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.
Cite
@article{arxiv.1709.09507,
title = {A general framework for parallelizing Dyskstra splitting},
author = {C. H. Jeffrey Pang},
journal= {arXiv preprint arXiv:1709.09507},
year = {2017}
}