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dc.contributor.authorClason, Christian
dc.contributor.authorValkonen, Tuomo
dc.date.accessioned2021-04-05T06:12:29Z
dc.date.available2021-04-05T06:12:29Z
dc.date.issued2017-01
dc.identifier.citationClason, C., & Valkonen, T. (2017). Primal-Dual Extragradient Methods for Nonlinear Nonsmooth PDE-Constrained Optimization. SIAM Journal on Optimization, 27(3), 1314–1339. doi:10.1137/16m1080859
dc.identifier.issn1052-6234
dc.identifier.issn1095-7189
dc.identifier.doi10.1137/16m1080859
dc.identifier.urihttp://hdl.handle.net/10754/668528
dc.description.abstractWe 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.
dc.description.sponsorshipWhile TV was in Cambridge, he was supported by the King Abdullah University of Science and Technology (KAUST) award KUK-I1-007-43, and EPSRC grants EP/J009539/1 “Sparse & Higher-order Image Restoration” and EP/M00483X/1 “Efficient Computational Tools for Inverse Imaging Problems.” Part of this work was also done while TV was in Quito, where he was supported by a Prometeo scholarship of the Senescyt (Ecuadorian Ministry of Science, Technology, Education, and Innovation). CC is supported by the German Science Foundation DFG under grant Cl 487/1-1.
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.urlhttps://epubs.siam.org/doi/10.1137/16M1080859
dc.rightsArchived with thanks to SIAM Journal on Optimization
dc.titlePrimal-Dual Extragradient Methods for Nonlinear Nonsmooth PDE-Constrained Optimization
dc.typeArticle
dc.identifier.journalSIAM Journal on Optimization
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionFaculty of Mathematics, University Duisburg-Essen, Essen, 45117, Germany
dc.contributor.institutionDepartment of Mathematical Sciences, University of Liverpool, Liverpool, United Kingdom
dc.identifier.volume27
dc.identifier.issue3
dc.identifier.pages1314-1339
dc.identifier.arxivid1606.06219
kaust.grant.numberKUK-I1-007-43
dc.identifier.eid2-s2.0-85032863912


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