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In this note, we show a sublinear nonergodic convergence rate for thealgorithm developed in [Bai, et al. Generalized symmetric ADMM for separableconvex optimization. Comput. Optim. Appl. 70, 129-170 (2018)], as well as itslinear convergence under assumptions that the sub-differential of eachcomponent objective function is piecewise linear and all the constraint setsare polyhedra. These remaining convergence results are established for thestepsize parameters of dual variables belonging to a special isosceles triangleregion, which aims to strengthen our understanding for convergence of thegeneralized symmetric ADMM.

Convergence Revisit on Generalized Symmetric ADMM