Distributed Proximal Splitting Algorithms with Rates and Acceleration

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.

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Cited by in corpus (5)

• Federated Learning Based on Dynamic Regularization
• Faster First-Order Primal-Dual Methods for Linear Programming using Restarts and Sharpness
• Dualize, Split, Randomize: Toward Fast Nonsmooth Optimization Algorithms
• An Optimal Algorithm for Strongly Convex Minimization under Affine Constraints
• A primal-dual splitting algorithm for monotone inclusions with applications