Design of Continuous-time ADMM and Convergence Analysis Based on Passivity

This paper presents a continuous-time version of an optimization algorithm called Alternating Direction Method of Multipliers (ADMM), and analyzes convergence of the optimization dynamics based on passivity. First, a convex optimization problem is formulated as an equivalent ADMM form. We then present a novel continuous-time ADMM and prove convergence to a subset of optimal solutions of the convex optimization problem based on the theory of interconnected passive systems, where the cost function is assumed to be not strictly convex but just convex. Finally, the effectiveness of the present algorithm is demonstrated in a numerical simulation.