dc.contributor.author Chambolle, Antonin dc.contributor.author Ehrhardt, Matthias J. dc.contributor.author Richtarik, Peter dc.contributor.author Schonlieb, Carola Bibiane dc.date.accessioned 2019-02-24T08:34:14Z dc.date.available 2019-02-24T08:34:14Z dc.date.issued 2018-10-02 dc.identifier.citation Chambolle A, Ehrhardt MJ, Richtárik P, Schönlieb C-B (2018) Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications. SIAM Journal on Optimization 28: 2783–2808. Available: http://dx.doi.org/10.1137/17M1134834. dc.identifier.issn 1052-6234 dc.identifier.issn 1095-7189 dc.identifier.doi 10.1137/17M1134834 dc.identifier.uri http://hdl.handle.net/10754/631138 dc.description.abstract We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general convex-concave saddle point problems and problems that are either partially smooth / strongly convex or fully smooth / strongly convex. We perform the analysis for arbitrary samplings of dual variables, and we obtain known deterministic results as a special case. Several variants of our stochastic method significantly outperform the deterministic variant on a variety of imaging tasks. dc.description.sponsorship The work of the first author was supported by the ANR, 'EANOI' project I1148 / ANR-12-IS01-0003 (joint with FWF); part of this work was done while he was hosted in Churchill College and DAMTP, Centre for Mathematical Sciences, University of Cambridge, thanks to support from the French Embassy in the UK and the Cantab Capital Institute for the Mathematics of Information. The work of the second and fourth authors was supported by Leverhulme Trust project Breaking the non-convexity barrier,"" EPSRC grant EP/M00483X/1, EPSRC centre grant EP/N014588/1, the Cantab Capital Institute for the Mathematics of Information, and from CHiPS (Horizon 2020 RISE project grant). The second author carried out initial work supported by the EPSRC platform grant EP/M020533/1. Moreover, the fourth author is thankful for support by The Alan Turing Institute. The work of the third author was supported by EPSRC Fellowship in Mathematical Sciences grant EP/N005538/1, entitled Randomized algorithms for extreme convex optimization."" dc.publisher Society for Industrial & Applied Mathematics (SIAM) dc.relation.url https://epubs.siam.org/doi/10.1137/17M1134834 dc.rights Published by SIAM under the terms of the Creative Commons 4.0 license dc.rights.uri http://creativecommons.org/licenses/by/4.0/ dc.subject Convex optimization dc.subject Imaging dc.subject Primal-dual algorithms dc.subject Saddle point problems dc.subject Stochastic optimization dc.title Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications dc.type Article dc.contributor.department Computer Science Program dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.contributor.department Extreme Computing Research Center dc.contributor.department Visual Computing Center (VCC) dc.identifier.journal SIAM Journal on Optimization dc.eprint.version Publisher's Version/PDF dc.contributor.institution CMAP, CNRS, Ecole Polytechnique, Palaiseau, 91128, , , , France dc.contributor.institution Department for Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, , United Kingdom dc.contributor.institution Alan Turing Institute, London, NW1 2DB, , United Kingdom dc.contributor.institution School of Mathematics, University of Edinburgh, Edinburgh, EH9 3PD, , United Kingdom kaust.person Richtarik, Peter refterms.dateFOA 2019-02-24T08:40:44Z dc.date.published-online 2018-10-02 dc.date.published-print 2018-01
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