We initially establish the \(O(1/K^2)\) (K represents the number of iterations) ergodic convergence rate of the alternating direction method of multipliers (ADMM) with dual step size from 0 to 2 and dynamically updating the penalty parameter. The convergence rate is derived under the assumption that the two objective functions involved are linear and strongly convex, respectively. In contrast, there is no convergence rate analysis for ADMM with dual step size ranging from 0 to 2 and dynamically updating the penalty parameter. Furthermore, we analyze the convergence to the solution.
