An Interior-Point Method for Large-Scale $\ell_1$-Regularized Least Squares

By Seung-Jean Kim, Kwangmoo Koh, Michael Lustig, Stephen P. Boyd, Dimitry M. Gorinevsky. IEEE Journal on Selected Topics in Signal Processing, 2007

1,886 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mathematical Physics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/5acfb2abca580a40f2f6890371c2387527dfefc0

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Citations in the corpus

Sparse coding based visual tracking: Review and experimental comparison (2013, background): “(4) as a quadratic programming problem, namely, gradient projection sparse representation (GPSR) [24] and truncated Newton interior-point method (TNIPM) [25].”
Sparse Subspace Clustering: Algorithm, Theory, and Applications (2012, methodology): “i = Y ci, cii = 0, (4) which can be solved efficiently using convex programming tools [48], [49], [50] and is known to prefer sparse solutions [29], [30], [31].”
Optimization for machine learning (2010, methodology): “Other methods, for example interior point methods (Koh et al., 2007; Kim et al., 2007; Boyd and Vandenberghe, 2004), achieve sparsity only asymptotically.”
Solving inverse problems using data-driven models (2019, methodology): “A few examples are interior-point methods (Candès et al. 2006, Kim et al. 2007), projected gradient methods (Figueiredo, Nowak and Wright 2007), iterative soft thresholding (see Section 8.2.7) (Daubechies et al. 2004, Fornasier and Rauhut 2008) and fast proximal gradient methods (FISTA and…”
Sparse Shape Representation using the Laplace-Beltrami Eigenfunctions and Its Application to Modeling Subcortical Structures (2012, methodology): “Therefore, instead of using LSE, we introduce the additional l1-norm penalty to sparsely filter out insignificant low degree coefficients by minimizing [13]:”
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery (2009, methodology): “1 regularized least squares (l1 ls) [38].”
Compressive Sensing in Electromagnetics - A Review (2015, positive): “b x 1⁄4 arg min x kAx e yk‘1 n o (16) the “‘1-regularized least-square” method [34]”
Sparse Representation Based Fisher Discrimination Dictionary Learning for Image Classification (2014, methodology): “In the proposed FDDL algorithm, the update of coding coefficients for each sample is a sparse coding problem, whose time complexity is approximately O(q2 p) (Kim et al. 2007; Nesterov and Nemirovskii 1994), where ε ≥ 1.”
A Survey of Sparse Representation: Algorithms and Applications (2015, methodology): “For further description and analyses, please refer to the literature [74].”
Sparse multitask regression for identifying common mechanism of response to therapeutic targets (2010, methodology): “We use the l1-ls solver [16] for large scale L1 regularized least-square problems, which are based on the truncated Newton interior-point method.”
Real time robust L1 tracker using accelerated proximal gradient approach (2012, methodology): “The numerical methods for solving 1-norm related minimization in [15] is based on the interior point method [10], which is very slow when solving large-scale 1-norm minimizations.”
Compressed Sensing for Wireless Communications: Useful Tips and Tricks (2015, background): “Speed of optimization for the BPDN has been substantially improved in [13].”