A Finite Smoothing Algorithm for Linear l1 Estimation

In this paper a new method for solving the linear $l_1 $ problem is described, analysed, and tested. The method is based on smoothing the nondifferentiable $l_1 $ 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.