Truncated Nonsmooth Newton Multigrid Methods for Block-Separable Minimization Problems

Research output: Contribution to journalResearch articleContributedpeer-review



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 non-linear 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.


Original languageEnglish
Pages (from-to)454-481
Number of pages28
JournalIMA Journal of Numerical Analysis
Issue number1
Publication statusPublished - 2019

External IDs

Scopus 85063391209
ORCID /0000-0003-1093-6374/work/142250553



  • nonsmooth optimization, convex optimization, multigrid, separable problems