Algorithms for ℓ1-Minimization

  • Simon Foucart
  • Holger Rauhut
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


This chapter presents a selection of three algorithms designed specifically to compute solutions of 1-minimization problems. The algorithms, chosen with simplicity of analysis and diversity of techniques in mind, are the homotopy method, Chambolle and Pock’s primal–dual algorithm, and the iteratively reweighted least squares algorithm. Other algorithms are also mentioned but discussed in less detail.


1-minimization homotopy method LARS algorithm Chambolle and Pock’s algorithm iteratively reweighted least square algorithm 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Simon Foucart
    • 1
  • Holger Rauhut
    • 2
  1. 1.Department of MathematicsDrexel UniversityPhiladelphiaUSA
  2. 2.Lehrstuhl C für Mathematik (Analysis)RWTH Aachen UniversityAachenGermany

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