  Appropriate selection of the penalty parameter is crucial to obtaining good
performance from the Alternating Direction Method of Multipliers (ADMM). While
analytic results for optimal selection of this parameter are very limited,
there is a heuristic method that appears to be relatively successful in a
number of different problems. The contribution of this paper is to demonstrate
that their is a potentially serious flaw in this heuristic approach, and to
propose a modification that at least partially addresses it.
