A theory of generalized proximity for ADMM

The alternating direction method of multipliers has become in recent years the most widely used proximal method for signal processing. In this paper, we lay the groundwork for a new notion of proximity and use it to illustrate that the method (ADMM) is actually somewhat of a maladroit rearrangement of a new, more practical procedure that generalizes the Douglas-Rachford algorithm. Compared to ADMM, the algorithm that we propose enjoys not only a more sensible form, but also a more general convergence result.