  We describe an active-set method for the minimization of an objective
function $\phi$ that is the sum of a smooth convex function and an
$\ell_1$-regularization term. A distinctive feature of the method is the way in
which active-set identification and {second-order} subspace minimization steps
are integrated to combine the predictive power of the two approaches. At every
iteration, the algorithm selects a candidate set of free and fixed variables,
performs an (inexact) subspace phase, and then assesses the quality of the new
active set. If it is not judged to be acceptable, then the set of free
variables is restricted and a new active-set prediction is made. We establish
global convergence for our approach, and compare the new method against the
state-of-the-art code LIBLINEAR.
