swMATH ID: 12218
Software Authors: Zaiwen Wen, Wotao Yin
Description: FPC_AS (fixed-point continuation and active set) is a MATLAB solver for the l1-regularized least squares problem: A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization, and continuation. We propose a fast algorithm for solving the ℓ 1 -regularized minimization problem min x∈ℝ n μ∥x∥ 1 +∥Ax-b∥ 2 2 for recovering sparse solutions to an undetermined system of linear equations Ax=b. The algorithm is divided into two stages that are performed repeatedly. In the first stage a first-order iterative “shrinkage” method yields an estimate of the subset of components of x likely to be nonzero in an optimal solution. Restricting the decision variables x to this subset and fixing their signs at their current values reduces the ℓ 1 -norm ∥x∥ 1 to a linear function of x. The resulting subspace problem, which involves the minimization of a smaller and smooth quadratic function, is solved in the second phase. Our code FPC_AS embeds this basic two-stage algorithm in a continuation (homotopy) approach by assigning a decreasing sequence of values to μ. This code exhibits state-of-the-art performance in terms of both its speed and its ability to recover sparse signals
Homepage: http://www.caam.rice.edu/~optimization/L1/FPC_AS/
Dependencies: Matlab
Related Software: PDCO; SPGL1; NESTA; TwIST; CoSaMP; LIBSVM; L-BFGS; UNLocBoX; Matlab; RecPF; ParNes; Yall1; IMRO; UCI-ml; L1TestPack; TFOCS; glmnet; Saga; Sparco; L1-MAGIC
Referenced in: 69 Publications
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Referenced by 162 Authors

7 Cheng, Wanyou
5 Wen, Zaiwen
5 Yin, Wotao
3 Aybat, Necdet Serhat
3 Becker, Stephen R.
3 Dai, Yu-Hong
3 Goldfarb, Donald
3 Li, Donghui
3 Rinaldi, Francesco
2 Candès, Emmanuel J.
2 Chen, Zixin
2 Hu, Qingjie
2 Sun, Defeng
2 Toh, Kim Chuan
2 Xiao, Lin
2 Xiao, Yunhai
2 Zhang, Hongchao
2 Zhang, Tong
2 Zhang, Yin
1 Ayanzadeh, Ramin
1 Azmi, Behzad
1 Beck, James L.
1 Bian, Fengmiao
1 Bobin, Jérôme
1 Byrd, Richard H.
1 Cao, Shuhan
1 Chen, Hongsheng
1 Chen, Jianli
1 Chen, Lifeng
1 Chen, Xiaojun
1 Cheng, Lizhi
1 Chin, Gillian M.
1 Ciril, Igor
1 Darbon, Jerome
1 De Santis, Marianna
1 Eghbali, Reza
1 Esmaeili, Hamid
1 Fadili, Jalal M.
1 Fang, Shu-Cherng
1 Fazel, Maryam
1 Fountoulakis, Kimon
1 Gao, Zhenghong
1 Gondzio, Jacek
1 Grant, Michael C.
1 Gu, Ming
1 Hager, William W.
1 Hale, Elaine T.
1 Hare, Warren L.
1 He, Qi
1 Huan, Xun
1 Huang, Jiangtao
1 Huang, Yakui
1 Huang, Yong
1 Huang, Zilin
1 Jia, Zeyu
1 Jiang, Hao
1 Jiang, Shan
1 Jin, Qingwei
1 Jin, Rong
1 Karimi, Sahar
1 Kimiaei, Morteza
1 Kızılkale, Can
1 Klöckner, Dennis
1 Kunisch, Karl
1 Lacaze, Guilhem
1 Lee, Jason D.
1 Li, Chongjun
1 Li, Hui
1 Li, Xiangyang
1 Li, Xudong
1 Li, Yingying
1 Li, Yongfeng
1 Lim, Lek-Heng
1 Lin, Meixia
1 Lin, Qihang
1 Liu, Han
1 Liu, Hongwei
1 Liu, Xin
1 Liu, Xinwei
1 Liu, Yong-Jin
1 Lorenz, Dirk Alfred
1 Lou, Yifei
1 Lu, Zhaosong
1 Lucidi, Stefano
1 Ma, Shiqian
1 Morgenthaler, Jan
1 Mousavi, Ahmad
1 Najm, Habib N.
1 Nocedal, Jorge
1 Nutini, Julie
1 Ochs, Peter
1 Oefelein, Joseph C.
1 Osher, Stanley Joel
1 Öztoprak, Figen
1 Patrinos, Panagiotis
1 Peng, Zheng
1 Pfetsch, Marc E.
1 Pinar, Mustafa Çelebi
1 Porcelli, Margherita
1 Qi, Liqun
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