IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v140y2009i1d10.1007_s10957-008-9471-6.html
   My bibliography  Save this article

Approximation Schemes for Functional Optimization Problems

Author

Listed:
  • S. Giulini

    (University of Genoa)

  • M. Sanguineti

    (University of Genoa)

Abstract

Approximation schemes for functional optimization problems with admissible solutions dependent on a large number d of variables are investigated. Suboptimal solutions are considered, expressed as linear combinations of n-tuples from a basis set of simple computational units with adjustable parameters. Different choices of basis sets are compared, which allow one to obtain suboptimal solutions using a number n of basis functions that does not grow “fast” with the number d of variables in the admissible decision functions for a fixed desired accuracy. In these cases, one mitigates the “curse of dimensionality,” which often makes unfeasible traditional linear approximation techniques for functional optimization problems, when admissible solutions depend on a large number d of variables.

Suggested Citation

  • S. Giulini & M. Sanguineti, 2009. "Approximation Schemes for Functional Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 33-54, January.
    • Handle: RePEc:spr:joptap:v:140:y:2009:i:1:d:10.1007_s10957-008-9471-6
    DOI: 10.1007/s10957-008-9471-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-008-9471-6
    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/s10957-008-9471-6?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. A. Alessandri & C. Cervellera & M. Sanguineti, 2007. "Functional Optimal Estimation Problems and Their Solution by Nonlinear Approximation Schemes," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 445-466, September.
    2. R. Zoppoli & M. Sanguineti & T. Parisini, 2002. "Approximating Networks and Extended Ritz Method for the Solution of Functional Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 403-440, February.
    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. Mauro Gaggero & Giorgio Gnecco & Marcello Sanguineti, 2014. "Approximate dynamic programming for stochastic N-stage optimization with application to optimal consumption under uncertainty," Computational Optimization and Applications, Springer, vol. 58(1), pages 31-85, May.
    2. G. Gnecco & M. Sanguineti, 2010. "Estimates of Variation with Respect to a Set and Applications to Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 53-75, April.
    3. G. Gnecco & M. Sanguineti, 2010. "Suboptimal Solutions to Dynamic Optimization Problems via Approximations of the Policy Functions," Journal of Optimization Theory and Applications, Springer, vol. 146(3), pages 764-794, September.
    4. Giorgio Gnecco, 2016. "On the Curse of Dimensionality in the Ritz Method," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 488-509, February.

    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. Giorgio Gnecco, 2016. "On the Curse of Dimensionality in the Ritz Method," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 488-509, February.
    2. Angelo Alessandri & Giorgio Gnecco & Marcello Sanguineti, 2010. "Minimizing Sequences for a Family of Functional Optimal Estimation Problems," Journal of Optimization Theory and Applications, Springer, vol. 147(2), pages 243-262, November.
    3. G. Gnecco & M. Sanguineti, 2010. "Estimates of Variation with Respect to a Set and Applications to Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 53-75, April.
    4. A. Alessandri & L. Cassettari & R. Mosca, 2009. "Nonparametric nonlinear regression using polynomial and neural approximators: a numerical comparison," Computational Management Science, Springer, vol. 6(1), pages 5-24, February.
    5. G. Gnecco & M. Sanguineti, 2010. "Suboptimal Solutions to Dynamic Optimization Problems via Approximations of the Policy Functions," Journal of Optimization Theory and Applications, Springer, vol. 146(3), pages 764-794, September.
    6. Mauro Gaggero & Giorgio Gnecco & Marcello Sanguineti, 2013. "Dynamic Programming and Value-Function Approximation in Sequential Decision Problems: Error Analysis and Numerical Results," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 380-416, February.
    7. M. Baglietto & C. Cervellera & M. Sanguineti & R. Zoppoli, 2010. "Management of water resource systems in the presence of uncertainties by nonlinear approximation techniques and deterministic sampling," Computational Optimization and Applications, Springer, vol. 47(2), pages 349-376, October.
    8. Andrea Bacigalupo & Giorgio Gnecco & Marco Lepidi & Luigi Gambarotta, 2020. "Machine-Learning Techniques for the Optimal Design of Acoustic Metamaterials," Journal of Optimization Theory and Applications, Springer, vol. 187(3), pages 630-653, December.
    9. Cristiano Cervellera & Danilo Macciò & Marco Muselli, 2010. "Functional Optimization Through Semilocal Approximate Minimization," Operations Research, INFORMS, vol. 58(5), pages 1491-1504, October.
    10. Angelo Alessandri & Patrizia Bagnerini & Roberto Cianci & Mauro Gaggero, 2019. "Optimal Propagating Fronts Using Hamilton-Jacobi Equations," Mathematics, MDPI, vol. 7(11), pages 1-10, November.
    11. Mauro Gaggero & Giorgio Gnecco & Marcello Sanguineti, 2014. "Approximate dynamic programming for stochastic N-stage optimization with application to optimal consumption under uncertainty," Computational Optimization and Applications, Springer, vol. 58(1), pages 31-85, May.
    12. Cervellera, C. & Macciò, D., 2011. "A comparison of global and semi-local approximation in T-stage stochastic optimization," European Journal of Operational Research, Elsevier, vol. 208(2), pages 109-118, January.
    13. A. Alessandri & C. Cervellera & M. Sanguineti, 2007. "Functional Optimal Estimation Problems and Their Solution by Nonlinear Approximation Schemes," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 445-466, September.

    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:140:y:2009:i:1:d:10.1007_s10957-008-9471-6. 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.