  The Truncated Nonsmooth Newton Multigrid (TNNMG) method is a robust and
efficient solution method for a wide range of block-separable convex
minimization problems, typically stemming from discretizations of nonlinear and
nonsmooth partial differential equations. This paper proves global convergence
of the method under weak conditions both on the objective functional, and on
the local inexact subproblem solvers that are part of the method. It also
discusses a range of algorithmic choices that allows to customize the algorithm
for many specific problems. Numerical examples are deliberately omitted,
because many such examples have already been published elsewhere.
