For multi-block alternating direction method of multipliers(ADMM), where the objective function can be decomposed into multiple block components, we show that with block symmetric Gauss-Seidel iteration, the algorithm will converge quickly. The method will apply a block symmetric Gauss-Seidel iteration in the primal update and a linear correction that can be derived in view of Richard iteration. We also establish the linear convergence rate for linear systems.
@article{arxiv.1705.08389,
title = {A Derandomized Algorithm for RP-ADMM with Symmetric Gauss-Seidel Method},
author = {Jinchao Xu and Kailai Xu and Yinyu Ye},
journal= {arXiv preprint arXiv:1705.08389},
year = {2017}
}