Subdifferentiable functions and partial data communication in a distributed deterministic asynchronous Dykstra's algorithm

TL;DR

This paper extends a decentralized asynchronous Dykstra's algorithm to include subdifferentiable functions and partial data communication, enhancing its applicability to time-varying graph scenarios.

Contribution

It introduces a method to incorporate subdifferentiable functions into the algorithm using a bundle method approach and allows for partial data communication.

Findings

Incorporation of subdifferentiable functions via a bundle method.

Algorithm supports partial data communication.

Applicable to time-varying graph structures.

Abstract

We described a decentralized distributed deterministic asynchronous Dykstra's algorithm that allows for time-varying graphs in an earlier paper. In this paper, we show how to incorporate subdifferentiable functions into the framework using a step similar to the bundle method. We point out that our algorithm also allows for partial data communications. We discuss a standard step for treating the composition of a convex and linear function.