  The Augmented Lagragian Method (ALM) and Alternating Direction Method of
Multiplier (ADMM) have been powerful optimization methods for general convex
programming subject to linear constraint. We consider the convex problem whose
objective consists of a smooth part and a nonsmooth but simple part. We propose
the Fast Proximal Augmented Lagragian Method (Fast PALM) which achieves the
convergence rate $O(1/K^2)$, compared with $O(1/K)$ by the traditional PALM. In
order to further reduce the per-iteration complexity and handle the
multi-blocks problem, we propose the Fast Proximal ADMM with Parallel Splitting
(Fast PL-ADMM-PS) method. It also partially improves the rate related to the
smooth part of the objective function. Experimental results on both synthesized
and real world data demonstrate that our fast methods significantly improve the
previous PALM and ADMM.
