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Stochastic Primal Dual Hybrid Gradient Algorithm with Adaptive Step-Sizes

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorChambolle, Antonin
HAL ID: 184536
ORCID: 0000-0002-9465-4659
hal.structure.identifierEDF R&D [EDF R&D ]
dc.contributor.authorDelplancke, Claire
hal.structure.identifierDepartment of Mathematical Sciences [Bath]
dc.contributor.authorEhrhardt, Matthias
hal.structure.identifierDepartment of Applied Mathematics and Theoretical Physics [Cambridge] [DAMTP]
dc.contributor.authorSchönlieb, Carola-Bibiane
hal.structure.identifierDepartment of Applied Mathematics and Theoretical Physics [Cambridge] [DAMTP]
dc.contributor.authorTang, Junqi
dc.date.accessioned2023-03-02T14:29:09Z
dc.date.available2023-03-02T14:29:09Z
dc.date.issued2023
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/24517
dc.language.isoenen
dc.subject.ddc510en
dc.titleStochastic Primal Dual Hybrid Gradient Algorithm with Adaptive Step-Sizesen
dc.typeDocument de travail / Working paper
dc.description.abstractenIn this work we propose a new primal-dual algorithm with adaptive step-sizes. The stochastic primal-dual hybrid gradient (SPDHG) algorithm with constant step-sizes has become widely applied in large-scale convex optimization across many scientific fields due to its scalability. While the product of the primal and dual step-sizes is subject to an upper-bound in order to ensure convergence, the selection of the ratio of the step-sizes is critical in applications. Upto-now there is no systematic and successful way of selecting the primal and dual step-sizes for SPDHG. In this work, we propose a general class of adaptive SPDHG (A-SPDHG) algorithms, and prove their convergence under weak assumptions. We also propose concrete parametersupdating strategies which satisfy the assumptions of our theory and thereby lead to convergent algorithms. Numerical examples on computed tomography demonstrate the effectiveness of the proposed schemes.en
dc.publisher.cityParisen
dc.identifier.citationpages24en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris Dauphine-PSLen
dc.subject.ddclabelMathématiquesen
dc.identifier.citationdate2023
dc.description.ssrncandidatenon
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dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2023-02-27T12:06:35Z
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