An ADMM Algorithm for a Class of Total Variation Regularized Estimation Problems

By B. Wahlberg, Stephen P. Boyd, Mariette Annergren, Yang Wang. 2012

280 citations recorded by the source corpus.

We present an alternating augmented Lagrangian method for convex optimization problems where the cost function is the sum of two terms, one that is separable in the variable blocks, and a second th ...

Subfields: Computational Mechanics, Management Science and Operations Research, Statistics and Probability

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Citations in the corpus

MRFalign: Protein Homology Detection through Alignment of Markov Random Fields (2014, methodology): “Some heuristics algorithms were proposed for choosing at each iteration, such as [43, 44].”
A Splitting Method for Optimal Control (2013, methodology): “Therefore, the total cost of finding the proximal step is no more than order T (n + m)3 flops, executed on a single processor; we can reduce this by employing multiple processors and carrying out the proximal optimizations in parallel.”
A Direct Algorithm for 1-D Total Variation Denoising (2013, methodology): “Evidence of this is that iterative methods are regularly proposed for 1-D TV denoising [32]–[34].”
Network Lasso: Clustering and Optimization in Large Graphs (2015, methodology): “The network lasso can be thought of as a special case of certain methods (Bayesian inference, general convex optimization) and a generalization of others (fused lasso [23], total variation [24, 26]).”
Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation (2015, background): “In theory, the value of σλ does not affect the reconstruction for a convex optimization problem, but in practice, a well-chosen value of σλ can substantially speed up ADMM convergence [24], [58], [59]; so the careful choice of σλ is important.”
Optimal Parameter Selection for the Alternating Direction Method of Multipliers (ADMM): Quadratic Problems (2013, methodology): “The method has found a large number of applications in diverse areas such as compressed sensing [2], regularized estimation [3], image processing [4], machine learning [5], and resource allocation in wireless networks [6].”
A Survey of Optimization Methods From a Machine Learning Perspective (2019, background): “In addition, under some speciﬁc problems, it can even deliver better convergence than the standard batch gradient descent.”
Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding (2013, background): “These techniques have been used in a broad range of applications including imaging [39–41], control [42–46], estimation [47], signal processing [48–51], finance [52], distributed optimization [53,54], and many others.”
MSplit LBI: Realizing Feature Selection and Dense Estimation Simultaneously in Few-shot and Zero-shot Learning (2018, methodology): “To deal with L 1 penalty and other constrains, the operator splitting ideas are adopted by introducing an augmented variable satisfying the sparsity (or non-negative) constraints, such as ADMM Wahlberg et al. (2012); Boyd et al. (2011).”