TVAL3: TV minimization by Augmented Lagrangian and ALternating direction ALgorithms: 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.

References in zbMATH (referenced in 23 articles , 1 standard article )

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  1. Kruse, René-Marcel; Silbersdorff, Alexander; Säfken, Benjamin: Model averaging for linear mixed models via augmented Lagrangian (2022)
  2. Chen, Yunmei; Liu, Hongcheng; Ye, Xiaojing; Zhang, Qingchao: Learnable descent algorithm for nonsmooth nonconvex image reconstruction (2021)
  3. Galli, Leonardo; Galligari, Alessandro; Sciandrone, Marco: A unified convergence framework for nonmonotone inexact decomposition methods (2020)
  4. García-Marina, V.; Fernández de Bustos, I.; Urkullu, G.; Ansola, R.: Optimum dimensional synthesis of planar mechanisms with geometric constraints (2020)
  5. Kikuchi, Paula A.; Oliveira, Aurelio R. L.: New preconditioners applied to linear programming and the compressive sensing problems (2020)
  6. Glaubitz, Jan; Gelb, Anne: High order edge sensors with (\ell^1) regularization for enhanced discontinuous Galerkin methods (2019)
  7. Liu, Ya-Feng; Liu, Xin; Ma, Shiqian: On the nonergodic convergence rate of an inexact augmented Lagrangian framework for composite convex programming (2019)
  8. Liu, Zexian; Liu, Hongwei; Wang, Xiping: Accelerated augmented Lagrangian method for total variation minimization (2019)
  9. Theeda, Prasad; Kumar, P. U. Praveen; Sastry, C. S.; Jampana, P. V.: Reconstruction of sparse-view tomography via preconditioned Radon sensing matrix (2019)
  10. Xue, Jize; Zhao, Yongqiang; Liao, Wenzhi; Chan, Jonathan Cheung-Wai: Hyper-Laplacian regularized nonlocal low-rank matrix recovery for hyperspectral image compressive sensing reconstruction (2019)
  11. Zhu, Jiehua; Li, Xiezhang: A smoothed (l_0)-norm and (l_1)-norm regularization algorithm for computed tomography (2019)
  12. Sanders, Toby: Parameter selection for HOTV regularization (2018)
  13. Scarnati, Theresa; Gelb, Anne; Platte, Rodrigo B.: Using (\ell_1) regularization to improve numerical partial differential equation solvers (2018)
  14. Zhang, Linan; Schaeffer, Hayden: Stability and error estimates of BV solutions to the Abel inverse problem (2018)
  15. Chen, Yunmei; Li, Xianqi; Ouyang, Yuyuan; Pasiliao, Eduardo: Accelerated Bregman operator splitting with backtracking (2017)
  16. Chow, Yat Tin; Wu, Tianyu; Yin, Wotao: Cyclic coordinate-update algorithms for fixed-point problems: analysis and applications (2017)
  17. Keshvari, Abolfazl: A penalized method for multivariate concave least squares with application to productivity analysis (2017)
  18. Sanders, Toby; Gelb, Anne; Platte, Rodrigo B.: Composite SAR imaging using sequential joint sparsity (2017)
  19. Dassios, Ioannis; Fountoulakis, Kimon; Gondzio, Jacek: A preconditioner for a primal-dual Newton conjugate gradient method for compressed sensing problems (2015)
  20. Schaeffer, Hayden; Yang, Yi; Osher, Stanley: Space-time regularization for video decompression (2015)

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