Primal-Dual Extragradient Methods for Nonlinear Nonsmooth PDE-Constrained Optimization

Christian Clason, Tuomo Valkonen

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We study the extension of the Chambolle-Pock primal-dual algorithm to nonsmooth optimization problems involving nonlinear operators between function spaces. Local convergence is shown under technical conditions including metric regularity of the corresponding primal-dual optimality conditions. We also show convergence for a Nesterov-type accelerated variant, provided one part of the functional is strongly convex. We show the applicability of the accelerated algorithm to examples of inverse problems with L1 and L∞ fitting terms as well as of state-constrained optimal control problems, where convergence can be guaranteed after introducing an (arbitrarily small, still nonsmooth) Moreau-Yosida regularization. This is verified in numerical examples.
Original languageEnglish (US)
Pages (from-to)1314-1339
Number of pages26
JournalSIAM Journal on Optimization
Volume27
Issue number3
DOIs
StatePublished - Jan 2017
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software

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