Huber approximation for the non-linear ℓ1ℓ1 problem

The smooth Huber approximation to the non-linear ℓ1ℓ1 problem was proposed by Tishler and Zang (1982), and further developed in Yang (1995). In the present paper, we use the ideas of Gould (1989) to give a new algorithm with rate of convergence results for the smooth Huber approximation. Results of computational tests are reported.