IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v160y2014i1d10.1007_s10957-013-0354-0.html
   My bibliography  Save this article

Derivative-Free Optimization Via Proximal Point Methods

Author

Listed:
  • W. L. Hare

    (University of British Columbia, Okanagan Campus (UBCO))

  • Y. Lucet

    (UBCO)

Abstract

Derivative-Free Optimization (DFO) examines the challenge of minimizing (or maximizing) a function without explicit use of derivative information. Many standard techniques in DFO are based on using model functions to approximate the objective function, and then applying classic optimization methods to the model function. For example, the details behind adapting steepest descent, conjugate gradient, and quasi-Newton methods to DFO have been studied in this manner. In this paper we demonstrate that the proximal point method can also be adapted to DFO. To that end, we provide a derivative-free proximal point (DFPP) method and prove convergence of the method in a general sense. In particular, we give conditions under which the gradient values of the iterates converge to 0, and conditions under which an iterate corresponds to a stationary point of the objective function.

Suggested Citation

  • W. L. Hare & Y. Lucet, 2014. "Derivative-Free Optimization Via Proximal Point Methods," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 204-220, January.
  • Handle: RePEc:spr:joptap:v:160:y:2014:i:1:d:10.1007_s10957-013-0354-0
    DOI: 10.1007/s10957-013-0354-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-013-0354-0
    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/s10957-013-0354-0?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. Krzysztof C. Kiwiel, 2010. "An Inexact Bundle Approach to Cutting-Stock Problems," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 131-143, February.
    2. Charles Audet & J. Dennis & Sébastien Digabel, 2010. "Globalization strategies for Mesh Adaptive Direct Search," Computational Optimization and Applications, Springer, vol. 46(2), pages 193-215, June.
    3. W. Hare, 2009. "A proximal method for identifying active manifolds," Computational Optimization and Applications, Springer, vol. 43(2), pages 295-306, June.
    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. Tommaso Giovannelli & Giampaolo Liuzzi & Stefano Lucidi & Francesco Rinaldi, 2022. "Derivative-free methods for mixed-integer nonsmooth constrained optimization," Computational Optimization and Applications, Springer, vol. 82(2), pages 293-327, June.
    2. Jiyuan Zhang & Bin Zhang & Shiqian Xu & Qihong Feng & Xianmin Zhang & Derek Elsworth, 2021. "Interpretation of Gas/Water Relative Permeability of Coal Using the Hybrid Bayesian-Assisted History Matching: New Insights," Energies, MDPI, vol. 14(3), pages 1-19, January.
    3. Wim Ackooij & Welington Oliveira, 2014. "Level bundle methods for constrained convex optimization with various oracles," Computational Optimization and Applications, Springer, vol. 57(3), pages 555-597, April.
    4. Cui, Yaodong & Huang, Baixiong, 2012. "Reducing the number of cuts in generating three-staged cutting patterns," European Journal of Operational Research, Elsevier, vol. 218(2), pages 358-365.
    5. Moody Chu & Matthew Lin & Liqi Wang, 2014. "A study of singular spectrum analysis with global optimization techniques," Journal of Global Optimization, Springer, vol. 60(3), pages 551-574, November.
    6. Boukouvala, Fani & Misener, Ruth & Floudas, Christodoulos A., 2016. "Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO," European Journal of Operational Research, Elsevier, vol. 252(3), pages 701-727.
    7. Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2016. "Bin packing and cutting stock problems: Mathematical models and exact algorithms," European Journal of Operational Research, Elsevier, vol. 255(1), pages 1-20.
    8. J. Martínez & F. Sobral, 2013. "Constrained derivative-free optimization on thin domains," Journal of Global Optimization, Springer, vol. 56(3), pages 1217-1232, July.
    9. Charles Audet & Andrew R. Conn & Sébastien Le Digabel & Mathilde Peyrega, 2018. "A progressive barrier derivative-free trust-region algorithm for constrained optimization," Computational Optimization and Applications, Springer, vol. 71(2), pages 307-329, November.
    10. Giovanni Stracquadanio & Elisa Pappalardo & Panos M. Pardalos, 2012. "A Mesh Adaptive Basin Hopping Method for the Design of Circular Antenna Arrays," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 1008-1024, December.

    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:160:y:2014:i:1:d:10.1007_s10957-013-0354-0. 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.