Thao, Nguyen H.

[["dc.bibliographiccitation.firstpage","701"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Set-Valued and Variational Analysis"],["dc.bibliographiccitation.lastpage","729"],["dc.bibliographiccitation.volume","25"],["dc.contributor.author","Kruger, Alexander Y."],["dc.contributor.author","Luke, D. Russell"],["dc.contributor.author","Thao, Nguyen H."],["dc.date.accessioned","2020-12-10T14:11:55Z"],["dc.date.available","2020-12-10T14:11:55Z"],["dc.date.issued","2017"],["dc.identifier.doi","10.1007/s11228-017-0436-5"],["dc.identifier.eissn","1877-0541"],["dc.identifier.issn","1877-0533"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/71250"],["dc.language.iso","en"],["dc.notes.intern","DOI Import GROB-354"],["dc.notes.intern","DOI-Import GROB-394"],["dc.relation","RTG 2088: Research Training Group 2088 Discovering structure in complex data: Statistics meets Optimization and Inverse Problems"],["dc.title","About Subtransversality of Collections of Sets"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]

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[["dc.bibliographiccitation.journal","Mathematical Programming"],["dc.contributor.author","Kruger, Alexander Y."],["dc.contributor.author","Luke, Russell"],["dc.contributor.author","Thao, Nguyen H."],["dc.date.accessioned","2017-09-07T11:50:03Z"],["dc.date.available","2017-09-07T11:50:03Z"],["dc.date.issued","2016"],["dc.identifier.doi","10.1007/s10107-016-1039-x"],["dc.identifier.gro","3147580"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/5067"],["dc.notes.intern","DOI-Import GROB-394"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Springer Nature"],["dc.relation","RTG 2088: Research Training Group 2088 Discovering structure in complex data: Statistics meets Optimization and Inverse Problems"],["dc.relation.issn","0025-5610"],["dc.title","Set regularities and feasibility problems"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1"],["dc.bibliographiccitation.issue","1-2"],["dc.bibliographiccitation.journal","Mathematical Programming"],["dc.bibliographiccitation.lastpage","31"],["dc.bibliographiccitation.volume","180"],["dc.contributor.author","Luke, D. Russell"],["dc.contributor.author","Teboulle, Marc"],["dc.contributor.author","Thao, Nguyen H."],["dc.date.accessioned","2020-12-10T14:11:10Z"],["dc.date.available","2020-12-10T14:11:10Z"],["dc.date.issued","2018"],["dc.identifier.doi","10.1007/s10107-018-1343-8"],["dc.identifier.eissn","1436-4646"],["dc.identifier.issn","0025-5610"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/70991"],["dc.language.iso","en"],["dc.notes.intern","DOI Import GROB-354"],["dc.notes.intern","DOI-Import GROB-394"],["dc.relation","RTG 2088: Research Training Group 2088 Discovering structure in complex data: Statistics meets Optimization and Inverse Problems"],["dc.title","Necessary conditions for linear convergence of iterated expansive, set-valued mappings"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["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"]]