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dc.contributor.authorPinto, Pedro
dc.contributor.authorPischke, Nicholas
dc.date.accessioned2024-04-16T10:31:21Z
dc.date.available2024-04-16T10:31:21Z
dc.date.issued2024-04-16
dc.identifier.urihttp://publications.mfo.de/handle/mfo/4134
dc.description.abstractWe provide quantitative results on the asymptotic behavior of Dykstra’s algorithm with Bregman projections, a combination of the well-known Dykstra’s algorithm and the method of cyclic Bregman projections, designed to find best approximations and solve the convex feasibility problem in a non-Hilbertian setting. The result we provide arise through the lens of proof mining, a program in mathematical logic which extracts computational information from non-effective proofs. Concretely, we provide a highly uniform and computable rate of metastability of low complexity and, moreover, we also specify general circumstances in which one can obtain full and effective rates of convergence. As a byproduct of our quantitative analysis, we also for the first time establish the strong convergence of Dykstra’s method with Bregman projections in infinite dimensional (reflexive) Banach spaces.en_US
dc.description.sponsorshipThis research was supported through the program “Oberwolfach Leibniz Fellows” by the Mathematisches Forschungsinstitut Oberwolfach in 2024. Further, the authors were supported by the DFG Project KO 1737/6-2.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2024-04
dc.subjectConvex Feasibilityen_US
dc.subjectBest Approximationen_US
dc.subjectProjection Methodsen_US
dc.subjectDykstra’s Algorithmen_US
dc.subjectBregman Projectionsen_US
dc.subjectLegendre Functionsen_US
dc.subjectRates of Convergenceen_US
dc.subjectMetastabilityen_US
dc.subjectProof Miningen_US
dc.titleOn Dykstra’s Algorithm with Bregman Projectionsen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2024-04
local.scientificprogramOWLF 2024en_US
local.series.idOWP-2024-04en_US
local.subject.msc41en_US
local.subject.msc90en_US
local.subject.msc03en_US
local.subject.msc65en_US
dc.identifier.urnurn:nbn:de:101:1-2404180901076.180889673458
dc.identifier.ppn1886208808


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