A Finite Smoothing Algorithm for Linear l₁ Estimation

In this paper a new method for solving the linear l₁ problem is described, analysed, and tested. The method is based on smoothing the nondifferentiable l₁ function. The smoothing can be done in a well-onditioned manner since the method has finite convergence. Extensive numerical tests demonstrate significant superiority to existing simplex-type codes. Furthermore, the tests show that the new algorithm is very well suited for vector processing.