Truncated Nonsmooth Newton Multigrid Methods for Block-Separable Minimization Problems
For researchers solving nonsmooth PDE-constrained optimization problems, this provides theoretical convergence guarantees for a robust method.
The paper proves global convergence of the Truncated Nonsmooth Newton Multigrid method for block-separable convex minimization problems under weak conditions, and discusses algorithmic customization options.
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.