Corpus ID: 1627040

A Primal-Dual Homotopy Algorithm for ℓ1-Minimization with ℓ∞-Constraints

@article{Brauer2016APH,
  title={A Primal-Dual Homotopy Algorithm for ℓ1-Minimization with ℓ∞-Constraints},
  author={Christoph Brauer and Dirk A. Lorenz and Andreas M. Tillmann},
  journal={ArXiv},
  year={2016},
  volume={abs/1610.10022}
}
  • Christoph Brauer, Dirk A. Lorenz, Andreas M. Tillmann
  • Published in ArXiv 2016
  • Mathematics, Computer Science
  • In this paper we propose a primal-dual homotopy method for `1minimization problems with infinity norm constraints in the context of sparse reconstruction. The natural homotopy parameter is the value of the bound for the constraints and we show that there exists a piecewise linear solution path with finitely many break points for the primal problem and a respective piecewise constant path for the dual problem. We show that by solving a small linear program, one can jump to the next primal break… CONTINUE READING

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