Augmented Lagrangian alternating direction method for matrix separation based on low-rank factorization

By Yuan Shen, Zaiwen Wen, Yin Zhang. Optim. Methods Softw., 2014

330 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/ef872f76b9d0a9e171b633c8473934212296b003

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Citations in the corpus

Efficient $l_{1}$ -Norm-Based Low-Rank Matrix Approximations for Large-Scale Problems Using Alternating Rectified Gradient Method (2015, methodology): “and Wl1-ARGD) in Sections IV and V, and the performances were compared with those of other methods that can handle missing data (ALADM-MC, which is a matrix completion (MC) version of ALADM [8], Regl1-ALM [10]).”
Global Convergence of ADMM in Nonconvex Nonsmooth Optimization (2015, background): “Indeed, the nonconvex case of the problem (1) has found wide applications in, for example, matrix completion and separation [73,72,77,54,57], asset allocation [65], tensor factorization [35], phase retrieval [66], compressive sensing [10], optimal power flow [74], direction fields correction [32], n”
A Distributed, Asynchronous and Incremental Algorithm for Nonconvex Optimization: An ADMM Based Approach (2014, background): “However, despite various successful numerical attempts (see, e.g., [34]–[42]), little is known about whether ADMM is capable of handling nonconvex optimization problems, or whether it can be used in an asynchronous setting.”
Tensor Factorization for Low-Rank Tensor Completion (2018, neutral): “Besides, by directly restricting the rank of the estimation, the low-rank factorization methods can also well recover the low-rank data and achieve stateof-the-art completion results in image/video inpainting [25], [27], [28], and collaborative filtering [26], [29].”
Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm (2012, methodology): “A possible acceleration technique may involve applying an extension of the classic augmented-Lagrangianbased alternating direction method (ADM) for convex optimization to the factorization model (see [31,37,41] for such ADM extensions).”
Robust Low-Rank Tensor Recovery: Models and Algorithms (2013, methodology): “First, we use a technique from [41] to convert condition (3.”
Group sparse optimization by alternating direction method (2013, neutral): “Finally, the multipliers λ1 and λ2 are updated in the standard way { λ1 ← λ1 − γ1β1(z − x), λ2 ← λ2 − γ2β2(Ax− b), (14)”
Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset (2015, methodology): “The authors would like to thank the following researchers: Zhouchen Lin (Visual Computing Group, Microsoft Research Asia) who has kindly provided the solver LADMAP [232] and the l1-filtering [236], Shiqian Ma (Institute for Mathematics and Its Applications, Univ. of Minnesota, USA) who has kindly pr”