IDEAS home Printed from
   My bibliography  Save this article

An efficient augmented Lagrangian method with applications to total variation minimization


  • Chengbo Li


  • Wotao Yin


  • Hong Jiang


  • Yin Zhang



Based on the classic augmented Lagrangian multiplier method, we propose, analyze and test an algorithm for solving a class of equality-constrained non-smooth optimization problems (chiefly but not necessarily convex programs) with a particular structure. The algorithm effectively combines an alternating direction technique with a nonmonotone line search to minimize the augmented Lagrangian function at each iteration. We establish convergence for this algorithm, and apply it to solving problems in image reconstruction with total variation regularization. We present numerical results showing that the resulting solver, called TVAL3, is competitive with, and often outperforms, other state-of-the-art solvers in the field. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Chengbo Li & Wotao Yin & Hong Jiang & Yin Zhang, 2013. "An efficient augmented Lagrangian method with applications to total variation minimization," Computational Optimization and Applications, Springer, vol. 56(3), pages 507-530, December.
  • Handle: RePEc:spr:coopap:v:56:y:2013:i:3:p:507-530
    DOI: 10.1007/s10589-013-9576-1

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.


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

    Cited by:

    1. Keshvari, Abolfazl, 2017. "A penalized method for multivariate concave least squares with application to productivity analysis," European Journal of Operational Research, Elsevier, vol. 257(3), pages 1016-1029.


    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:coopap:v:56:y:2013:i:3:p:507-530. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.