Fixed-Point Continuation for l1-Minimization: Methodology and Convergence

By Elaine T. Hale, Wotao Yin, Yin Zhang. SIAM Journal on Optimization, 2008

928 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/07b5e2f08bc1be6da9269e9c61e113d6e3526ff0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Lei Zhang
2. Wotao Yin
3. Wangmeng Zuo
4. Zhouchen Lin
5. Francis R. Bach
6. E.J. Candes
7. Julien Mairal
8. Xiangchu Feng

In Computational Theory and Mathematics

1. Stephen P. Boyd
2. Julien Mairal
3. Jieping Ye
4. Neal Parikh
5. Wotao Yin
6. E.J. Candes
7. Jun Liu
8. Yi Ma

In Numerical Analysis

1. Jieping Ye
2. Wotao Yin
3. Yi Ma
4. Zhouchen Lin
5. Yin Zhang
6. Zaiwen Wen
7. E.J. Candes
8. Stephen P. Boyd

Citations in the corpus

• Templates for convex cone problems with applications to sparse signal recovery (2010, methodology): “Hence, NESTA is efficient when AA∗ is a projector or, more generally, when the eigenvalues of AA∗ are well clustered.”
• Infrared Small Target Detection Based on Partial Sum of the Tensor Nuclear Norm (2019, background): “(soft thresholding operator) [53] Let τ > 0 and X, Y ∈ Rn1×n2 , define a l1 norm minimization problem as argmin X τ‖X‖1 + 1 2 ‖X−Y‖(2)F (4)”
• RASL: Robust alignment by sparse and low-rank decomposition for linearly correlated images (2010, methodology): “It has been suggested in [13, 22, 17] that employing a continuation technique on μ can yield drastically faster convergence when compared to using a fixed μ.”
• An alternating direction algorithm for matrix completion with nonnegative factors (2011, methodology): “(4) FPCA solves the same model using iterations based on an iterative shrinkagethresholding algorithm [15].”
• Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices via Convex Optimization (2009, methodology): “Our algorithm for solving (125) combines the algorithms of [4] for nuclear norm minimization and [31] for `(1)-norm minimization.”
• Incremental Majorization-Minimization Optimization with Application to Large-Scale Machine Learning (2014, methodology): “For instance, this is the case of gradientbased or proximal methods [3, 13, 24, 40, 48], expectation-maximization (EM) algorithms in statistics [16, 37], difference-of-convex (DC) programming [26], boosting [12, 15], some variational Bayes techniques used in machine learning [47], and the mean-shift”
• Proximal Algorithms (2013, positive): “For particular problems, such as the lasso, it is possible to prove additional stronger results about the performance of the proximal gradient method [102, 67, 58, 35].”
• Compressed Sensing With Quantized Measurements (2010, methodology): “In [27], the authors prove that this iteration converges to an op-”
• Approximation accuracy, gradient methods, and error bound for structured convex optimization (2010, background): “Homotopy approaches have been proposed to follow the solution as τ varies between 0 and ∞ [54, 63, 110].”
• FISTA-Net: Learning a Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging (2020, neutral): “adaptive LASSO which uses a large θ for the small k, and gradually reduces it as k increases to improve the accuracy [61].”
• Split Bregman Methods and Frame Based Image Restoration (2009, methodology): “The convergence of the above algorithm in various forms was analyzed in the above-mentioned papers.”