Convergence rate of distributed Dykstra's algorithm with sets defined as level sets of convex functions

TL;DR

This paper analyzes the convergence rate of a distributed optimization algorithm when some constraints are convex function level sets, supported by numerical experiments validating the theoretical findings.

Contribution

It provides new theoretical convergence rate results for distributed Dykstra's algorithm with convex function level set constraints.

Findings

Theoretical convergence rates are established.

Numerical experiments confirm the theoretical predictions.

Abstract

We investigate the convergence rate of the distributed Dykstra's algorithm when some of the sets are defined as the level sets of convex functions. We carry out numerical experiments to compare with the theoretical results obtained.