English

Linear and sublinear convergence rates for a subdifferentiable distributed deterministic asynchronous Dykstra's algorithm

Optimization and Control 2018-08-23 v2

Abstract

In two earlier papers, we designed a distributed deterministic asynchronous algorithm for minimizing the sum of subdifferentiable and proximable functions and a regularizing quadratic on time-varying graphs based on Dykstra's algorithm, or block coordinate dual ascent. Each node in the distributed optimization problem is the sum of a known regularizing quadratic and a function to be minimized. In this paper, we prove sublinear convergence rates for the general algorithm, and a linear rate of convergence if the function on each node is smooth with Lipschitz gradient.

Keywords

Cite

@article{arxiv.1807.00110,
  title  = {Linear and sublinear convergence rates for a subdifferentiable distributed deterministic asynchronous Dykstra's algorithm},
  author = {C. H. Jeffrey Pang},
  journal= {arXiv preprint arXiv:1807.00110},
  year   = {2018}
}

Comments

29 pages. New in this submission: Numerical experiments, and some updates to improve clarity

R2 v1 2026-06-23T02:46:43.773Z