  In this paper, we provide a finitely terminated yet efficient approach to
compute the Euclidean projection onto the ordered weighted $\ell_1$ (OWL1) norm
ball. In particular, an efficient semismooth Newton method is proposed for
solving the dual of a reformulation of the original projection problem. Global
and local quadratic convergence results, as well as the finite termination
property, of the algorithm are proved. Numerical comparisons with the two
best-known methods demonstrate the efficiency of our method. In addition, we
derive the generalized Jacobian of the studied projector which, we believe, is
crucial for the future designing of fast second order nonsmooth methods for
solving general OWL1 norm constrained problems.
