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Linear convergence analysis of the use of gradient projection methods on total variation problems

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  • Pengwen Chen
  • Changfeng Gui

Abstract

Optimization problems using total variation frequently appear in image analysis models, in which the sharp edges of images are preserved. Direct gradient descent methods usually yield very slow convergence when used for such optimization problems. Recently, many duality-based gradient projection methods have been proposed to accelerate the speed of convergence. In this dual formulation, the cost function of the optimization problem is singular, and the constraint set is not a polyhedral set. In this paper, we establish two inequalities related to projected gradients and show that, under some non-degeneracy conditions, the rate of convergence is linear. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Pengwen Chen & Changfeng Gui, 2013. "Linear convergence analysis of the use of gradient projection methods on total variation problems," Computational Optimization and Applications, Springer, vol. 54(2), pages 283-315, March.
    • Handle: RePEc:spr:coopap:v:54:y:2013:i:2:p:283-315
    DOI: 10.1007/s10589-011-9412-4
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    References listed on IDEAS

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    1. NESTEROV, Yu., 2007. "Gradient methods for minimizing composite objective function," LIDAM Discussion Papers CORE 2007076, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Mingqiang Zhu & Stephen Wright & Tony Chan, 2010. "Duality-based algorithms for total-variation-regularized image restoration," Computational Optimization and Applications, Springer, vol. 47(3), pages 377-400, November.
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