FPC_AS 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; L-BFGS; LIBSVM; UNLocBoX; Matlab; RecPF; ParNes; Yall1; IMRO; UCI-ml; L1TestPack; TFOCS; glmnet; Saga; Sparco; L1-MAGIC Cited in: 72 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization, and continuation. Zbl 1215.49039Wen, Zaiwen; Yin, Wotao; Goldfarb, Donald; Zhang, Yin 2010 all top 5 Cited by 166 Authors 8 Cheng, Wanyou 6 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 3 Sun, Defeng 3 Toh, Kim Chuan 3 Zhang, Tong 2 Candès, Emmanuel J. 2 Chen, Zixin 2 Hu, Qingjie 2 Xiao, Lin 2 Xiao, Yunhai 2 Zhang, Hongchao 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 Chang, Tsung-Hui 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 Milzarek, Andre 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 ...and 66 more Authors all top 5 Cited in 31 Serials 12 SIAM Journal on Optimization 8 SIAM Journal on Scientific Computing 5 Journal of Scientific Computing 5 Computational Optimization and Applications 4 Mathematical Programming. Series A. Series B 3 Optimization Methods & Software 3 SIAM Journal on Imaging Sciences 3 Science China. Mathematics 2 Computer Methods in Applied Mechanics and Engineering 2 Applied Numerical Mathematics 2 Journal of Global Optimization 2 Numerical Algorithms 2 Inverse Problems and Imaging 2 Mathematical Programming Computation 1 Mathematics of Computation 1 ACM Transactions on Mathematical Software 1 The Annals of Statistics 1 Calcolo 1 Journal of Computational and Applied Mathematics 1 Journal of Optimization Theory and Applications 1 SIAM Journal on Control and Optimization 1 Journal of Computational Mathematics 1 Machine Learning 1 Applied and Computational Harmonic Analysis 1 INFORMS Journal on Computing 1 Optimization and Engineering 1 Journal of Applied Mathematics 1 Optimization Letters 1 Journal of the Operations Research Society of China 1 SIAM/ASA Journal on Uncertainty Quantification 1 Journal of Mathematical Modeling all top 5 Cited in 11 Fields 64 Operations research, mathematical programming (90-XX) 45 Numerical analysis (65-XX) 15 Information and communication theory, circuits (94-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 5 Statistics (62-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Computer science (68-XX) 2 Systems theory; control (93-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Operator theory (47-XX) Citations by Year