The alternating direction method of multipliers (ADMM) is a benchmark for solving a two-block linearly constrained convex minimization model whose objective function is the sum of two functions without coupled variables. Meanwhile, it is known that the convergence is not guaranteed if the ADMM is directly extended to a multiple-block convex minimization model whose objective function has more t...

We construct a family of functions suitable for establishing lower bounds on the oracle complexity first-order minimization smooth strongly-convex functions. Based this construction, we derive new under various inaccuracy criteria. The match known upper up to constant factor, and when solution is measured by its distance set, bound exactly matches obtained recent Information-Theoretic Exact Met...