  We consider the problem of minimizing an objective function that is the sum
of a convex function and a group sparsity-inducing regularizer. Problems that
integrate such regularizers arise in modern machine learning applications,
often for the purpose of obtaining models that are easier to interpret and that
have higher predictive accuracy. We present a new method for solving such
problems that utilize subspace acceleration, domain decomposition, and support
identification. Our analysis shows, under common assumptions, that the iterate
sequence generated by our framework is globally convergent, converges to an
$\epsilon$-approximate solution in at most $O(\epsilon^{-(1+p)})$
(respectively, $O(\epsilon^{-(2+p)})$) iterations for all $\epsilon$ bounded
above and large enough (respectively, all $\epsilon$ bounded above) where $p >
0$ is an algorithm parameter, and exhibits superlinear local convergence.
Preliminary numerical results for the task of binary classification based on
regularized logistic regression show that our approach is efficient and robust,
with the ability to outperform a state-of-the-art method.
