Restarted Fixed-Point Acceleration of Proximal ADMM for Capped-$\ell_1$ Penalized Optimization

We consider box-constrained optimization with a convex, Lipschitz continuous loss function that may be nonsmooth and a capped-$\ell_1$ penalty. Exploiting the convex branch representation of the capped-$\ell_1$ penalty, we construct an associated nonexpansive fixed-point mapping for each branch and,