IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v119y2003i3d10.1023_bjota.0000006687.57272.b6.html
   My bibliography  Save this article

Augmented Lagrangian Active Set Methods for Obstacle Problems

Author

Listed:
  • T. Kärkkäinen

    (University of Jyväskylä)

  • K. Kunisch

    (University of Graz)

  • P. Tarvainen

Abstract

Active set strategies for two-dimensional and three-dimensional, unilateral and bilateral obstacle problems are described. Emphasis is given to algorithms resulting from the augmented Lagrangian (i.e., primal-dual formulation of the discretized obstacle problems), for which convergence and rate of convergence are considered. For the bilateral case, modifications of the basic primal-dual algorithm are also introduced and analyzed. Finally, efficient computer realizations that are based on multigrid and multilevel methods are suggested and different aspects of the proposed techniques are investigated through numerical experiments.

Suggested Citation

  • T. Kärkkäinen & K. Kunisch & P. Tarvainen, 2003. "Augmented Lagrangian Active Set Methods for Obstacle Problems," Journal of Optimization Theory and Applications, Springer, vol. 119(3), pages 499-533, December.
    • Handle: RePEc:spr:joptap:v:119:y:2003:i:3:d:10.1023_b:jota.0000006687.57272.b6
    DOI: 10.1023/B:JOTA.0000006687.57272.b6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/B:JOTA.0000006687.57272.b6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/B:JOTA.0000006687.57272.b6?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.

    Citations

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


    Cited by:

    1. Arregui, Iñigo & Salvador, Beatriz & Vázquez, Carlos, 2017. "PDE models and numerical methods for total value adjustment in European and American options with counterparty risk," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 31-53.
    2. Salvador, Beatriz & Oosterlee, Cornelis W., 2021. "Corrigendum to ``Total value adjustment for a stochastic volatility model. A comparison with the Black–Scholes model''," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    3. Ráfales, Jonatan & Vázquez, Carlos, 2024. "Jump–diffusion productivity models in equilibrium problems with heterogeneous agents," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 313-331.
    4. Salvador, Beatriz & Oosterlee, Cornelis W., 2021. "Total value adjustment for a stochastic volatility model. A comparison with the Black–Scholes model," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    5. Calvo-Garrido, Maria del Carmen & Pascucci, Andrea & Vázquez Cendón, Carlos, 2012. "Mathematical analysis and numerical methods for pricing pension plans allowing early retirement," MPRA Paper 36494, University Library of Munich, Germany.
    6. Calvo-Garrido, María del Carmen & Vázquez, Carlos, 2015. "Effects of jump-diffusion models for the house price dynamics in the pricing of fixed-rate mortgages, insurance and coinsurance," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 730-742.

    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:119:y:2003:i:3:d:10.1023_b:jota.0000006687.57272.b6. 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.