2006. "Least squares collocation solution of elliptic problems in general regions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(1), pages 226-230.
    2. Antanas Žilinskas, 2010. "On similarities between two models of global optimization: statistical models and radial basis functions," Journal of Global Optimization, Springer, vol. 48(1), pages 173-182, September.
    Full references (including those not matched with items on IDEAS)

    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. H. Alwardi & S. Wang & L. Jennings & S. Richardson, 2012. "An adaptive least-squares collocation radial basis function method for the HJB equation," Journal of Global Optimization, Springer, vol. 52(2), pages 305-322, February.
    2. M. Rivier & P. M. Congedo, 2019. "Surrogate-assisted Bounding-Box approach for optimization problems with tunable objectives fidelity," Journal of Global Optimization, Springer, vol. 75(4), pages 1079-1109, December.
    3. Ma, Jichao & Wei, Gaofeng & Liu, Dandan & Liu, Gongtian, 2017. "The numerical analysis of piezoelectric ceramics based on the Hermite-type RPIM," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 170-182.
    4. Yaroslav D. Sergeyev & Marat S. Mukhametzhanov & Dmitri E. Kvasov & Daniela Lera, 2016. "Derivative-Free Local Tuning and Local Improvement Techniques Embedded in the Univariate Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 186-208, October.
    5. Albertas Gimbutas & Antanas Žilinskas, 2018. "An algorithm of simplicial Lipschitz optimization with the bi-criteria selection of simplices for the bi-section," Journal of Global Optimization, Springer, vol. 71(1), pages 115-127, May.
    6. Daniela Lera & Yaroslav D. Sergeyev, 2018. "GOSH: derivative-free global optimization using multi-dimensional space-filling curves," Journal of Global Optimization, Springer, vol. 71(1), pages 193-211, May.
    7. Kvasov, Dmitri E. & Mukhametzhanov, Marat S., 2018. "Metaheuristic vs. deterministic global optimization algorithms: The univariate case," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 245-259.
    8. Grishagin, Vladimir & Israfilov, Ruslan & Sergeyev, Yaroslav, 2018. "Convergence conditions and numerical comparison of global optimization methods based on dimensionality reduction schemes," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 270-280.
    9. Sergeyev, Yaroslav D. & Kvasov, Dmitri E. & Mukhametzhanov, Marat S., 2017. "Operational zones for comparing metaheuristic and deterministic one-dimensional global optimization algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 96-109.
    10. R. Cavoretto & A. Rossi & M. S. Mukhametzhanov & Ya. D. Sergeyev, 2021. "On the search of the shape parameter in radial basis functions using univariate global optimization methods," Journal of Global Optimization, Springer, vol. 79(2), pages 305-327, February.
    11. Ray-Bing Chen & Yuan Wang & C. F. Jeff Wu, 2020. "Finding optimal points for expensive functions using adaptive RBF-based surrogate model via uncertainty quantification," Journal of Global Optimization, Springer, vol. 77(4), pages 919-948, August.

    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:56:y:2013:i:4:p:1361-1373. 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.