  We analyze several generic proximal splitting algorithms well suited for
large-scale convex nonsmooth optimization. We derive sublinear and linear
convergence results with new rates on the function value suboptimality or
distance to the solution, as well as new accelerated versions, using varying
stepsizes. In addition, we propose distributed variants of these algorithms,
which can be accelerated as well. While most existing results are ergodic, our
nonergodic results significantly broaden our understanding of primal-dual
optimization algorithms.
