PRIMAL-DUAL EXTRAGRADIENT METHODS FOR NONLINEAR NONSMOOTH PDE-CONSTRAINED OPTIMIZATION

Clason, C and Valkonen, T ORCID: 0000-0001-6683-3572 (2017) PRIMAL-DUAL EXTRAGRADIENT METHODS FOR NONLINEAR NONSMOOTH PDE-CONSTRAINED OPTIMIZATION. SIAM JOURNAL ON OPTIMIZATION, 27 (3). pp. 1314-1339.

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Official URL: https://epubs.siam.org/doi/10.1137/16M1080859

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 $L^1$ and $L^\infty$ 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.

Item Type:	Article
Uncontrolled Keywords:	primal-dual, PDE-constrained, nonsmooth, nonlinear, extragradient
Depositing User:	Symplectic Admin
Date Deposited:	30 Jun 2017 09:24
Last Modified:	19 Jan 2023 07:01
DOI:	10.1137/16M1080859
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3008226