  We develop a fast and robust algorithm for solving large scale convex
composite optimization models with an emphasis on the $\ell_1$-regularized
least squares regression (Lasso) problems. Despite the fact that there exist a
large number of solvers in the literature for the Lasso problems, we found that
no solver can efficiently handle difficult large scale regression problems with
real data. By leveraging on available error bound results to realize the
asymptotic superlinear convergence property of the augmented Lagrangian
algorithm, and by exploiting the second order sparsity of the problem through
the semismooth Newton method, we are able to propose an algorithm, called {\sc
Ssnal}, to efficiently solve the aforementioned difficult problems. Under very
mild conditions, which hold automatically for Lasso problems, both the primal
and the dual iteration sequences generated by {\sc Ssnal} possess a fast linear
convergence rate, which can even be superlinear asymptotically. Numerical
comparisons between our approach and a number of state-of-the-art solvers, on
real data sets, are presented to demonstrate the high efficiency and robustness
of our proposed algorithm in solving difficult large scale Lasso problems.
