Luke, Russell

[["dc.bibliographiccitation.firstpage","446"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","SIAM Review"],["dc.bibliographiccitation.lastpage","449"],["dc.bibliographiccitation.volume","51"],["dc.contributor.author","Luke, D. Russell"],["dc.date.accessioned","2019-07-10T08:13:29Z"],["dc.date.available","2019-07-10T08:13:29Z"],["dc.date.issued","2009"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/6000"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/61257"],["dc.language.iso","en"],["dc.notes.intern","Migrated from goescholar"],["dc.rights.access","openAccess"],["dc.subject","Inverse Problems"],["dc.subject.ddc","510"],["dc.title","The Factorization Method for Inverse Problems. By Andreas Kirsch and Natalia Grinberg."],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1143"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Mathematics of Operations Research"],["dc.bibliographiccitation.lastpage","1176"],["dc.bibliographiccitation.volume","43"],["dc.contributor.author","Thao, Nguyen H."],["dc.contributor.author","Tam, Matthew K."],["dc.contributor.author","Luke, Russell"],["dc.date.accessioned","2019-07-09T11:50:21Z"],["dc.date.available","2019-07-09T11:50:21Z"],["dc.date.issued","2018"],["dc.description.abstract","We develop a framework for quantitative convergence analysis of Picard iterations of expansive set-valued fixed point mappings. There are two key components of the analysis. The first is a natural generalization of single-valued averaged mappings to expansive set-valued mappings that characterizes a type of strong calmness of the fixed point mapping. The second component to this analysis is an extension of the well-established notion of metric subregularity—or inverse calmness—of the mapping at fixed points. Convergence of expansive fixed point iterations is proved using these two properties, and quantitative estimates are a natural by-product of the framework. To demonstrate the application of the theory, we prove, for the first time, a number of results showing local linear convergence of nonconvex cyclic projections for inconsistent (and consistent) feasibility problems, local linear convergence of the forward-backward algorithm for structured optimization without convexity, strong or otherwise, and local linear convergence of the Douglas-Rachford algorithm for structured nonconvex minimization. This theory includes earlier approaches for known results, convex and nonconvex, as special cases."],["dc.identifier.arxiv","1605.05725"],["dc.identifier.doi","10.1287/moor.2017.0898"],["dc.identifier.gro","3146834"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/15920"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/59756"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.intern","DOI-Import GROB-394"],["dc.notes.intern","Merged from goescholar"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation","RTG 2088: Research Training Group 2088 Discovering structure in complex data: Statistics meets Optimization and Inverse Problems"],["dc.rights","CC BY 4.0"],["dc.rights.uri","https://creativecommons.org/licenses/by/4.0"],["dc.subject.ddc","510"],["dc.title","Quantitative Convergence Analysis of Iterated Expansive, Set-Valued Mappings"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]