IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v130y2006i3d10.1007_s10957-006-9118-4.html
   My bibliography  Save this article

Parametric Method for Global Optimization

Author

Listed:
  • S. De Marchi

    (University of Verona)

  • I. Raykov

    (Ohio University)

Abstract

This paper considers constrained and unconstrained parametric global optimization problems in a real Hilbert space. We assume that the gradient of the cost functional is Lipschitz continuous but not smooth. A suitable choice of parameters implies the linear or superlinear (supergeometric) convergence of the iterative method. From the numerical experiments, we conclude that our algorithm is faster than other existing algorithms for continuous but nonsmooth problems, when applied to unconstrained global optimization problems. However, because we solve 2n + 1 subproblems for a large number n of independent variables, our algorithm is somewhat slower than other algorithms, when applied to constrained global optimization.

Suggested Citation

  • S. De Marchi & I. Raykov, 2006. "Parametric Method for Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 411-430, September.
    • Handle: RePEc:spr:joptap:v:130:y:2006:i:3:d:10.1007_s10957-006-9118-4
    DOI: 10.1007/s10957-006-9118-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-006-9118-4
    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/s10957-006-9118-4?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. Daniel Ralph, 1994. "Global Convergence of Damped Newton's Method for Nonsmooth Equations via the Path Search," Mathematics of Operations Research, INFORMS, vol. 19(2), pages 352-389, May.
    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. Efstratios Pistikopoulos & Luis Dominguez & Christos Panos & Konstantinos Kouramas & Altannar Chinchuluun, 2012. "Theoretical and algorithmic advances in multi-parametric programming and control," Computational Management Science, Springer, vol. 9(2), pages 183-203, May.
    2. N. Pavel & I. Raykov, 2008. "Parametric Proximal-Point Methods," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 85-107, October.

    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. Victor DeMiguel & Huifu Xu, 2009. "A Stochastic Multiple-Leader Stackelberg Model: Analysis, Computation, and Application," Operations Research, INFORMS, vol. 57(5), pages 1220-1235, October.
    2. Hu, X. & Ralph, R., 2006. "Using EPECs to model bilevel games in restructured electricity markets with locational prices," Cambridge Working Papers in Economics 0619, Faculty of Economics, University of Cambridge.
    3. Xinmin Hu & Daniel Ralph & Eric K. Ralph & Peter Bardsley & Michael C. Ferris, 2004. "Electricity Generation with Looped Transmission Networks: Bidding to an ISO," Working Papers EP65, Energy Policy Research Group, Cambridge Judge Business School, University of Cambridge.
    4. N. Pavel & I. Raykov, 2008. "Parametric Proximal-Point Methods," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 85-107, October.
    5. Roland Hildebrand, 2021. "Optimal step length for the Newton method: case of self-concordant functions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(2), pages 253-279, October.
    6. Maeda, Koushi & Suzuki, Xohuhiro & Kaiser, Harry M., 2001. "An Economic Evaluation Of The New Agricultural Trade Negotiations: A Nonlinear Imperfectly Competitive Spatial Equilibrium Approach," Working Papers 7231, Cornell University, Department of Applied Economics and Management.
    7. Xinmin Hu & Daniel Ralph, 2007. "Using EPECs to Model Bilevel Games in Restructured Electricity Markets with Locational Prices," Operations Research, INFORMS, vol. 55(5), pages 809-827, October.

    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:130:y:2006:i:3:d:10.1007_s10957-006-9118-4. 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.