Parallel random block-coordinate forward–backward algorithm: a unified convergence analysis

We study the block-coordinate forward–backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary probabilities. The algorithm allows different stepsizes along the block-coordinates to fully exploit the smoothness properties of the objective fu...

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Published in:	Mathematical programming Vol. 193; no. 1; pp. 225 - 269
Main Authors:	Salzo, Saverio, Villa, Silvia
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2022 Springer Springer Nature B.V
Subjects:	Algorithms Analysis Calculus of Variations and Optimal Control; Optimization Combinatorics Convergence Convexity Error analysis Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Smoothness Theoretical Random block-coordinate descent 65K05 Convex optimization 90C25 Convergence rates Error bounds 90C06 49M27 Arbitrary sampling Stochastic quasi-Fejér sequences Parallel algorithms Forward–backward algorithm
ISSN:	0025-5610, 1436-4646
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Abstract	We study the block-coordinate forward–backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary probabilities. The algorithm allows different stepsizes along the block-coordinates to fully exploit the smoothness properties of the objective function. In the convex case and in an infinite dimensional setting, we establish almost sure weak convergence of the iterates and the asymptotic rate o (1/ n ) for the mean of the function values. We derive linear rates under strong convexity and error bound conditions. Our analysis is based on an abstract convergence principle for stochastic descent algorithms which allows to extend and simplify existing results.
AbstractList	We study the block-coordinate forward-backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary probabilities. The algorithm allows different stepsizes along the block-coordinates to fully exploit the smoothness properties of the objective function. In the convex case and in an infinite dimensional setting, we establish almost sure weak convergence of the iterates and the asymptotic rate o(1/n) for the mean of the function values. We derive linear rates under strong convexity and error bound conditions. Our analysis is based on an abstract convergence principle for stochastic descent algorithms which allows to extend and simplify existing results. We study the block-coordinate forward–backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary probabilities. The algorithm allows different stepsizes along the block-coordinates to fully exploit the smoothness properties of the objective function. In the convex case and in an infinite dimensional setting, we establish almost sure weak convergence of the iterates and the asymptotic rate o (1/ n ) for the mean of the function values. We derive linear rates under strong convexity and error bound conditions. Our analysis is based on an abstract convergence principle for stochastic descent algorithms which allows to extend and simplify existing results.
Audience	Academic
Author	Villa, Silvia Salzo, Saverio
Author_xml	– sequence: 1 givenname: Saverio orcidid: 0000-0003-0494-9101 surname: Salzo fullname: Salzo, Saverio email: saverio.salzo@iit.it organization: Istituto Italiano di Tecnologia – sequence: 2 givenname: Silvia surname: Villa fullname: Villa, Silvia organization: Università degli Studi di Genova, DIMA
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Keywords	Random block-coordinate descent 65K05 Convex optimization 90C25 Convergence rates Error bounds 90C06 49M27 Arbitrary sampling Stochastic quasi-Fejér sequences Parallel algorithms Forward–backward algorithm
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References	QuZRichtàrikPCoordinate descent with arbitrary sampling II: expected separable over approximationOptim. Methods Softw.201631858884353456110.1080/10556788.2016.1190361 Garrigos, G., Rosasco, L., Villa, S.: Convergence of the forward–backward algorithm: beyond the worst-case with the help of geometry. arXiv:1703.09477 (2017) DavisDYinYGlowinskiROsherSJYinWConvergence rate analysis of several splitting schemesSplitting Methods in Communication, Imaging, Science, and Engineering2016ChamSpringer11516310.1007/978-3-319-41589-5_4 NemirovskiAJuditskyALanGShapiroARobust stochastic approximation approach to stochastic programmingSIAM J. Optim.20091915741609248604110.1137/070704277 RichtàrikPTakàčMIteration complexity of randomized block-coordinate descent methods for minimizing a composite functionMath. Program. Ser. A2014144138317995310.1007/s10107-012-0614-z QuZRichtàrikPZhangTQuartz: randomized dual coordinate ascent with arbitrary samplingAdv. Neural Inform. Process. Syst.201528865873 LeventhalDLewisASRandomized method for linear constraints: convergence rates and conditioningMath. Oper. Res.201035641654272406810.1287/moor.1100.0456 KnoppKInfinite Sequences and Series1956New YorkDover Publications Inc0070.05807 FercoqOQuZRestarting the accelerated coordinate descent method with a rough strong convexity estimateComput. Optim. Appl.2020756391404707310.1007/s10589-019-00137-2 RichtàrikPTakàčMOn optimal probabilities in stochastic coordinate descent methodsOptim. Lett.20161012331243352984310.1007/s11590-015-0916-1 NesterovYEfficiency of coordinate descent methods on huge-scale optimization problemsSIAM J. Optim.201222341362296885710.1137/100802001 RichtàrikPTakàčMParallel coordinate descent methods for big data optimizationMath. Program. Ser. A2016156156484345920710.1007/s10107-015-0901-6 Ermol’evYMOn the method of generalized stochastic gradients and quasi-Fejér sequencesCybernetics1969520822010.1007/BF01071091 BauschkeHHCombettesPLConvex Analysis and Monotone Operator Theory in Hilbert Spaces20172New YorkSpringer10.1007/978-3-319-48311-5 LuZXiaoLOn the complexity analysis of randomized block-coordinate descent methodsMath. Program. Ser. A2015152615642336949510.1007/s10107-014-0800-2 DrusvyatskiyDLewisASError bounds, quadratic growth, and linear convergence of proximal methodsMath. Oper. Res.201843919948384607810.1287/moor.2017.0889 CombettesPLWajsVRSignal recovery by proximal forward–backward splittingMultiscale Model. Simul.2005411681200220384910.1137/050626090 BertsekasDPIncremental proximal methods for large scale convex optimizationMath. Program. Ser. B2011129163283787910.1007/s10107-011-0472-0 NecoaraINesterovYGlineurFRandom block coordinate descent methods for linearly constrained optimization over networksJ. Optim. Theory Appl.2017173227254362664510.1007/s10957-016-1058-z NecoaraINesterovYGlineurFLinear convergence of first order methods for non-strongly convex optimizationMath. Program.201917569107394288610.1007/s10107-018-1232-1 QuZRichtàrikPCoordinate descent with arbitrary sampling I: algorithms and complexityOptim. Method Softw.201631829857353456010.1080/10556788.2016.1190360 DünnerCForteSTakàčMJaggiMPrimal–dual rates and certificatesInt. Conf. Mach. Learn. PMLR201648783792 LuoZ-QTsengPError bounds and convergence analysis of feasible descent methods: a general approachAnn. Oper. Res.199346157178126001610.1007/BF02096261 StrohmerTVershyninRA randomized Kaczmarz algorithm with exponential convergenceJ. Fourier Anal. Appl.2009152262278250092410.1007/s00041-008-9030-4 KarimiHNutiniJSchmidtMFrasconiPLandwehrNMancoGVreekenJLinear convergence of gradient and proximal-gradient methods under the Polyak–Łojasiewicz conditionMachine Learning and Knowledge Discovery in Databases2016ChamSpringer79581110.1007/978-3-319-46128-1_50 KiwielKKConvergence of approximate and incremental subgradient methods for convex optimizationSIAM J. Optim.200614807840208594410.1137/S1052623400376366 RichtàrikPTakàčMDistributed coordinate descent method for learning with big dataJ. Mach. Learn. Res.20161712535170981360.68709 SalzoSThe variable metric forward–backward splitting algorithm under mild differentiability assumptionsSIAM J. Optim.20172721532181370789910.1137/16M1073741 WangP-WLinC-JIteration complexity of feasible descent methods for convex optimizationJ. Mach. Learn. Res.2014151523154832147901319.90051 CombettesPLPesquetJ-CStochastic quasi-Fejér block-coordinate fixed point iterations with random sweeping II: mean-square and linear convergenceMath. Program. Ser. B2018174119 FercoqOBianchiPA coordinate-descent primal–dual algorithm with large step size and possibly nonseparable functionsSIAM J. Optim.201929100134389664210.1137/18M1168480 TaylorABHendrickxJMGlineurFSmooth strongly convex interpolation and exact worst-case performance of first-order methodsMath. Program.2017161307345359278010.1007/s10107-016-1009-3 DurrettRProbability, Theory and Examples20104New YorkCambridge University Press10.1017/CBO9780511779398 TappendenRTakàčMRichtàrikPOn the complexity of parallel coordinate descentOptim. Methods Softw.201833373395375060810.1080/10556788.2017.1392517 CombettesPLPesquetJ-CStochastic quasi-Fejér block-coordinate fixed point iterations with random sweepingSIAM J. Optim.20152521121124810.1137/140971233 LinJRosascoLVillaSZhouD-XModified Fejér sequences and applicationsComput. Optim. Appl.20187195113384117810.1007/s10589-017-9962-1 NesterovYIntroductory Lectures on Convex Optimization. A Basic Course2004BostonKluwer Academic Publishers10.1007/978-1-4419-8853-9 BeckATetruashviliLOn the convergence of the block coordinate descent type methodsSIAM J. Optim.201323420372060311664910.1137/120887679 FercoqORichtàrikPAccelerated, parallel, and proximal coordinate descentSIAM J. Optim.20152519972023340468710.1137/130949993 NecoaraIClipiciDParallel random coordinate descent method for composite minimization: convergence analysis and error boundsSIAM J. Optim.201626197226344991410.1137/130950288 WrightSCoordinate descent algorithmsMath. Program. Ser. B2015151334334754810.1007/s10107-015-0892-3 O Fercoq (1602_CR12) 2019; 29 P Richtàrik (1602_CR34) 2016; 156 Z Qu (1602_CR29) 2015; 28 Z Lu (1602_CR21) 2015; 152 Z-Q Luo (1602_CR22) 1993; 46 P Richtàrik (1602_CR35) 2016; 10 D Leventhal (1602_CR19) 2010; 35 O Fercoq (1602_CR13) 2015; 25 Z Qu (1602_CR31) 2016; 31 Z Qu (1602_CR30) 2016; 31 A Beck (1602_CR2) 2013; 23 PL Combettes (1602_CR6) 2005; 4 I Necoara (1602_CR25) 2019; 175 R Tappenden (1602_CR38) 2018; 33 J Lin (1602_CR20) 2018; 71 DP Bertsekas (1602_CR3) 2011; 129 I Necoara (1602_CR23) 2016; 26 1602_CR15 I Necoara (1602_CR24) 2017; 173 PL Combettes (1602_CR4) 2015; 25 P Richtàrik (1602_CR32) 2016; 17 S Salzo (1602_CR36) 2017; 27 A Nemirovski (1602_CR26) 2009; 19 HH Bauschke (1602_CR1) 2017 K Knopp (1602_CR17) 1956 S Wright (1602_CR41) 2015; 151 P Richtàrik (1602_CR33) 2014; 144 C Dünner (1602_CR9) 2016; 48 Y Nesterov (1602_CR27) 2004 T Strohmer (1602_CR37) 2009; 15 YM Ermol’ev (1602_CR11) 1969; 5 O Fercoq (1602_CR14) 2020; 75 KK Kiwiel (1602_CR18) 2006; 14 PL Combettes (1602_CR5) 2018; 174 P-W Wang (1602_CR40) 2014; 15 R Durrett (1602_CR10) 2010 D Davis (1602_CR7) 2016 H Karimi (1602_CR16) 2016 Y Nesterov (1602_CR28) 2012; 22 D Drusvyatskiy (1602_CR8) 2018; 43 AB Taylor (1602_CR39) 2017; 161
References_xml	– reference: CombettesPLPesquetJ-CStochastic quasi-Fejér block-coordinate fixed point iterations with random sweepingSIAM J. Optim.20152521121124810.1137/140971233 – reference: BeckATetruashviliLOn the convergence of the block coordinate descent type methodsSIAM J. Optim.201323420372060311664910.1137/120887679 – reference: LeventhalDLewisASRandomized method for linear constraints: convergence rates and conditioningMath. Oper. Res.201035641654272406810.1287/moor.1100.0456 – reference: NecoaraINesterovYGlineurFRandom block coordinate descent methods for linearly constrained optimization over networksJ. Optim. Theory Appl.2017173227254362664510.1007/s10957-016-1058-z – reference: BauschkeHHCombettesPLConvex Analysis and Monotone Operator Theory in Hilbert Spaces20172New YorkSpringer10.1007/978-3-319-48311-5 – reference: KarimiHNutiniJSchmidtMFrasconiPLandwehrNMancoGVreekenJLinear convergence of gradient and proximal-gradient methods under the Polyak–Łojasiewicz conditionMachine Learning and Knowledge Discovery in Databases2016ChamSpringer79581110.1007/978-3-319-46128-1_50 – reference: TaylorABHendrickxJMGlineurFSmooth strongly convex interpolation and exact worst-case performance of first-order methodsMath. Program.2017161307345359278010.1007/s10107-016-1009-3 – reference: QuZRichtàrikPZhangTQuartz: randomized dual coordinate ascent with arbitrary samplingAdv. Neural Inform. Process. Syst.201528865873 – reference: QuZRichtàrikPCoordinate descent with arbitrary sampling II: expected separable over approximationOptim. Methods Softw.201631858884353456110.1080/10556788.2016.1190361 – reference: RichtàrikPTakàčMDistributed coordinate descent method for learning with big dataJ. Mach. Learn. Res.20161712535170981360.68709 – reference: LuoZ-QTsengPError bounds and convergence analysis of feasible descent methods: a general approachAnn. Oper. Res.199346157178126001610.1007/BF02096261 – reference: KnoppKInfinite Sequences and Series1956New YorkDover Publications Inc0070.05807 – reference: DurrettRProbability, Theory and Examples20104New YorkCambridge University Press10.1017/CBO9780511779398 – reference: Garrigos, G., Rosasco, L., Villa, S.: Convergence of the forward–backward algorithm: beyond the worst-case with the help of geometry. arXiv:1703.09477 (2017) – reference: NecoaraINesterovYGlineurFLinear convergence of first order methods for non-strongly convex optimizationMath. Program.201917569107394288610.1007/s10107-018-1232-1 – reference: RichtàrikPTakàčMParallel coordinate descent methods for big data optimizationMath. Program. Ser. A2016156156484345920710.1007/s10107-015-0901-6 – reference: Ermol’evYMOn the method of generalized stochastic gradients and quasi-Fejér sequencesCybernetics1969520822010.1007/BF01071091 – reference: CombettesPLWajsVRSignal recovery by proximal forward–backward splittingMultiscale Model. Simul.2005411681200220384910.1137/050626090 – reference: DünnerCForteSTakàčMJaggiMPrimal–dual rates and certificatesInt. Conf. Mach. Learn. PMLR201648783792 – reference: DavisDYinYGlowinskiROsherSJYinWConvergence rate analysis of several splitting schemesSplitting Methods in Communication, Imaging, Science, and Engineering2016ChamSpringer11516310.1007/978-3-319-41589-5_4 – reference: TappendenRTakàčMRichtàrikPOn the complexity of parallel coordinate descentOptim. Methods Softw.201833373395375060810.1080/10556788.2017.1392517 – reference: FercoqORichtàrikPAccelerated, parallel, and proximal coordinate descentSIAM J. Optim.20152519972023340468710.1137/130949993 – reference: CombettesPLPesquetJ-CStochastic quasi-Fejér block-coordinate fixed point iterations with random sweeping II: mean-square and linear convergenceMath. Program. Ser. B2018174119 – reference: LuZXiaoLOn the complexity analysis of randomized block-coordinate descent methodsMath. Program. Ser. A2015152615642336949510.1007/s10107-014-0800-2 – reference: NesterovYEfficiency of coordinate descent methods on huge-scale optimization problemsSIAM J. Optim.201222341362296885710.1137/100802001 – reference: LinJRosascoLVillaSZhouD-XModified Fejér sequences and applicationsComput. Optim. Appl.20187195113384117810.1007/s10589-017-9962-1 – reference: QuZRichtàrikPCoordinate descent with arbitrary sampling I: algorithms and complexityOptim. Method Softw.201631829857353456010.1080/10556788.2016.1190360 – reference: StrohmerTVershyninRA randomized Kaczmarz algorithm with exponential convergenceJ. Fourier Anal. Appl.2009152262278250092410.1007/s00041-008-9030-4 – reference: NesterovYIntroductory Lectures on Convex Optimization. A Basic Course2004BostonKluwer Academic Publishers10.1007/978-1-4419-8853-9 – reference: RichtàrikPTakàčMOn optimal probabilities in stochastic coordinate descent methodsOptim. Lett.20161012331243352984310.1007/s11590-015-0916-1 – reference: FercoqOBianchiPA coordinate-descent primal–dual algorithm with large step size and possibly nonseparable functionsSIAM J. Optim.201929100134389664210.1137/18M1168480 – reference: FercoqOQuZRestarting the accelerated coordinate descent method with a rough strong convexity estimateComput. Optim. Appl.2020756391404707310.1007/s10589-019-00137-2 – reference: BertsekasDPIncremental proximal methods for large scale convex optimizationMath. Program. Ser. B2011129163283787910.1007/s10107-011-0472-0 – reference: NemirovskiAJuditskyALanGShapiroARobust stochastic approximation approach to stochastic programmingSIAM J. Optim.20091915741609248604110.1137/070704277 – reference: SalzoSThe variable metric forward–backward splitting algorithm under mild differentiability assumptionsSIAM J. Optim.20172721532181370789910.1137/16M1073741 – reference: WrightSCoordinate descent algorithmsMath. Program. Ser. B2015151334334754810.1007/s10107-015-0892-3 – reference: KiwielKKConvergence of approximate and incremental subgradient methods for convex optimizationSIAM J. Optim.200614807840208594410.1137/S1052623400376366 – reference: NecoaraIClipiciDParallel random coordinate descent method for composite minimization: convergence analysis and error boundsSIAM J. Optim.201626197226344991410.1137/130950288 – reference: WangP-WLinC-JIteration complexity of feasible descent methods for convex optimizationJ. Mach. Learn. Res.2014151523154832147901319.90051 – reference: DrusvyatskiyDLewisASError bounds, quadratic growth, and linear convergence of proximal methodsMath. Oper. Res.201843919948384607810.1287/moor.2017.0889 – reference: RichtàrikPTakàčMIteration complexity of randomized block-coordinate descent methods for minimizing a composite functionMath. Program. Ser. A2014144138317995310.1007/s10107-012-0614-z – ident: 1602_CR15 – volume: 129 start-page: 163 year: 2011 ident: 1602_CR3 publication-title: Math. Program. Ser. B doi: 10.1007/s10107-011-0472-0 – volume: 43 start-page: 919 year: 2018 ident: 1602_CR8 publication-title: Math. Oper. Res. doi: 10.1287/moor.2017.0889 – volume: 22 start-page: 341 year: 2012 ident: 1602_CR28 publication-title: SIAM J. Optim. doi: 10.1137/100802001 – volume-title: Probability, Theory and Examples year: 2010 ident: 1602_CR10 doi: 10.1017/CBO9780511779398 – volume: 35 start-page: 641 year: 2010 ident: 1602_CR19 publication-title: Math. Oper. Res. doi: 10.1287/moor.1100.0456 – volume: 23 start-page: 2037 issue: 4 year: 2013 ident: 1602_CR2 publication-title: SIAM J. Optim. doi: 10.1137/120887679 – volume-title: Convex Analysis and Monotone Operator Theory in Hilbert Spaces year: 2017 ident: 1602_CR1 doi: 10.1007/978-3-319-48311-5 – volume: 28 start-page: 865 year: 2015 ident: 1602_CR29 publication-title: Adv. Neural Inform. Process. Syst. – volume: 26 start-page: 197 year: 2016 ident: 1602_CR23 publication-title: SIAM J. Optim. doi: 10.1137/130950288 – volume: 156 start-page: 156 year: 2016 ident: 1602_CR34 publication-title: Math. Program. Ser. A doi: 10.1007/s10107-015-0901-6 – volume: 48 start-page: 783 year: 2016 ident: 1602_CR9 publication-title: Int. Conf. Mach. Learn. PMLR – volume: 175 start-page: 69 year: 2019 ident: 1602_CR25 publication-title: Math. Program. doi: 10.1007/s10107-018-1232-1 – volume-title: Introductory Lectures on Convex Optimization. A Basic Course year: 2004 ident: 1602_CR27 doi: 10.1007/978-1-4419-8853-9 – volume: 75 start-page: 63 year: 2020 ident: 1602_CR14 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-019-00137-2 – volume: 29 start-page: 100 year: 2019 ident: 1602_CR12 publication-title: SIAM J. Optim. doi: 10.1137/18M1168480 – volume: 10 start-page: 1233 year: 2016 ident: 1602_CR35 publication-title: Optim. Lett. doi: 10.1007/s11590-015-0916-1 – volume: 46 start-page: 157 year: 1993 ident: 1602_CR22 publication-title: Ann. Oper. Res. doi: 10.1007/BF02096261 – volume: 31 start-page: 829 year: 2016 ident: 1602_CR30 publication-title: Optim. Method Softw. doi: 10.1080/10556788.2016.1190360 – volume-title: Infinite Sequences and Series year: 1956 ident: 1602_CR17 – start-page: 115 volume-title: Splitting Methods in Communication, Imaging, Science, and Engineering year: 2016 ident: 1602_CR7 doi: 10.1007/978-3-319-41589-5_4 – volume: 14 start-page: 807 year: 2006 ident: 1602_CR18 publication-title: SIAM J. Optim. doi: 10.1137/S1052623400376366 – volume: 15 start-page: 262 issue: 2 year: 2009 ident: 1602_CR37 publication-title: J. Fourier Anal. Appl. doi: 10.1007/s00041-008-9030-4 – volume: 33 start-page: 373 year: 2018 ident: 1602_CR38 publication-title: Optim. Methods Softw. doi: 10.1080/10556788.2017.1392517 – volume: 19 start-page: 1574 year: 2009 ident: 1602_CR26 publication-title: SIAM J. Optim. doi: 10.1137/070704277 – volume: 4 start-page: 1168 year: 2005 ident: 1602_CR6 publication-title: Multiscale Model. Simul. doi: 10.1137/050626090 – volume: 25 start-page: 1997 year: 2015 ident: 1602_CR13 publication-title: SIAM J. Optim. doi: 10.1137/130949993 – volume: 144 start-page: 1 year: 2014 ident: 1602_CR33 publication-title: Math. Program. Ser. A doi: 10.1007/s10107-012-0614-z – volume: 161 start-page: 307 year: 2017 ident: 1602_CR39 publication-title: Math. Program. doi: 10.1007/s10107-016-1009-3 – start-page: 795 volume-title: Machine Learning and Knowledge Discovery in Databases year: 2016 ident: 1602_CR16 doi: 10.1007/978-3-319-46128-1_50 – volume: 5 start-page: 208 year: 1969 ident: 1602_CR11 publication-title: Cybernetics doi: 10.1007/BF01071091 – volume: 31 start-page: 858 year: 2016 ident: 1602_CR31 publication-title: Optim. Methods Softw. doi: 10.1080/10556788.2016.1190361 – volume: 27 start-page: 2153 year: 2017 ident: 1602_CR36 publication-title: SIAM J. Optim. doi: 10.1137/16M1073741 – volume: 151 start-page: 3 year: 2015 ident: 1602_CR41 publication-title: Math. Program. Ser. B doi: 10.1007/s10107-015-0892-3 – volume: 173 start-page: 227 year: 2017 ident: 1602_CR24 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-016-1058-z – volume: 17 start-page: 1 year: 2016 ident: 1602_CR32 publication-title: J. Mach. Learn. Res. – volume: 15 start-page: 1523 year: 2014 ident: 1602_CR40 publication-title: J. Mach. Learn. Res. – volume: 71 start-page: 95 year: 2018 ident: 1602_CR20 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-017-9962-1 – volume: 25 start-page: 1121 issue: 2 year: 2015 ident: 1602_CR4 publication-title: SIAM J. Optim. doi: 10.1137/140971233 – volume: 174 start-page: 1 year: 2018 ident: 1602_CR5 publication-title: Math. Program. Ser. B – volume: 152 start-page: 615 year: 2015 ident: 1602_CR21 publication-title: Math. Program. Ser. A doi: 10.1007/s10107-014-0800-2
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Snippet	We study the block-coordinate forward–backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary... We study the block-coordinate forward-backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary...
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SubjectTerms	Algorithms Analysis Calculus of Variations and Optimal Control; Optimization Combinatorics Convergence Convexity Error analysis Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Smoothness Theoretical
Title	Parallel random block-coordinate forward–backward algorithm: a unified convergence analysis
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