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The alternating direction method with multipliers (ADMM) has been one of most powerful and successful methods for solving various convex or nonconvex composite problems that arise in the fields of image & signal processing and machine learning.
S. Łojasiewicz, Une propri été topologique des sous-ensembles analytiques r¡äeels, Les Équations aux Dérivées Partielles, Éditions du Centre National de la Recherche Scientifique Paris, 87–89, 1963
1963
Earlier work this paper cites.
L. M. Bregman, The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex programming, USSR Computational Mathematics and Mathematical Physics, 7(3): 200–217, 1967
1967
Earlier work this paper cites.
R. Glowinski, A. Marroco, Sur lapproximation par elements finis dordre un, et la resolu- tion par penalisation-dualite dune classe de problemes de Dirichlet nonlineaires, Rev. Francaise dAut. Inf. Rech. Oper., R-2:41–76, 1975
1975
Earlier work this paper cites.
D. Gabay and B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite element approximation, Computers & Mathematics with Applications, 2:17–40, 1976
1976
Earlier work this paper cites.
J. Eckstein, Splitting methods for monotone operators with applications to parallel optimization, 1989, Ph.D Thesis, Operations Research Center, MIT
1989
Earlier work this paper cites.
J. Eckstein, D. P. Bertsekas, On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, 55(1):293–318, 1992
1992
Earlier work this paper cites.
L. Rudin, S. Osher, E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60:259–268, 1992
1992
Earlier work this paper cites.
G. Chen, M. Teboulle, A proximal-based decomposition method for convex minimization problems, Mathematical Programming, 64(1-3): 81–101, 1994
1994
Earlier work this paper cites.
K. Kurdyka, On gradients of functions definable in o-minimal structures, Annales de l¡¯institut Fourier (Grenoble) 48(3):769–783, 1998
1998
Earlier work this paper cites.
A. Banerjee, S. Merugu, I. Dhillon, et al., Clustering with Bregman divergences, Journal of Machine Learning Research, 6: 1705–1749, 2005
2005
Earlier work this paper cites.
B. Mordukhovich, Variational Analysis and Generalized Differentiation, I: Basic Theory, Springer-Verlag, Berlin, 2006
2006
Earlier work this paper cites.
J. Bolte, A. Daniilidis, A. Lewis, The Łojasiewicz inequality for nonsmooth sub-analytic functions with applications to subgradient dynamical systems, SIAM J. Optim., 17:1205–1223, 2007
2007
Earlier work this paper cites.
R. Chartrand, Exact reconstruction of sparse signals via nonconvex minimization, IEEE Signal Processing Letters, 14(10): 707-710, 2007
2007
Earlier work this paper cites.
E. J. Candès, M. B. Wakinm, S.P. Boyd, Enhancing sparsity by reweighted ℓ 1 \ell_{1} minimization. Journal of Fourier Analysis and Applications, 14(5): 877–905, 2008
2008
Earlier work this paper cites.
R. Chartrand, V. Staneva, Restricted isometry properties and nonconvex compressive sensing, Inverse Problems, 24: 1-14, 2008
2008
Earlier work this paper cites.
J. Wright, A. Yang, A. Ganesh, et al., Robust face recognition via sparse representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 31(2): 210-227, 2008
2008
Earlier work this paper cites.
E. Esser, Applications of Lagrangian-based alternating direction methods and connections to split Bregman, CAM report 9:31, 2009
2009
Cited alongside, same era.
X. Chen, M. Zhou, Convergence of reweighted l1 minimization algorithms and unique solution of truncated lp minimization, Department of Applied Mathematics, The Hong Kong Polytechnic University, 2010
2010
Cited alongside, same era.
M. Lai, J. Wang, An unconstrained l q l_{q} minimization with 0 < q ≤ 1 0<q\leq 1 for sparse solution of underdetermined linear systems, SIAM J. Optim., 21, 82–101, 2010
2010
Cited alongside, same era.
T. Zhang, Analysis of multi-stage convex relaxation for sparse regularization, Journal of Machine Learning Research, 11: 1081-1107, 2010
2010
Cited alongside, same era.
Y. Zhang, An alternating direction algorithm for nonnegative matrix factorization, preprint, 2010
H. Attouch, J. Bolte, B.F. Svaiter, Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods, Mathematical Programming, 137(1-2): 91-129, 2013
2013
Later among the works it cites.
2013
Later among the works it cites.
2013
Later among the works it cites.
A. Kaban, Fractional norm regularization: learning with very few relevant features, IEEE Trans. Neural Networks and Learning Systems, 24(6): 953-963, 2013
2013
Later among the works it cites.
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2010
Cited alongside, same era.
S. Boyd, N. Parikh, E. Chu, et al., Distributed optimization and statistical learning via the alternating direction method of multipliers, Foundations and Trends in Machine Learning, 3(1): 1–122, 2011
2011
Cited alongside, same era.
Y. Qian, S. Jia, J. Zhou, et al., Hyperspectral unmixing via L 1 / 2 L_{1/2} sparsity-constrained nonnegative matrix factorization, IEEE Transaction on Geoscience and Remote Sensing, 49(11): 4282-4297, 2011
2011
Cited alongside, same era.
2011
Cited alongside, same era.
W. Deng, W. Yin, On the global linear convergence of alternating direction methods, 2012, preprint
2012
Cited alongside, same era.
T. Goldstein, B. O. Donoghue, S. Setzer, Fast alternating direction optimization methods, UCLA CAM technical report, 2012
2012
Cited alongside, same era.
B. He, X. Yuan, On the O(1/n) convergence rate of the Douglas-Rachford alternating direction method, SIAM Journal on Numerical Analysis, 50(2):700–709, 2012
2012
Cited alongside, same era.
H. Wang, A. Banerjee, Online alternating direction method. In International Conference on Machine Learning (ICML), 2012
2012
Cited alongside, same era.
2013
Later among the works it cites.
R. Monteiro, B. Svaiter, Iteration-complexity of block-decomposition algorithms and the alternating direction method of multipliers, SIAM Journal on Optimization, 23(1):475–507, 2013
2013
Later among the works it cites.
Y. Xu, W. Yin, A block coordinate descent method for regularized multiconvex optimization with applications to nonnegative tensor factorization and completion, SIAM J. Imaging Sciences, 6(3): 1758–1789, 2013
2013
Later among the works it cites.
J. Zeng, Z. Xu, B. Zhang, et al., Accelerated L 1 / 2 L_{1/2} regularization based SAR imaging via BCR and reduced Newton skills, Signal Processing, 93: 1831-1844, 2013
2013
Later among the works it cites.
J. Bolte, S. Sabach, M. Teboulle, Proximal alternating linearized minimization for nonconvex and nonsmooth problems, Mathematical Programming, 146(1-2):459–494, 2014
2014
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2014
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2014
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Z. Lu, Iterative reweighted minimization methods for l p l_{p} regularized unconstrained nonlinear programming, Mathematical Programming, 147:277-307, 2014
2014
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H. Wang, A. Banerjee, Bregman Alternating Direction Method of Multipliers, Neural Information Processing System (NIPS), 2014
2014
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J. Zeng, S. Lin, Y. Wang, Z. Xu, L 1 / 2 L_{1/2} Regularization: Convergence of Iterative Half Thresholding Algorithm, IEEE Transactions on Signal Processing, 62(9):2317–2329, 2014
2014
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R. Zhang, J. Kwok, Asynchronous distributed ADMM for consensus optimization, Proceedings of the 31st International Conference on Machine Learning (ICML-14). 2014: 1701–1709
2014
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