Distributed Proximal Splitting Algorithms with Rates and Acceleration

TL;DR

This paper provides a comprehensive analysis of proximal splitting algorithms for large-scale convex nonsmooth optimization, introducing new convergence rates, accelerated methods, and distributed variants with nonergodic guarantees.

Contribution

It introduces new convergence rates, accelerated versions, and distributed variants of proximal splitting algorithms with nonergodic analysis for convex nonsmooth optimization.

Findings

Derived sublinear and linear convergence rates.

Proposed accelerated algorithms with varying stepsizes.

Developed distributed algorithms with nonergodic convergence guarantees.

Abstract

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.