A general framework for parallelizing Dyskstra splitting

TL;DR

This paper introduces a comprehensive framework for parallelizing Dykstra's splitting method, unifying existing algorithms and proving their convergence, which enhances computational efficiency for convex optimization problems.

Contribution

It presents a general parallelization framework for Dykstra's splitting, encompassing classical and product space methods, with proven convergence.

Findings

Unified framework for parallel Dykstra's splitting

Inclusion of classical and product space algorithms as special cases

Proof of convergence for the proposed methods

Abstract

We show a general framework of parallelizing Dykstra splitting that includes the classical Dykstra's algorithm and the product space formulation as special cases, and prove their convergence. The key idea is to split up the function whose conjugate takes in the sum of all dual variables in the dual formulation.