AUTHOR=Condat Laurent , Malinovsky Grigory , Richtárik Peter 

TITLE=Distributed Proximal Splitting Algorithms with Rates and Acceleration

JOURNAL=Frontiers in Signal Processing

VOLUME=1

YEAR=2022

URL=https://www.frontiersin.org/journals/signal-processing/articles/10.3389/frsip.2021.776825

DOI=10.3389/frsip.2021.776825

ISSN=2673-8198

ABSTRACT=<p>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.</p>