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An efficient augmented Lagrangian method with applications to total variation minimization

Author

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  • Chengbo Li

    ()

  • Wotao Yin

    ()

  • Hong Jiang

    ()

  • Yin Zhang

    ()

Abstract

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
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    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.

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