Understanding Limitation of Two Symmetrized Orders by Worst-case Complexity

It was recently found that the standard version of multi-block cyclic ADMM diverges. Interestingly, Gaussian Back Substitution ADMM (GBS-ADMM) and symmetric Gauss-Seidel ADMM (sGS-ADMM) do not have the divergence issue. Therefore, it seems that symmetrization can improve the performance of the classical cyclic order. In another recent work, cyclic CD (Coordinate Descent) was shown to … Read more