FPC_AS
| swMATH ID: | 12218 |
| Software Authors: | Wen, Zaiwen; Yin, Wotao |
| 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; ParNes; UNLocBoX; glmnet; UCI-ml; TFOCS; Matlab; RecPF; Yall1; IMRO; L1TestPack; CUTEr; LBFGS-B; iPiano |
| Cited in: | 80 Documents |
Standard Articles
| 1 Publication describing the Software, including 1 Publication in zbMATH | Year |
|---|---|
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A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization, and continuation. Zbl 1215.49039 Wen, Zaiwen; Yin, Wotao; Goldfarb, Donald; Zhang, Yin |
2010
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Cited by 184 Authors
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Cited in 34 Serials
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