  This paper derives new inexact variants of the Douglas-Rachford splitting
method for maximal monotone operators and the alternating direction method of
multipliers (ADMM) for convex optimization. The analysis is based on a new
inexact version of the proximal point algorithm that includes both an inertial
step and overrelaxation. We apply our new inexact ADMM method to LASSO and
logistic regression problems and obtain somewhat better computational
performance than earlier inexact ADMM methods.
