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Motivated by learning problems including max-norm regularized matrix completion and clustering, robust PCA and sparse inverse covariance selection, we propose a novel optimization algorithm for minimizing a convex objective which decomposes into three parts: a smooth part, a simple non-smooth Lipschitz part, and a simple non-smooth non-Lipschitz part.
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On a generalization of the iterative soft-thresholding algorithm for the case of non-separable penalty
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L. Li and K.-C. Toh · 2010
Cited alongside, same era.
Sparse inverse covariance selection via alternating linearization methods
K. Scheinberg, S. Ma, and D. Goldfarb · 2010
Cited alongside, same era.
Trading accuracy for sparsity in optimization problems with sparsity constraints
S. Shalev-Shwartz, N. Srebro, and T. Zhang · 2010
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A fast augmented Lagrangian algorithm for learning low-rank matrices
R. Tomioka, T. Suzuki, M. Sugiyama, and H. Kashima · 2010
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H. H. Bauschke and P. L. Combettes · 2011
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Excessive gap technique in nonsmooth convex minimization
Y. Nesterov
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Smooth minimization of non-smooth functions
Y. Nesterov
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Fast alternating linearization methods for minimizing the sum of two convex functions
D. Goldfarb, S. Ma, and K. Scheinberg · 2012
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H. Ouyang and A. Gray · 2012
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