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A variable fixing version of the two-block nonlinear constrained Gauss–Seidel algorithm for $$\ell _1$$ ℓ 1 -regularized least-squares

Author

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  • Margherita Porcelli
  • Francesco Rinaldi

Abstract

The problem of finding sparse solutions to underdetermined systems of linear equations is very common in many fields as e.g. signal/image processing and statistics. A standard tool for dealing with sparse recovery is the $$\ell _1$$ ℓ 1 -regularized least-squares approach that has recently attracted the attention of many researchers. In this paper, we describe a new version of the two-block nonlinear constrained Gauss–Seidel algorithm for solving $$\ell _1$$ ℓ 1 -regularized least-squares that at each step of the iteration process fixes some variables to zero according to a simple active-set strategy. We prove the global convergence of the new algorithm and we show its efficiency reporting the results of some preliminary numerical experiments. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Margherita Porcelli & Francesco Rinaldi, 2014. "A variable fixing version of the two-block nonlinear constrained Gauss–Seidel algorithm for $$\ell _1$$ ℓ 1 -regularized least-squares," Computational Optimization and Applications, Springer, vol. 59(3), pages 565-589, December.
    • Handle: RePEc:spr:coopap:v:59:y:2014:i:3:p:565-589
    DOI: 10.1007/s10589-014-9653-0
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