A proximal fully parallel splitting method with a relaxation factor for separable convex programming
In this paper, we propose a proximal fully parallel splitting method with a relaxation factor for solving separable convex minimization model with linear constraints, where the objective function is the sum of m individual functions without coupled variables. With a full Jacobian decomposition, we d...
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| Published in: | Applied numerical mathematics Vol. 195; pp. 17 - 38 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.01.2024
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| ISSN: | 0168-9274 |
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| Abstract | In this paper, we propose a proximal fully parallel splitting method with a relaxation factor for solving separable convex minimization model with linear constraints, where the objective function is the sum of m individual functions without coupled variables. With a full Jacobian decomposition, we decompose the subproblem associated with the augmented Lagrangian method into m smaller subproblems and then add a quadratic proximal term to each decomposed subproblem, which makes the resulting ones easier to solve for many applications. In order to accelerate the numerical performance, we attach a positive relaxation factor to update the Lagrange multiplier, which also allows more flexibility in the design of algorithms. Moreover, we refine the step size of the underrelaxation step, which enlarges several existing ones in the literature. We prove that the proposed method is globally convergent, and show the worst-case O(1/k) convergence rate in a nonergodic sense. Finally, the efficiency and robustness of the proposed method are also demonstrated by solving the ℓ1 norm problem, the ℓ1-regularized least squares problem, the exchange problem and the total variation image restoration problem. |
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| AbstractList | In this paper, we propose a proximal fully parallel splitting method with a relaxation factor for solving separable convex minimization model with linear constraints, where the objective function is the sum of m individual functions without coupled variables. With a full Jacobian decomposition, we decompose the subproblem associated with the augmented Lagrangian method into m smaller subproblems and then add a quadratic proximal term to each decomposed subproblem, which makes the resulting ones easier to solve for many applications. In order to accelerate the numerical performance, we attach a positive relaxation factor to update the Lagrange multiplier, which also allows more flexibility in the design of algorithms. Moreover, we refine the step size of the underrelaxation step, which enlarges several existing ones in the literature. We prove that the proposed method is globally convergent, and show the worst-case O(1/k) convergence rate in a nonergodic sense. Finally, the efficiency and robustness of the proposed method are also demonstrated by solving the ℓ1 norm problem, the ℓ1-regularized least squares problem, the exchange problem and the total variation image restoration problem. |
| Author | Wu, Jiansheng Yin, Jianghua Jian, Jinbao Ma, Guodong Jiang, Xianzhen |
| Author_xml | – sequence: 1 givenname: Jianghua orcidid: 0000-0002-0990-4327 surname: Yin fullname: Yin, Jianghua organization: School of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning 530006, China – sequence: 2 givenname: Jinbao orcidid: 0000-0001-8048-7397 surname: Jian fullname: Jian, Jinbao email: jianjb@gxu.edu.cn organization: School of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning 530006, China – sequence: 3 givenname: Xianzhen surname: Jiang fullname: Jiang, Xianzhen organization: School of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning 530006, China – sequence: 4 givenname: Jiansheng surname: Wu fullname: Wu, Jiansheng organization: College of Mathematics and Computer Science, Guangxi Science and Technology Normal University, Laibin 546199, China – sequence: 5 givenname: Guodong surname: Ma fullname: Ma, Guodong organization: School of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning 530006, China |
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| Cites_doi | 10.1561/2200000016 10.1007/s10851-010-0251-1 10.1137/110822347 10.1137/080724265 10.1007/s10957-018-1338-x 10.1016/j.ejor.2010.07.020 10.1093/imanum/dry092 10.1111/j.1467-9868.2011.00771.x 10.1155/2017/9674528 10.1007/s12532-010-0017-1 10.1016/0167-2789(92)90242-F 10.1145/1961189.1961199 10.1137/0314056 10.1080/02331934.2020.1728756 10.1016/j.apnum.2020.09.016 10.1090/S0002-9947-1956-0084194-4 10.1137/110836936 10.1007/s10915-015-0048-x 10.1137/090768813 10.1007/s10107-018-1247-7 10.1007/s10107-017-1205-9 10.1090/S0025-5718-2014-02829-9 10.1109/TPAMI.2011.282 10.1080/10556788.2016.1200044 10.1007/s10107-014-0826-5 10.1007/s10915-010-9408-8 10.1137/100781894 10.1007/s10589-021-00338-8 10.1007/s10107-019-01423-x 10.1137/050626090 10.1137/110860185 10.1007/s10915-016-0318-2 10.1007/s11075-019-00819-2 10.1007/BF00927673 10.1109/TII.2019.2937513 10.1007/s10589-019-00087-9 10.1137/130922793 10.1093/imanum/drq039 10.1007/s10957-012-0003-z 10.1007/s10589-020-00206-x 10.1016/j.cam.2013.07.010 10.4208/csiam-am.SO-2021-0021 10.1016/0898-1221(76)90003-1 10.1137/140971178 10.1090/S0025-5718-2012-02598-1 10.1007/s10589-017-9971-0 |
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| Keywords | Step size Splitting algorithm Convergence rate Augmented Lagrangian method Relaxation factor |
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| References | He, Xu, Yuan (br0050) 2011; 32 Rudin, Osher, Fatemi (br0580) 1992; 60 Han, He, Xu (br0310) 2014; 256 Powell (br0120) 1969 Shen, Zuo, Yu (br0380) 2021; 160 Wang, Desai, He (br0340) 2017; 32 Bai, Han, Sun, Zhang (br0510) 2022; 3 Boyd, Parikh, Chu, Peleato, Eckstein (br0040) 2010; 3 Gu, Jiang, Han (br0450) 2015 Rockafellar (br0520) 1970 Gonzales, Woods (br0610) 2008 Eckstein, Fukushima (br0180) 1994 Fortin, Glowinski (br0420) 1982 Eckstein, Yao (br0200) 2015; 11 Han, Yuan, Zhang (br0100) 2014; 83 Glowinski, Marroco (br0160) 1975; 9 He, Yuan (br0400) 2015; 1 Glowinski (br0410) 1984 Sun, Zhang (br0070) 2010; 207 Zhang, Burger, Osher (br0560) 2011; 46 Börgens, Kanzow (br0350) 2019; 73 Martinet (br0140) 1970; 4 He, Hou, Yuan (br0290) 2015; 25 Tao, Yuan (br0460) 2018; 179 Bai, Li, Xu, Zhang (br0370) 2018; 70 Gabay, Mercier (br0170) 1976; 2 Pratt (br0600) 2001 He, Ma, Yuan (br0470) 2020; 40 Wen, Goldfarb, Yin (br0080) 2010; 2 Chan, Tao, Yuan (br0030) 2013; 6 Glowinski (br0190) 2014 Bai, Hager, Zhang (br0500) 2022; 81 Rockafellar (br0130) 1976; 14 Hestenes (br0110) 1969; 4 Han, Yuan (br0240) 2012; 155 Li, Sun, Toh (br0280) 2019; 175 Ma (br0490) 2020; 85 Tibshirani (br0570) 2011; 73 He, Tao, Yuan (br0250) 2012; 22 Sun, Liu, Sun (br0320) 2017; 2017 Yang, Luo, Xu, Zhang, Dong (br0210) 2020; 16 Deng, Lai, Peng, Yin (br0330) 2017; 71 Wang, Yang, Yin, Zhang (br0010) 2008; 1 Yang, Yuan (br0540) 2013; 82 Douglas, Rachford (br0150) 1956; 82 Chang, Lin (br0590) 2011; 2 Fortin, Glowinski (br0430) 1983 Blum, Oettli (br0300) 1975 Deng, Yin (br0550) 2016; 66 Chen, Li, Sun, Toh (br0090) 2021; 185 Chen, He, Ye, Yuan (br0230) 2016; 155 Tao, Yuan (br0060) 2011; 21 Chambolle, Pock (br0020) 2011; 40 Lin, Ma, Zhang (br0260) 2015; 25 Peng, Ganesh, Wright, Xu, Ma (br0220) 2012; 34 He, Yuan (br0390) 2012; 50 Chen, Li, Liu, Ye (br0270) 2019; 173 Combettes, Wajs (br0620) 2005; 4 Shen, Zhang, Zhang (br0360) 2021; 70 Chen, He, Yuan (br0440) 2012; 32 Facchinei, Pang (br0530) 2003 Tao (br0480) 2020; 77 Glowinski (10.1016/j.apnum.2023.09.003_br0160) 1975; 9 Gonzales (10.1016/j.apnum.2023.09.003_br0610) 2008 Chen (10.1016/j.apnum.2023.09.003_br0440) 2012; 32 Rockafellar (10.1016/j.apnum.2023.09.003_br0520) 1970 Wang (10.1016/j.apnum.2023.09.003_br0340) 2017; 32 Peng (10.1016/j.apnum.2023.09.003_br0220) 2012; 34 Powell (10.1016/j.apnum.2023.09.003_br0120) 1969 Chen (10.1016/j.apnum.2023.09.003_br0270) 2019; 173 Gabay (10.1016/j.apnum.2023.09.003_br0170) 1976; 2 He (10.1016/j.apnum.2023.09.003_br0400) 2015; 1 Pratt (10.1016/j.apnum.2023.09.003_br0600) 2001 Deng (10.1016/j.apnum.2023.09.003_br0330) 2017; 71 Bai (10.1016/j.apnum.2023.09.003_br0510) 2022; 3 Douglas (10.1016/j.apnum.2023.09.003_br0150) 1956; 82 Facchinei (10.1016/j.apnum.2023.09.003_br0530) 2003 Sun (10.1016/j.apnum.2023.09.003_br0070) 2010; 207 He (10.1016/j.apnum.2023.09.003_br0390) 2012; 50 Han (10.1016/j.apnum.2023.09.003_br0100) 2014; 83 Tao (10.1016/j.apnum.2023.09.003_br0460) 2018; 179 Chang (10.1016/j.apnum.2023.09.003_br0590) 2011; 2 Boyd (10.1016/j.apnum.2023.09.003_br0040) 2010; 3 He (10.1016/j.apnum.2023.09.003_br0470) 2020; 40 Shen (10.1016/j.apnum.2023.09.003_br0360) 2021; 70 Han (10.1016/j.apnum.2023.09.003_br0310) 2014; 256 He (10.1016/j.apnum.2023.09.003_br0290) 2015; 25 Chen (10.1016/j.apnum.2023.09.003_br0230) 2016; 155 Chambolle (10.1016/j.apnum.2023.09.003_br0020) 2011; 40 Chen (10.1016/j.apnum.2023.09.003_br0090) 2021; 185 Eckstein (10.1016/j.apnum.2023.09.003_br0200) 2015; 11 He (10.1016/j.apnum.2023.09.003_br0250) 2012; 22 Bai (10.1016/j.apnum.2023.09.003_br0500) 2022; 81 Hestenes (10.1016/j.apnum.2023.09.003_br0110) 1969; 4 Gu (10.1016/j.apnum.2023.09.003_br0450) Fortin (10.1016/j.apnum.2023.09.003_br0420) 1982 Shen (10.1016/j.apnum.2023.09.003_br0380) 2021; 160 He (10.1016/j.apnum.2023.09.003_br0050) 2011; 32 Li (10.1016/j.apnum.2023.09.003_br0280) 2019; 175 Tibshirani (10.1016/j.apnum.2023.09.003_br0570) 2011; 73 Tao (10.1016/j.apnum.2023.09.003_br0060) 2011; 21 Börgens (10.1016/j.apnum.2023.09.003_br0350) 2019; 73 Deng (10.1016/j.apnum.2023.09.003_br0550) 2016; 66 Ma (10.1016/j.apnum.2023.09.003_br0490) 2020; 85 Han (10.1016/j.apnum.2023.09.003_br0240) 2012; 155 Rudin (10.1016/j.apnum.2023.09.003_br0580) 1992; 60 Tao (10.1016/j.apnum.2023.09.003_br0480) 2020; 77 Wang (10.1016/j.apnum.2023.09.003_br0010) 2008; 1 Sun (10.1016/j.apnum.2023.09.003_br0320) 2017; 2017 Martinet (10.1016/j.apnum.2023.09.003_br0140) 1970; 4 Combettes (10.1016/j.apnum.2023.09.003_br0620) 2005; 4 Eckstein (10.1016/j.apnum.2023.09.003_br0180) 1994 Wen (10.1016/j.apnum.2023.09.003_br0080) 2010; 2 Yang (10.1016/j.apnum.2023.09.003_br0540) 2013; 82 Bai (10.1016/j.apnum.2023.09.003_br0370) 2018; 70 Chan (10.1016/j.apnum.2023.09.003_br0030) 2013; 6 Lin (10.1016/j.apnum.2023.09.003_br0260) 2015; 25 Blum (10.1016/j.apnum.2023.09.003_br0300) 1975 Glowinski (10.1016/j.apnum.2023.09.003_br0190) 2014 Zhang (10.1016/j.apnum.2023.09.003_br0560) 2011; 46 Rockafellar (10.1016/j.apnum.2023.09.003_br0130) 1976; 14 Yang (10.1016/j.apnum.2023.09.003_br0210) 2020; 16 Fortin (10.1016/j.apnum.2023.09.003_br0430) 1983 Glowinski (10.1016/j.apnum.2023.09.003_br0410) 1984 |
| References_xml | – volume: 179 start-page: 163 year: 2018 end-page: 196 ident: br0460 article-title: On Glowinski's open question on the alternating direction method of multipliers publication-title: J. Optim. Theory Appl. – volume: 77 start-page: 91 year: 2020 end-page: 123 ident: br0480 article-title: Convergence study of indefinite proximal ADMM with a relaxation factor publication-title: Comput. Optim. Appl. – volume: 60 start-page: 259 year: 1992 end-page: 268 ident: br0580 article-title: Nonlinear total variation based noise removal algorithms publication-title: Physica D – volume: 82 start-page: 421 year: 1956 end-page: 439 ident: br0150 article-title: On the numerical solution of heat conduction problems in two and three space variables publication-title: Trans. Am. Math. Soc. – start-page: 115 year: 1994 end-page: 134 ident: br0180 article-title: Reformulations and applications of the alternating direction method of multipliers publication-title: Large Scale Optimization – volume: 6 start-page: 680 year: 2013 end-page: 697 ident: br0030 article-title: Constrained total variation deblurring models and fast algorithms based on alternating direction method of multipliers publication-title: SIAM J. Imaging Sci. – volume: 85 start-page: 399 year: 2020 end-page: 425 ident: br0490 article-title: Convergence study on the proximal alternating direction method with larger step size publication-title: Numer. Algorithms – year: 2001 ident: br0600 article-title: Digital Image Processing: PIKS Inside – volume: 2 start-page: 17 year: 1976 end-page: 40 ident: br0170 article-title: A dual algorithm for the solution of nonlinear variational problems via finite element approximation publication-title: Comput. Math. Appl. – volume: 256 start-page: 36 year: 2014 end-page: 51 ident: br0310 article-title: A proximal parallel splitting method for minimizing sum of convex functions with linear constraints publication-title: J. Comput. Appl. Math. – volume: 32 start-page: 227 year: 2012 end-page: 245 ident: br0440 article-title: Matrix completion via alternating direction method publication-title: IMA J. Numer. Anal. – year: 1970 ident: br0520 article-title: Convex Analysis – volume: 4 start-page: 1168 year: 2005 end-page: 1200 ident: br0620 article-title: Signal recovery by proximal forward-backward splitting publication-title: Multiscale Model. Simul. – volume: 83 start-page: 2263 year: 2014 end-page: 2291 ident: br0100 article-title: An augmented Lagrangian based parallel splitting method for separable convex minimization with applications to image processing publication-title: Math. Compet. – volume: 22 start-page: 313 year: 2012 end-page: 340 ident: br0250 article-title: Alternating direction method with Gaussian back substitution for separable convex programming publication-title: SIAM J. Optim. – volume: 73 start-page: 273 year: 2011 end-page: 282 ident: br0570 article-title: Regression shrinkage and selection via the lasso: a retrospective publication-title: J. R. Stat. Soc. Ser. B, Stat. Methodol. – volume: 16 start-page: 1858 year: 2020 end-page: 1872 ident: br0210 article-title: A distributed dual consensus ADMM based on partition for DC-DOPF with carbon emission trading publication-title: IEEE Trans. Ind. Inform. – year: 1984 ident: br0410 article-title: Numerical Methods for Nonlinear Variational Problems – volume: 82 start-page: 301 year: 2013 end-page: 329 ident: br0540 article-title: Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization publication-title: Math. Compet. – volume: 4 start-page: 154 year: 1970 end-page: 158 ident: br0140 article-title: Régularization, d'inéquations variationelles par approximations succesives publication-title: Rev. Fr. Inform. Rech. Opér. – volume: 3 start-page: 448 year: 2022 end-page: 479 ident: br0510 article-title: Convergence analysis of an inexact accelerated stochastic ADMM with larger stepsizes publication-title: CSIAM Trans. Appl. Math. – volume: 46 start-page: 20 year: 2011 end-page: 46 ident: br0560 article-title: A unified primal-dual algorithm framework based on Bregman iteration publication-title: J. Sci. Comput. – volume: 1 start-page: 145 year: 2015 end-page: 174 ident: br0400 article-title: Block-wise alternating direction method of multipliers for multiple-block convex programming and beyond publication-title: J. Comput. Math. – volume: 185 start-page: 111 year: 2021 end-page: 161 ident: br0090 article-title: On the equivalence of inexact proximal ALM and ADMM for a class of convex composite programming publication-title: Math. Program. – year: 1982 ident: br0420 article-title: Méthodes de Lagrangien Augmenté: Applications à la Résolution Numérique de Problèmes aux Limites – year: 1983 ident: br0430 article-title: Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems – start-page: 283 year: 1969 end-page: 298 ident: br0120 article-title: A method for nonlinear constraints in minimization problems publication-title: Optimization – volume: 32 start-page: 136 year: 2011 end-page: 152 ident: br0050 article-title: Solving large-scale least squares covariance matrix problems by alternating direction methods publication-title: SIAM J. Matrix Anal. Appl. – volume: 40 start-page: 120 year: 2011 end-page: 145 ident: br0020 article-title: A first-order primal-dual algorithm for convex problems with applications to imaging publication-title: J. Math. Imaging Vis. – volume: 70 start-page: 129 year: 2018 end-page: 170 ident: br0370 article-title: Generalized symmetric ADMM for separable convex optimization publication-title: Comput. Optim. Appl. – volume: 73 start-page: 755 year: 2019 end-page: 790 ident: br0350 article-title: Regularized Jacobi-type ADMM-methods for a class of separable convex optimization problems in Hilbert spaces publication-title: Comput. Optim. Appl. – volume: 34 start-page: 2233 year: 2012 end-page: 2246 ident: br0220 article-title: RASL: robust alignment by sparse and low-rank decomposition for linearly correlated images publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – volume: 175 start-page: 395 year: 2019 end-page: 418 ident: br0280 article-title: A block symmetric Gauss-Seidel decomposition theorem for convex composite quadratic programming and its applications publication-title: Math. Program. – volume: 21 start-page: 57 year: 2011 end-page: 81 ident: br0060 article-title: Recovering low-rank and sparse components of matrices from incomplete and noisy observations publication-title: SIAM J. Optim. – volume: 81 start-page: 479 year: 2022 end-page: 518 ident: br0500 article-title: An inexact accelerated stochastic ADMM for separable convex optimization publication-title: Comput. Optim. Appl. – volume: 50 start-page: 700 year: 2012 end-page: 709 ident: br0390 article-title: On the publication-title: SIAM J. Numer. Anal. – volume: 2 start-page: 1 year: 2011 end-page: 27 ident: br0590 article-title: LIBSVM: a library for support vector machines publication-title: ACM Trans. Intell. Syst. Technol. – year: 1975 ident: br0300 publication-title: Mathematical Optimization – volume: 66 start-page: 889 year: 2016 end-page: 916 ident: br0550 article-title: On the global and linear convergence of the generalized alternating direction method of multipliers publication-title: J. Sci. Comput. – volume: 71 start-page: 712 year: 2017 end-page: 736 ident: br0330 article-title: Parallel multi-block ADMM with publication-title: J. Sci. Comput. – volume: 3 start-page: 1 year: 2010 end-page: 122 ident: br0040 article-title: Distributed optimization and statistical learning via the alternating direction method of multipliers publication-title: Found. Trends Mach. Learn. – volume: 25 start-page: 2274 year: 2015 end-page: 2312 ident: br0290 article-title: On full Jacobian decomposition of the augmented Lagrangian method for separable convex programming publication-title: SIAM J. Optim. – start-page: 59 year: 2014 end-page: 82 ident: br0190 article-title: On alternating direction methods of multipliers: a historical perspective publication-title: Modeling, Simulation and Optimization for Science and Technology, Computational Methods in Applied Sciences – volume: 1 start-page: 248 year: 2008 end-page: 272 ident: br0010 article-title: A new alternating minimization algorithm for total variation image reconstruction publication-title: SIAM J. Imaging Sci. – volume: 2 start-page: 203 year: 2010 end-page: 230 ident: br0080 article-title: Alternating direction augmented Lagrangian methods for semidefinite programming publication-title: Math. Program. Comput. – volume: 173 start-page: 37 year: 2019 end-page: 77 ident: br0270 article-title: Extended ADMM and BCD for nonseparable convex minimization models with quadratic coupling terms: convergence analysis and insights publication-title: Math. Program. – volume: 14 start-page: 877 year: 1976 end-page: 898 ident: br0130 article-title: Monotone operators and the proximal point algorithm publication-title: SIAM J. Control Optim. – volume: 2017 year: 2017 ident: br0320 article-title: A proximal fully parallel splitting method for stable principal component pursuit publication-title: Math. Probl. Eng. – volume: 160 start-page: 65 year: 2021 end-page: 83 ident: br0380 article-title: A partially proximal S-ADMM for separable convex optimization with linear constraints publication-title: Appl. Numer. Math. – volume: 155 start-page: 57 year: 2016 end-page: 79 ident: br0230 article-title: The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent publication-title: Math. Program. – volume: 4 start-page: 303 year: 1969 end-page: 320 ident: br0110 article-title: Multiplier and gradient methods publication-title: J. Optim. Theory Appl. – volume: 207 start-page: 1210 year: 2010 end-page: 1220 ident: br0070 article-title: A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs publication-title: Eur. J. Oper. Res. – year: 2015 ident: br0450 article-title: A semi-proximal-based strictly contractive Peaceman-Rachford splitting method – year: 2003 ident: br0530 article-title: Finite-Dimensional Variational Inequalities and Complementarity Problems, Volumes i and II – year: 2008 ident: br0610 article-title: Digital Image Processing – volume: 25 start-page: 1478 year: 2015 end-page: 1497 ident: br0260 article-title: On the global linear convergence of the ADMM with multiblock variables publication-title: SIAM J. Optim. – volume: 70 start-page: 631 year: 2021 end-page: 657 ident: br0360 article-title: A partial PPA block-wise ADMM for multi-block linearly constrained separable convex optimization publication-title: Optimization – volume: 155 start-page: 227 year: 2012 end-page: 238 ident: br0240 article-title: A note on the alternating direction method of multipliers publication-title: J. Optim. Theory Appl. – volume: 11 start-page: 619 year: 2015 end-page: 644 ident: br0200 article-title: Understanding the convergence of the alternating direction method of multipliers: theoretical and computational perspectives publication-title: Pac. J. Optim. – volume: 40 start-page: 1188 year: 2020 end-page: 1216 ident: br0470 article-title: Optimal proximal augmented Lagrangian method and its application to full Jacobian splitting for multi-block separable convex minimization problems publication-title: IMA J. Numer. Anal. – volume: 32 start-page: 39 year: 2017 end-page: 68 ident: br0340 article-title: A proximal partially parallel splitting method for separable convex programs publication-title: Optim. Methods Softw. – volume: 9 start-page: 41 year: 1975 end-page: 76 ident: br0160 article-title: Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéaires, M2AN publication-title: Math. Model. Numer. Anal. – volume: 3 start-page: 1 year: 2010 ident: 10.1016/j.apnum.2023.09.003_br0040 article-title: Distributed optimization and statistical learning via the alternating direction method of multipliers publication-title: Found. Trends Mach. Learn. doi: 10.1561/2200000016 – volume: 40 start-page: 120 issue: 1 year: 2011 ident: 10.1016/j.apnum.2023.09.003_br0020 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 – volume: 22 start-page: 313 issue: 2 year: 2012 ident: 10.1016/j.apnum.2023.09.003_br0250 article-title: Alternating direction method with Gaussian back substitution for separable convex programming publication-title: SIAM J. Optim. doi: 10.1137/110822347 – start-page: 283 year: 1969 ident: 10.1016/j.apnum.2023.09.003_br0120 article-title: A method for nonlinear constraints in minimization problems – volume: 1 start-page: 248 issue: 3 year: 2008 ident: 10.1016/j.apnum.2023.09.003_br0010 article-title: A new alternating minimization algorithm for total variation image reconstruction publication-title: SIAM J. Imaging Sci. doi: 10.1137/080724265 – volume: 179 start-page: 163 issue: 1 year: 2018 ident: 10.1016/j.apnum.2023.09.003_br0460 article-title: On Glowinski's open question on the alternating direction method of multipliers publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-018-1338-x – volume: 4 start-page: 154 year: 1970 ident: 10.1016/j.apnum.2023.09.003_br0140 article-title: Régularization, d'inéquations variationelles par approximations succesives publication-title: Rev. Fr. Inform. Rech. Opér. – volume: 207 start-page: 1210 issue: 3 year: 2010 ident: 10.1016/j.apnum.2023.09.003_br0070 article-title: A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2010.07.020 – volume: 40 start-page: 1188 issue: 2 year: 2020 ident: 10.1016/j.apnum.2023.09.003_br0470 article-title: Optimal proximal augmented Lagrangian method and its application to full Jacobian splitting for multi-block separable convex minimization problems publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/dry092 – volume: 73 start-page: 273 issue: 3 year: 2011 ident: 10.1016/j.apnum.2023.09.003_br0570 article-title: Regression shrinkage and selection via the lasso: a retrospective publication-title: J. R. Stat. Soc. Ser. B, Stat. Methodol. doi: 10.1111/j.1467-9868.2011.00771.x – volume: 2017 year: 2017 ident: 10.1016/j.apnum.2023.09.003_br0320 article-title: A proximal fully parallel splitting method for stable principal component pursuit publication-title: Math. Probl. Eng. doi: 10.1155/2017/9674528 – volume: 2 start-page: 203 issue: 3–4 year: 2010 ident: 10.1016/j.apnum.2023.09.003_br0080 article-title: Alternating direction augmented Lagrangian methods for semidefinite programming publication-title: Math. Program. Comput. doi: 10.1007/s12532-010-0017-1 – volume: 60 start-page: 259 issue: 1–4 year: 1992 ident: 10.1016/j.apnum.2023.09.003_br0580 article-title: Nonlinear total variation based noise removal algorithms publication-title: Physica D doi: 10.1016/0167-2789(92)90242-F – volume: 2 start-page: 1 issue: 3 year: 2011 ident: 10.1016/j.apnum.2023.09.003_br0590 article-title: LIBSVM: a library for support vector machines publication-title: ACM Trans. Intell. Syst. Technol. doi: 10.1145/1961189.1961199 – year: 1983 ident: 10.1016/j.apnum.2023.09.003_br0430 – volume: 14 start-page: 877 year: 1976 ident: 10.1016/j.apnum.2023.09.003_br0130 article-title: Monotone operators and the proximal point algorithm publication-title: SIAM J. Control Optim. doi: 10.1137/0314056 – year: 1975 ident: 10.1016/j.apnum.2023.09.003_br0300 – volume: 70 start-page: 631 issue: 3 year: 2021 ident: 10.1016/j.apnum.2023.09.003_br0360 article-title: A partial PPA block-wise ADMM for multi-block linearly constrained separable convex optimization publication-title: Optimization doi: 10.1080/02331934.2020.1728756 – start-page: 59 year: 2014 ident: 10.1016/j.apnum.2023.09.003_br0190 article-title: On alternating direction methods of multipliers: a historical perspective – year: 2001 ident: 10.1016/j.apnum.2023.09.003_br0600 – volume: 160 start-page: 65 year: 2021 ident: 10.1016/j.apnum.2023.09.003_br0380 article-title: A partially proximal S-ADMM for separable convex optimization with linear constraints publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2020.09.016 – volume: 82 start-page: 421 issue: 2 year: 1956 ident: 10.1016/j.apnum.2023.09.003_br0150 article-title: On the numerical solution of heat conduction problems in two and three space variables publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1956-0084194-4 – volume: 50 start-page: 700 issue: 2 year: 2012 ident: 10.1016/j.apnum.2023.09.003_br0390 article-title: On the O(1/n) convergence rate of the Douglas-Rachford alternating direction method publication-title: SIAM J. Numer. Anal. doi: 10.1137/110836936 – volume: 66 start-page: 889 issue: 3 year: 2016 ident: 10.1016/j.apnum.2023.09.003_br0550 article-title: On the global and linear convergence of the generalized alternating direction method of multipliers publication-title: J. Sci. Comput. doi: 10.1007/s10915-015-0048-x – volume: 1 start-page: 145 year: 2015 ident: 10.1016/j.apnum.2023.09.003_br0400 article-title: Block-wise alternating direction method of multipliers for multiple-block convex programming and beyond publication-title: J. Comput. Math. – volume: 32 start-page: 136 issue: 1 year: 2011 ident: 10.1016/j.apnum.2023.09.003_br0050 article-title: Solving large-scale least squares covariance matrix problems by alternating direction methods publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/090768813 – volume: 175 start-page: 395 issue: 1–2 year: 2019 ident: 10.1016/j.apnum.2023.09.003_br0280 article-title: A block symmetric Gauss-Seidel decomposition theorem for convex composite quadratic programming and its applications publication-title: Math. Program. doi: 10.1007/s10107-018-1247-7 – volume: 173 start-page: 37 issue: 1–2 year: 2019 ident: 10.1016/j.apnum.2023.09.003_br0270 article-title: Extended ADMM and BCD for nonseparable convex minimization models with quadratic coupling terms: convergence analysis and insights publication-title: Math. Program. doi: 10.1007/s10107-017-1205-9 – year: 1982 ident: 10.1016/j.apnum.2023.09.003_br0420 – year: 1984 ident: 10.1016/j.apnum.2023.09.003_br0410 – volume: 83 start-page: 2263 issue: 289 year: 2014 ident: 10.1016/j.apnum.2023.09.003_br0100 article-title: An augmented Lagrangian based parallel splitting method for separable convex minimization with applications to image processing publication-title: Math. Compet. doi: 10.1090/S0025-5718-2014-02829-9 – year: 2003 ident: 10.1016/j.apnum.2023.09.003_br0530 – volume: 11 start-page: 619 issue: 4 year: 2015 ident: 10.1016/j.apnum.2023.09.003_br0200 article-title: Understanding the convergence of the alternating direction method of multipliers: theoretical and computational perspectives publication-title: Pac. J. Optim. – volume: 34 start-page: 2233 issue: 11 year: 2012 ident: 10.1016/j.apnum.2023.09.003_br0220 article-title: RASL: robust alignment by sparse and low-rank decomposition for linearly correlated images publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/TPAMI.2011.282 – volume: 32 start-page: 39 issue: 1 year: 2017 ident: 10.1016/j.apnum.2023.09.003_br0340 article-title: A proximal partially parallel splitting method for separable convex programs publication-title: Optim. Methods Softw. doi: 10.1080/10556788.2016.1200044 – volume: 155 start-page: 57 issue: 1–2 year: 2016 ident: 10.1016/j.apnum.2023.09.003_br0230 article-title: The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent publication-title: Math. Program. doi: 10.1007/s10107-014-0826-5 – year: 2008 ident: 10.1016/j.apnum.2023.09.003_br0610 – volume: 46 start-page: 20 issue: 1 year: 2011 ident: 10.1016/j.apnum.2023.09.003_br0560 article-title: A unified primal-dual algorithm framework based on Bregman iteration publication-title: J. Sci. Comput. doi: 10.1007/s10915-010-9408-8 – volume: 21 start-page: 57 issue: 1 year: 2011 ident: 10.1016/j.apnum.2023.09.003_br0060 article-title: Recovering low-rank and sparse components of matrices from incomplete and noisy observations publication-title: SIAM J. Optim. doi: 10.1137/100781894 – volume: 81 start-page: 479 issue: 2 year: 2022 ident: 10.1016/j.apnum.2023.09.003_br0500 article-title: An inexact accelerated stochastic ADMM for separable convex optimization publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-021-00338-8 – volume: 185 start-page: 111 issue: 1–2 year: 2021 ident: 10.1016/j.apnum.2023.09.003_br0090 article-title: On the equivalence of inexact proximal ALM and ADMM for a class of convex composite programming publication-title: Math. Program. doi: 10.1007/s10107-019-01423-x – ident: 10.1016/j.apnum.2023.09.003_br0450 – start-page: 115 year: 1994 ident: 10.1016/j.apnum.2023.09.003_br0180 article-title: Reformulations and applications of the alternating direction method of multipliers – volume: 9 start-page: 41 year: 1975 ident: 10.1016/j.apnum.2023.09.003_br0160 article-title: Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéaires, M2AN publication-title: Math. Model. Numer. Anal. – volume: 4 start-page: 1168 issue: 4 year: 2005 ident: 10.1016/j.apnum.2023.09.003_br0620 article-title: Signal recovery by proximal forward-backward splitting publication-title: Multiscale Model. Simul. doi: 10.1137/050626090 – volume: 6 start-page: 680 issue: 1 year: 2013 ident: 10.1016/j.apnum.2023.09.003_br0030 article-title: Constrained total variation deblurring models and fast algorithms based on alternating direction method of multipliers publication-title: SIAM J. Imaging Sci. doi: 10.1137/110860185 – volume: 71 start-page: 712 issue: 2 year: 2017 ident: 10.1016/j.apnum.2023.09.003_br0330 article-title: Parallel multi-block ADMM with O(1/k) convergence publication-title: J. Sci. Comput. doi: 10.1007/s10915-016-0318-2 – volume: 85 start-page: 399 year: 2020 ident: 10.1016/j.apnum.2023.09.003_br0490 article-title: Convergence study on the proximal alternating direction method with larger step size publication-title: Numer. Algorithms doi: 10.1007/s11075-019-00819-2 – volume: 4 start-page: 303 issue: 5 year: 1969 ident: 10.1016/j.apnum.2023.09.003_br0110 article-title: Multiplier and gradient methods publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00927673 – volume: 16 start-page: 1858 issue: 3 year: 2020 ident: 10.1016/j.apnum.2023.09.003_br0210 article-title: A distributed dual consensus ADMM based on partition for DC-DOPF with carbon emission trading publication-title: IEEE Trans. Ind. Inform. doi: 10.1109/TII.2019.2937513 – volume: 73 start-page: 755 issue: 3 year: 2019 ident: 10.1016/j.apnum.2023.09.003_br0350 article-title: Regularized Jacobi-type ADMM-methods for a class of separable convex optimization problems in Hilbert spaces publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-019-00087-9 – volume: 25 start-page: 2274 issue: 4 year: 2015 ident: 10.1016/j.apnum.2023.09.003_br0290 article-title: On full Jacobian decomposition of the augmented Lagrangian method for separable convex programming publication-title: SIAM J. Optim. doi: 10.1137/130922793 – volume: 32 start-page: 227 issue: 1 year: 2012 ident: 10.1016/j.apnum.2023.09.003_br0440 article-title: Matrix completion via alternating direction method publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/drq039 – volume: 155 start-page: 227 issue: 1 year: 2012 ident: 10.1016/j.apnum.2023.09.003_br0240 article-title: A note on the alternating direction method of multipliers publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-012-0003-z – volume: 77 start-page: 91 issue: 1 year: 2020 ident: 10.1016/j.apnum.2023.09.003_br0480 article-title: Convergence study of indefinite proximal ADMM with a relaxation factor publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-020-00206-x – volume: 256 start-page: 36 year: 2014 ident: 10.1016/j.apnum.2023.09.003_br0310 article-title: A proximal parallel splitting method for minimizing sum of convex functions with linear constraints publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2013.07.010 – volume: 3 start-page: 448 issue: 3 year: 2022 ident: 10.1016/j.apnum.2023.09.003_br0510 article-title: Convergence analysis of an inexact accelerated stochastic ADMM with larger stepsizes publication-title: CSIAM Trans. Appl. Math. doi: 10.4208/csiam-am.SO-2021-0021 – volume: 2 start-page: 17 issue: 1 year: 1976 ident: 10.1016/j.apnum.2023.09.003_br0170 article-title: A dual algorithm for the solution of nonlinear variational problems via finite element approximation publication-title: Comput. Math. Appl. doi: 10.1016/0898-1221(76)90003-1 – volume: 25 start-page: 1478 issue: 3 year: 2015 ident: 10.1016/j.apnum.2023.09.003_br0260 article-title: On the global linear convergence of the ADMM with multiblock variables publication-title: SIAM J. Optim. doi: 10.1137/140971178 – year: 1970 ident: 10.1016/j.apnum.2023.09.003_br0520 – volume: 82 start-page: 301 issue: 281 year: 2013 ident: 10.1016/j.apnum.2023.09.003_br0540 article-title: Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization publication-title: Math. Compet. doi: 10.1090/S0025-5718-2012-02598-1 – volume: 70 start-page: 129 issue: 1 year: 2018 ident: 10.1016/j.apnum.2023.09.003_br0370 article-title: Generalized symmetric ADMM for separable convex optimization publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-017-9971-0 |
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| SubjectTerms | Augmented Lagrangian method Convergence rate Relaxation factor Splitting algorithm Step size |
| Title | A proximal fully parallel splitting method with a relaxation factor for separable convex programming |
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