A nested primal–dual FISTA-like scheme for composite convex optimization problems
We propose a nested primal–dual algorithm with extrapolation on the primal variable suited for minimizing the sum of two convex functions, one of which is continuously differentiable. The proposed algorithm can be interpreted as an inexact inertial forward–backward algorithm equipped with a prefixed...
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Published in | Computational optimization and applications Vol. 84; no. 1; pp. 85 - 123 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
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Springer US
2023
Springer Nature B.V |
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Abstract | We propose a nested primal–dual algorithm with extrapolation on the primal variable suited for minimizing the sum of two convex functions, one of which is continuously differentiable. The proposed algorithm can be interpreted as an inexact inertial forward–backward algorithm equipped with a prefixed number of inner primal–dual iterations for the proximal evaluation and a “warm–start” strategy for starting the inner loop, and generalizes several nested primal–dual algorithms already available in the literature. By appropriately choosing the inertial parameters, we prove the convergence of the iterates to a saddle point of the problem, and provide an
O
(1/
n
) convergence rate on the primal–dual gap evaluated at the corresponding ergodic sequences. Numerical experiments on some image restoration problems show that the combination of the “warm–start” strategy with an appropriate choice of the inertial parameters is strictly required in order to guarantee the convergence to the real minimum point of the objective function. |
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AbstractList | We propose a nested primal–dual algorithm with extrapolation on the primal variable suited for minimizing the sum of two convex functions, one of which is continuously differentiable. The proposed algorithm can be interpreted as an inexact inertial forward–backward algorithm equipped with a prefixed number of inner primal–dual iterations for the proximal evaluation and a “warm–start” strategy for starting the inner loop, and generalizes several nested primal–dual algorithms already available in the literature. By appropriately choosing the inertial parameters, we prove the convergence of the iterates to a saddle point of the problem, and provide an
O
(1/
n
) convergence rate on the primal–dual gap evaluated at the corresponding ergodic sequences. Numerical experiments on some image restoration problems show that the combination of the “warm–start” strategy with an appropriate choice of the inertial parameters is strictly required in order to guarantee the convergence to the real minimum point of the objective function. Abstract We propose a nested primal–dual algorithm with extrapolation on the primal variable suited for minimizing the sum of two convex functions, one of which is continuously differentiable. The proposed algorithm can be interpreted as an inexact inertial forward–backward algorithm equipped with a prefixed number of inner primal–dual iterations for the proximal evaluation and a “warm–start” strategy for starting the inner loop, and generalizes several nested primal–dual algorithms already available in the literature. By appropriately choosing the inertial parameters, we prove the convergence of the iterates to a saddle point of the problem, and provide an O (1/ n ) convergence rate on the primal–dual gap evaluated at the corresponding ergodic sequences. Numerical experiments on some image restoration problems show that the combination of the “warm–start” strategy with an appropriate choice of the inertial parameters is strictly required in order to guarantee the convergence to the real minimum point of the objective function. We propose a nested primal–dual algorithm with extrapolation on the primal variable suited for minimizing the sum of two convex functions, one of which is continuously differentiable. The proposed algorithm can be interpreted as an inexact inertial forward–backward algorithm equipped with a prefixed number of inner primal–dual iterations for the proximal evaluation and a “warm–start” strategy for starting the inner loop, and generalizes several nested primal–dual algorithms already available in the literature. By appropriately choosing the inertial parameters, we prove the convergence of the iterates to a saddle point of the problem, and provide an O(1/n) convergence rate on the primal–dual gap evaluated at the corresponding ergodic sequences. Numerical experiments on some image restoration problems show that the combination of the “warm–start” strategy with an appropriate choice of the inertial parameters is strictly required in order to guarantee the convergence to the real minimum point of the objective function. |
Author | Prato, M. Bonettini, S. Rebegoldi, S. |
Author_xml | – sequence: 1 givenname: S. surname: Bonettini fullname: Bonettini, S. organization: Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia – sequence: 2 givenname: M. surname: Prato fullname: Prato, M. organization: Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia – sequence: 3 givenname: S. orcidid: 0000-0002-1232-5481 surname: Rebegoldi fullname: Rebegoldi, S. email: simone.rebegoldi@unifi.it organization: Dipartimento di Ingegneria Industriale, Università di Firenze |
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Cites_doi | 10.1007/s10851-014-0523-2 10.1137/17M116001X 10.1088/0266-5611/27/12/125007 10.1137/090769521 10.1016/j.orl.2015.02.001 10.1137/15M1046095 10.1007/s10957-012-0245-9 10.1109/TIP.2010.2053941 10.1109/TIP.2003.819861 10.1007/s10851-010-0251-1 10.1109/TIP.2009.2028250 10.1515/9781400873173 10.1088/0266-5611/10/6/003 10.1007/978-1-4419-8853-9 10.1007/s10444-011-9254-8 10.1007/s10107-015-0957-3 10.1109/TMI.2003.809622 10.1023/B:JMIV.0000011321.19549.88 10.24033/bsmf.1625 10.3390/jimaging7060099 10.1007/s10957-015-0746-4 10.1214/12-STS394 10.1137/15M1019325 10.1007/s11075-018-0616-x 10.1137/080716542 10.1088/0266-5611/30/10/105003 10.1016/0167-2789(92)90242-F 10.1137/16M1080173 10.1007/s10543-019-00755-6 10.1007/s10851-014-0553-9 10.1137/050626090 10.1007/s10589-020-00186-y 10.1016/j.jvcir.2009.10.006 10.1007/s10107-009-0306-5 10.1137/110844805 10.1109/NSSMIC.2012.6551530 10.1088/2053-2563/aae109 10.1109/ISBI48211.2021.9434014 10.1007/978-1-4419-9569-8_10 10.1137/21M1391699 10.1007/978-3-319-58771-4_18 |
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Keywords | Forward–backward algorithms Inertial techniques Image deblurring Convex optimization Primal–dual algorithms |
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References | Bonettini, Loris, Porta, Prato (CR8) 2016; 26 Chambolle (CR13) 2004; 20 Loris, Verhoeven (CR29) 2011; 27 Chambolle, Pock (CR15) 2011; 40 Ma, Goldfarb, Chen (CR30) 2011; 128 Bottou, Curtis, Nocedal (CR10) 2018; 60 Vu (CR44) 2013; 38 Zanni, Benfenati, Bertero, Ruggiero (CR47) 2015; 52 Drori, Sabach, Teboulle (CR23) 2015; 43 Nesterov (CR33) 2004 Bertsekas (CR7) 1999 Bredies, Kunisch, Pock (CR11) 2010; 3 CR19 CR18 Bonettini, Rebegoldi, Ruggiero (CR9) 2018; 40 Burger, Müller, Papoutsellis, Schönlieb (CR12) 2014; 30 Figueiredo, Bioucas-Dias (CR24) 2010; 19 Beck, Teboulle (CR5) 2009; 2 Rockafellar (CR37) 1970 CR36 Combettes, Wajs (CR20) 2005; 4 Moreau (CR31) 1965; 93 Acar, Vogel (CR1) 1994; 10 Wang, Bovik, Sheikh, Simoncelli (CR45) 2004; 13 Salzo, Villa (CR39) 2012; 19 Lorenz, Pock (CR28) 2015; 51 Chen, Loris (CR17) 2019; 82 Beck, Teboulle (CR4) 2009; 18 Willett, Nowak (CR46) 2003; 22 Polyak (CR34) 1987 Attouch, Peypouquet (CR2) 2016; 26 CR6 Rasch, Chambolle (CR35) 2020; 76 Chambolle, Dossal (CR14) 2015; 166 Kongskov, Dong, Knudsen (CR26) 2019; 59 CR27 CR25 di Serafino, Landi, Viola (CR22) 2021; 7 Nesterov (CR32) 1983; 269 CR41 Villa, Salzo, Baldassarre, Verri (CR43) 2013; 23 CR40 Chambolle, Pock (CR16) 2016; 159 Rudin, Osher, Fatemi (CR38) 1992; 60 Condat (CR21) 2013; 158 Setzer, Steidl, Teuber (CR42) 2010; 21 Bach, Jenatton, Mairal, Obozinski (CR3) 2012; 27 Y Drori (410_CR23) 2015; 43 Y Nesterov (410_CR33) 2004 L Zanni (410_CR47) 2015; 52 A Beck (410_CR5) 2009; 2 M Burger (410_CR12) 2014; 30 B Polyak (410_CR34) 1987 410_CR40 Y Nesterov (410_CR32) 1983; 269 410_CR6 K Bredies (410_CR11) 2010; 3 410_CR41 S Villa (410_CR43) 2013; 23 H Attouch (410_CR2) 2016; 26 S Bonettini (410_CR9) 2018; 40 S Bonettini (410_CR8) 2016; 26 L Bottou (410_CR10) 2018; 60 410_CR25 I Loris (410_CR29) 2011; 27 MAT Figueiredo (410_CR24) 2010; 19 410_CR19 410_CR18 J Rasch (410_CR35) 2020; 76 D di Serafino (410_CR22) 2021; 7 A Chambolle (410_CR14) 2015; 166 BC Vu (410_CR44) 2013; 38 D Lorenz (410_CR28) 2015; 51 R Acar (410_CR1) 1994; 10 Z Wang (410_CR45) 2004; 13 L Condat (410_CR21) 2013; 158 RM Willett (410_CR46) 2003; 22 RD Kongskov (410_CR26) 2019; 59 S Ma (410_CR30) 2011; 128 S Salzo (410_CR39) 2012; 19 A Chambolle (410_CR13) 2004; 20 A Chambolle (410_CR15) 2011; 40 A Chambolle (410_CR16) 2016; 159 RT Rockafellar (410_CR37) 1970 S Setzer (410_CR42) 2010; 21 J Chen (410_CR17) 2019; 82 PL Combettes (410_CR20) 2005; 4 D Bertsekas (410_CR7) 1999 410_CR36 410_CR27 A Beck (410_CR4) 2009; 18 LI Rudin (410_CR38) 1992; 60 F Bach (410_CR3) 2012; 27 JJ Moreau (410_CR31) 1965; 93 |
References_xml | – volume: 51 start-page: 311 year: 2015 end-page: 325 ident: CR28 article-title: An inertial forward-backward algorithm for monotone inclusions publication-title: J. Math. Imaging Vis. doi: 10.1007/s10851-014-0523-2 contributor: fullname: Pock – volume: 40 start-page: A3180 issue: 5 year: 2018 end-page: A3210 ident: CR9 article-title: Inertial variable metric techniques for the inexact forward-backward algorithm publication-title: SIAM J. Sci. Comput. doi: 10.1137/17M116001X contributor: fullname: Ruggiero – ident: CR18 – volume: 27 year: 2011 ident: CR29 article-title: On a generalization of the iterative soft-thresholding algorithm for the case of non-separable penalty publication-title: Inverse Probl. doi: 10.1088/0266-5611/27/12/125007 contributor: fullname: Verhoeven – volume: 3 start-page: 492 year: 2010 end-page: 526 ident: CR11 article-title: Total generalized variation publication-title: SIAM J. Imaging Sci. doi: 10.1137/090769521 contributor: fullname: Pock – volume: 43 start-page: 209 issue: 2 year: 2015 end-page: 214 ident: CR23 article-title: A simple algorithm for a class of nonsmooth convex-concave saddle-point problems publication-title: Oper. Res. Lett. doi: 10.1016/j.orl.2015.02.001 contributor: fullname: Teboulle – volume: 26 start-page: 1824 issue: 3 year: 2016 end-page: 1834 ident: CR2 article-title: The rate of convergence of Nesterov’s accelerated forward-backward method is actually faster than publication-title: SIAM J. Optim. doi: 10.1137/15M1046095 contributor: fullname: Peypouquet – volume: 158 start-page: 460 issue: 2 year: 2013 end-page: 479 ident: CR21 article-title: A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-012-0245-9 contributor: fullname: Condat – volume: 19 start-page: 3133 issue: 12 year: 2010 end-page: 3145 ident: CR24 article-title: Restoration of Poissonian images using alternating direction optimization publication-title: IEEE Trans. Image Process. doi: 10.1109/TIP.2010.2053941 contributor: fullname: Bioucas-Dias – volume: 13 start-page: 600 year: 2004 end-page: 612 ident: CR45 article-title: Image quality assessment: from error visibility to structural similarity publication-title: IEEE Trans. Image Process. doi: 10.1109/TIP.2003.819861 contributor: fullname: Simoncelli – ident: CR6 – volume: 40 start-page: 120 year: 2011 end-page: 145 ident: CR15 article-title: A first-order primal-dual algorithm for convex problems with applications to imaging publication-title: J. Math. Imaging Vis. doi: 10.1007/s10851-010-0251-1 contributor: fullname: Pock – volume: 18 start-page: 2419 issue: 11 year: 2009 end-page: 34 ident: CR4 article-title: Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems publication-title: IEEE Trans. Image Processing doi: 10.1109/TIP.2009.2028250 contributor: fullname: Teboulle – year: 1970 ident: CR37 publication-title: Convex Analysis doi: 10.1515/9781400873173 contributor: fullname: Rockafellar – ident: CR40 – ident: CR25 – volume: 10 start-page: 1217 issue: 6 year: 1994 end-page: 1229 ident: CR1 article-title: Analysis of bounded variation penalty methods for ill-posed problems publication-title: Inverse Probl. doi: 10.1088/0266-5611/10/6/003 contributor: fullname: Vogel – ident: CR27 – year: 2004 ident: CR33 publication-title: Introductory lectures on convex optimization: a basic course doi: 10.1007/978-1-4419-8853-9 contributor: fullname: Nesterov – volume: 38 start-page: 667 issue: 3 year: 2013 end-page: 681 ident: CR44 article-title: A splitting algorithm for dual monotone inclusions involving cocoercive operators publication-title: Adv. Comput. Math. doi: 10.1007/s10444-011-9254-8 contributor: fullname: Vu – volume: 159 start-page: 253 year: 2016 end-page: 287 ident: CR16 article-title: On the ergodic convergence rates of a first-order primal-dual algorithm publication-title: Math. Program. doi: 10.1007/s10107-015-0957-3 contributor: fullname: Pock – volume: 22 start-page: 332 year: 2003 end-page: 350 ident: CR46 article-title: Platelets: A multiscale approach for recovering edges and surfaces in photon limited medical imaging publication-title: IEEE Trans. Med. Imaging doi: 10.1109/TMI.2003.809622 contributor: fullname: Nowak – volume: 20 start-page: 89 year: 2004 end-page: 97 ident: CR13 article-title: An algorithm for total variation minimization and applications publication-title: J. Math. Imaging Vis. doi: 10.1023/B:JMIV.0000011321.19549.88 contributor: fullname: Chambolle – volume: 93 start-page: 273 year: 1965 end-page: 299 ident: CR31 article-title: Proximité et dualité dans un espace hilbertien publication-title: Bull. Soc. Math. France doi: 10.24033/bsmf.1625 contributor: fullname: Moreau – ident: CR19 – volume: 7 start-page: 99 issue: 6 year: 2021 ident: CR22 article-title: Directional TGV-based image restoration under Poisson noise publication-title: J. Imaging doi: 10.3390/jimaging7060099 contributor: fullname: Viola – volume: 166 start-page: 968 issue: 3 year: 2015 end-page: 982 ident: CR14 article-title: On the convergence of the iterates of the “Fast Iterative Shrinkage/Thresholding Algorithm” publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-015-0746-4 contributor: fullname: Dossal – volume: 27 start-page: 450 issue: 4 year: 2012 end-page: 468 ident: CR3 article-title: Structured sparsity through convex optimization publication-title: Stat. Sci. doi: 10.1214/12-STS394 contributor: fullname: Obozinski – volume: 19 start-page: 1167 issue: 4 year: 2012 end-page: 1192 ident: CR39 article-title: Inexact and accelerated proximal point algorithms publication-title: J. Convex Anal. contributor: fullname: Villa – volume: 26 start-page: 891 issue: 2 year: 2016 end-page: 921 ident: CR8 article-title: Variable metric inexact line-search based methods for nonsmooth optimization publication-title: SIAM J. Optim. doi: 10.1137/15M1019325 contributor: fullname: Prato – volume: 82 start-page: 605 year: 2019 end-page: 621 ident: CR17 article-title: On starting and stopping criteria for nested primal-dual iterations publication-title: Numer. Algorithms doi: 10.1007/s11075-018-0616-x contributor: fullname: Loris – volume: 2 start-page: 183 year: 2009 end-page: 202 ident: CR5 article-title: A fast iterative shrinkage-thresholding algorithm for linear inverse problems publication-title: SIAM J. Imaging Sci. doi: 10.1137/080716542 contributor: fullname: Teboulle – volume: 30 year: 2014 ident: CR12 article-title: Total variation regularisation in measurement and image space for pet reconstruction publication-title: Inverse Probl. doi: 10.1088/0266-5611/30/10/105003 contributor: fullname: Schönlieb – ident: CR36 – volume: 60 start-page: 259 issue: 1–4 year: 1992 end-page: 268 ident: CR38 article-title: Nonlinear total variation based noise removal algorithms publication-title: J. Phys. D. doi: 10.1016/0167-2789(92)90242-F contributor: fullname: Fatemi – volume: 60 start-page: 223 issue: 2 year: 2018 end-page: 311 ident: CR10 article-title: Optimization methods for large-scale machine learning publication-title: SIAM Rev. doi: 10.1137/16M1080173 contributor: fullname: Nocedal – volume: 269 start-page: 543 year: 1983 end-page: 547 ident: CR32 article-title: A method for solving the convex programming problem with convergence rate publication-title: Soviet Math. Dokl. contributor: fullname: Nesterov – volume: 59 start-page: 903 year: 2019 end-page: 928 ident: CR26 article-title: Directional total generalized variation regularization publication-title: BIT Numer. Math. doi: 10.1007/s10543-019-00755-6 contributor: fullname: Knudsen – ident: CR41 – volume: 52 start-page: 397 issue: 3 year: 2015 end-page: 413 ident: CR47 article-title: Numerical methods for parameter estimation in Poisson data inversion publication-title: J. Math. Imaging Vis. doi: 10.1007/s10851-014-0553-9 contributor: fullname: Ruggiero – volume: 4 start-page: 1168 issue: 4 year: 2005 end-page: 1200 ident: CR20 article-title: Signal recovery by proximal forward-backward splitting publication-title: Multiscale Model. Simul. doi: 10.1137/050626090 contributor: fullname: Wajs – volume: 76 start-page: 381 year: 2020 end-page: 430 ident: CR35 article-title: Inexact first-order primal-dual algorithms publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-020-00186-y contributor: fullname: Chambolle – volume: 21 start-page: 193 year: 2010 end-page: 199 ident: CR42 article-title: Deblurring Poissonian images by split Bregman techniques publication-title: J. Vis. Commun. Image R. doi: 10.1016/j.jvcir.2009.10.006 contributor: fullname: Teuber – year: 1999 ident: CR7 publication-title: Nonlinear Programming contributor: fullname: Bertsekas – volume: 128 start-page: 321 year: 2011 end-page: 353 ident: CR30 article-title: Fixed point and Bregman iterative methods for matrix rank minimization publication-title: Math. Program. doi: 10.1007/s10107-009-0306-5 contributor: fullname: Chen – volume: 23 start-page: 1607 issue: 3 year: 2013 end-page: 1633 ident: CR43 article-title: Accelerated and inexact forward-backward algorithms publication-title: SIAM J. Optim. doi: 10.1137/110844805 contributor: fullname: Verri – year: 1987 ident: CR34 publication-title: Introduction to Optimization contributor: fullname: Polyak – volume: 18 start-page: 2419 issue: 11 year: 2009 ident: 410_CR4 publication-title: IEEE Trans. Image Processing doi: 10.1109/TIP.2009.2028250 contributor: fullname: A Beck – ident: 410_CR41 – ident: 410_CR18 doi: 10.1109/NSSMIC.2012.6551530 – volume: 43 start-page: 209 issue: 2 year: 2015 ident: 410_CR23 publication-title: Oper. Res. Lett. doi: 10.1016/j.orl.2015.02.001 contributor: fullname: Y Drori – volume: 23 start-page: 1607 issue: 3 year: 2013 ident: 410_CR43 publication-title: SIAM J. Optim. doi: 10.1137/110844805 contributor: fullname: S Villa – volume: 40 start-page: A3180 issue: 5 year: 2018 ident: 410_CR9 publication-title: SIAM J. Sci. Comput. doi: 10.1137/17M116001X contributor: fullname: S Bonettini – volume: 60 start-page: 259 issue: 1–4 year: 1992 ident: 410_CR38 publication-title: J. Phys. D. doi: 10.1016/0167-2789(92)90242-F contributor: fullname: LI Rudin – ident: 410_CR6 doi: 10.1088/2053-2563/aae109 – volume: 13 start-page: 600 year: 2004 ident: 410_CR45 publication-title: IEEE Trans. Image Process. doi: 10.1109/TIP.2003.819861 contributor: fullname: Z Wang – ident: 410_CR27 doi: 10.1109/ISBI48211.2021.9434014 – volume: 93 start-page: 273 year: 1965 ident: 410_CR31 publication-title: Bull. Soc. Math. France doi: 10.24033/bsmf.1625 contributor: fullname: JJ Moreau – volume: 22 start-page: 332 year: 2003 ident: 410_CR46 publication-title: IEEE Trans. Med. Imaging doi: 10.1109/TMI.2003.809622 contributor: fullname: RM Willett – volume: 27 year: 2011 ident: 410_CR29 publication-title: Inverse Probl. doi: 10.1088/0266-5611/27/12/125007 contributor: fullname: I Loris – volume: 30 year: 2014 ident: 410_CR12 publication-title: Inverse Probl. doi: 10.1088/0266-5611/30/10/105003 contributor: fullname: M Burger – volume: 52 start-page: 397 issue: 3 year: 2015 ident: 410_CR47 publication-title: J. Math. Imaging Vis. doi: 10.1007/s10851-014-0553-9 contributor: fullname: L Zanni – volume: 7 start-page: 99 issue: 6 year: 2021 ident: 410_CR22 publication-title: J. Imaging doi: 10.3390/jimaging7060099 contributor: fullname: D di Serafino – volume: 19 start-page: 1167 issue: 4 year: 2012 ident: 410_CR39 publication-title: J. Convex Anal. contributor: fullname: S Salzo – volume: 158 start-page: 460 issue: 2 year: 2013 ident: 410_CR21 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-012-0245-9 contributor: fullname: L Condat – volume-title: Introduction to Optimization year: 1987 ident: 410_CR34 contributor: fullname: B Polyak – ident: 410_CR19 doi: 10.1007/978-1-4419-9569-8_10 – volume: 21 start-page: 193 year: 2010 ident: 410_CR42 publication-title: J. Vis. Commun. Image R. doi: 10.1016/j.jvcir.2009.10.006 contributor: fullname: S Setzer – ident: 410_CR36 doi: 10.1137/21M1391699 – volume: 166 start-page: 968 issue: 3 year: 2015 ident: 410_CR14 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-015-0746-4 contributor: fullname: A Chambolle – ident: 410_CR40 – volume: 59 start-page: 903 year: 2019 ident: 410_CR26 publication-title: BIT Numer. Math. doi: 10.1007/s10543-019-00755-6 contributor: fullname: RD Kongskov – volume: 19 start-page: 3133 issue: 12 year: 2010 ident: 410_CR24 publication-title: IEEE Trans. Image Process. doi: 10.1109/TIP.2010.2053941 contributor: fullname: MAT Figueiredo – volume-title: Introductory lectures on convex optimization: a basic course year: 2004 ident: 410_CR33 doi: 10.1007/978-1-4419-8853-9 contributor: fullname: Y Nesterov – volume: 82 start-page: 605 year: 2019 ident: 410_CR17 publication-title: Numer. Algorithms doi: 10.1007/s11075-018-0616-x contributor: fullname: J Chen – volume: 26 start-page: 891 issue: 2 year: 2016 ident: 410_CR8 publication-title: SIAM J. Optim. doi: 10.1137/15M1019325 contributor: fullname: S Bonettini – volume: 159 start-page: 253 year: 2016 ident: 410_CR16 publication-title: Math. Program. doi: 10.1007/s10107-015-0957-3 contributor: fullname: A Chambolle – ident: 410_CR25 doi: 10.1007/978-3-319-58771-4_18 – volume: 27 start-page: 450 issue: 4 year: 2012 ident: 410_CR3 publication-title: Stat. Sci. doi: 10.1214/12-STS394 contributor: fullname: F Bach – volume-title: Nonlinear Programming year: 1999 ident: 410_CR7 contributor: fullname: D Bertsekas – volume: 269 start-page: 543 year: 1983 ident: 410_CR32 publication-title: Soviet Math. Dokl. contributor: fullname: Y Nesterov – volume-title: Convex Analysis year: 1970 ident: 410_CR37 doi: 10.1515/9781400873173 contributor: fullname: RT Rockafellar – volume: 38 start-page: 667 issue: 3 year: 2013 ident: 410_CR44 publication-title: Adv. Comput. Math. doi: 10.1007/s10444-011-9254-8 contributor: fullname: BC Vu – volume: 10 start-page: 1217 issue: 6 year: 1994 ident: 410_CR1 publication-title: Inverse Probl. doi: 10.1088/0266-5611/10/6/003 contributor: fullname: R Acar – volume: 4 start-page: 1168 issue: 4 year: 2005 ident: 410_CR20 publication-title: Multiscale Model. Simul. doi: 10.1137/050626090 contributor: fullname: PL Combettes – volume: 3 start-page: 492 year: 2010 ident: 410_CR11 publication-title: SIAM J. Imaging Sci. doi: 10.1137/090769521 contributor: fullname: K Bredies – volume: 20 start-page: 89 year: 2004 ident: 410_CR13 publication-title: J. Math. Imaging Vis. doi: 10.1023/B:JMIV.0000011321.19549.88 contributor: fullname: A Chambolle – volume: 40 start-page: 120 year: 2011 ident: 410_CR15 publication-title: J. Math. Imaging Vis. doi: 10.1007/s10851-010-0251-1 contributor: fullname: A Chambolle – volume: 51 start-page: 311 year: 2015 ident: 410_CR28 publication-title: J. Math. Imaging Vis. doi: 10.1007/s10851-014-0523-2 contributor: fullname: D Lorenz – volume: 60 start-page: 223 issue: 2 year: 2018 ident: 410_CR10 publication-title: SIAM Rev. doi: 10.1137/16M1080173 contributor: fullname: L Bottou – volume: 76 start-page: 381 year: 2020 ident: 410_CR35 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-020-00186-y contributor: fullname: J Rasch – volume: 26 start-page: 1824 issue: 3 year: 2016 ident: 410_CR2 publication-title: SIAM J. Optim. doi: 10.1137/15M1046095 contributor: fullname: H Attouch – volume: 2 start-page: 183 year: 2009 ident: 410_CR5 publication-title: SIAM J. Imaging Sci. doi: 10.1137/080716542 contributor: fullname: A Beck – volume: 128 start-page: 321 year: 2011 ident: 410_CR30 publication-title: Math. Program. doi: 10.1007/s10107-009-0306-5 contributor: fullname: S Ma |
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Snippet | We propose a nested primal–dual algorithm with extrapolation on the primal variable suited for minimizing the sum of two convex functions, one of which is... Abstract We propose a nested primal–dual algorithm with extrapolation on the primal variable suited for minimizing the sum of two convex functions, one of... |
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SubjectTerms | Accuracy Algorithms Computational geometry Convergence Convex analysis Convex and Discrete Geometry Convexity Experiments Image restoration Management Science Mathematics Mathematics and Statistics Operations Research Operations Research/Decision Theory Optimization Parameters Saddle points Statistics |
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Title | A nested primal–dual FISTA-like scheme for composite convex optimization problems |
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