https://github.com/c42f/l1homotopy.jl

The Homotopy algorithm for l1 minimization
https://github.com/c42f/l1homotopy.jl

Last synced: 5 months ago
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The Homotopy algorithm for l1 minimization

• Host: GitHub
• URL: https://github.com/c42f/l1homotopy.jl
• Owner: c42f
• License: other
• Created: 2017-08-11T21:56:39.000Z (almost 9 years ago)
• Default Branch: master
• Last Pushed: 2017-08-11T21:58:22.000Z (almost 9 years ago)
• Last Synced: 2025-03-15T18:14:15.718Z (about 1 year ago)
• Language: Julia
• Size: 5.86 KB
• Stars: 0
• Watchers: 3
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.md

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README

          
# L1Homotopy

Implementation of the Homotopy method for solving the L1 minimization problem,

    minimize  J(x) = ‖A*x - y‖₂² + λₑ‖x‖₁

    subject to  xᵢ > 0 for all i

The algorithm itself and the connection to other related algorithms such as

matching persuit and Least Angle Regression (LARS) is described in the paper

"Fast solution to L1-norm minimization problems when the solution may be sparse"

by David Donoho and Yaakov Tsaig.  The formulation above is labelled (D_λ) in

the paper, but there are several other equivalent formulations, including two

constrained formulations labelled (P_1) and (L_q) in the paper.  L_q is popular

for statistical model selection and is called Lasso in the statistical

literature.