A dynamical alternating direction method of multipliers for two-block optimization problems

In this paper, we propose a dynamical alternating direction method of multipliers (ADMM) for two-block separable optimization problems. The wellknown classical ADMM can be obtained after the time discretization of the dynamical system. Under suitable conditions, we prove that the trajectory asymptotically converges to a saddle point of the Lagrangian function of the problems. When the coefficient matrices in the constraint are the identity matrices, we prove the worst-case O (1/t ) convergence rate in ergodic sense.