"Problem Decomposition in Optimization:  Algorithmic Advances Beyond ADMM"

      Decomposition schemes like those comming from ADMM typically start by 
 posing a separable-type problem in the Fenchel duality format.  They then 
 pass to an augmented Lagrangian, which however can interfere with the 
 separability and cause a slow-down.  Progressive decoupling offers a more 
 flexible approach which can utilize augmented Lagrangians while maintaining 
 decomposability.  Based on a variable metric extension of the proximal 
 point algorithm that's applied in a twisted sort of way, progressive
 decoupling benefits from stopping criteria which can guarantee convergence 
 despite inexact minimization in each interation.   The convergence is 
 generically at a linear rate, and for convex problems, is global.  But the 
 method also works for nonconvex problems when initiated close enough to a 
 point that satisfies a natural extension of the strong sufficient condition 
 for local optimality known from nonlinear programming.