Two Convergent Primal–Dual Hybrid Gradient Type Methods for Convex Programming with Linear Constraints

As an effective tool for convex programming, the primal–dual hybrid gradient (PDHG) method has been widely applied in science and engineering computing field. However, the PDHG method may be divergent without further assumption. Based on the projection and contraction methods for monotone variationa...

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Vydáno v:Bulletin of the Iranian Mathematical Society Ročník 49; číslo 3
Hlavní autoři: Sun, Min, Liu, Jing, Tian, Maoying
Médium: Journal Article
Jazyk:angličtina
Vydáno: Singapore Springer Nature Singapore 01.06.2023
Témata:
Mathematics
Mathematics and Statistics
Original Paper
Convergence rate
Primal–dual hybrid gradient method
Global convergence
90C30
90C25
Convex programming
ISSN:1017-060X, 1735-8515
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Abstract As an effective tool for convex programming, the primal–dual hybrid gradient (PDHG) method has been widely applied in science and engineering computing field. However, the PDHG method may be divergent without further assumption. Based on the projection and contraction methods for monotone variational inequalities, this paper presents two convergent PDHG-type (C-PDHG) methods for the convex programming with linear constraints, whose proximal parameters r and s only need to satisfy r > 0 , s > 0 , r s > 1 4 ‖ A T A ‖ and r > 0 , s > 0 , respectively. The global convergence of the two new C-PDHG methods is proved. Furthermore, the convergence rate for linearly equality constrained programming is also studied. Finally, some numerical results on the linear support vector machine and the image reconstruction are reported to show the efficiency of the two C-PDHG methods.
AbstractList As an effective tool for convex programming, the primal–dual hybrid gradient (PDHG) method has been widely applied in science and engineering computing field. However, the PDHG method may be divergent without further assumption. Based on the projection and contraction methods for monotone variational inequalities, this paper presents two convergent PDHG-type (C-PDHG) methods for the convex programming with linear constraints, whose proximal parameters r and s only need to satisfy r > 0 , s > 0 , r s > 1 4 ‖ A T A ‖ and r > 0 , s > 0 , respectively. The global convergence of the two new C-PDHG methods is proved. Furthermore, the convergence rate for linearly equality constrained programming is also studied. Finally, some numerical results on the linear support vector machine and the image reconstruction are reported to show the efficiency of the two C-PDHG methods.
ArticleNumber 29
Author Liu, Jing
Sun, Min
Tian, Maoying
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  surname: Tian
  fullname: Tian, Maoying
  organization: Department of Physiology, Shandong Coal Mining Health School
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Cites_doi 10.1515/9781400873173
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10.1007/s10589-007-9109-x
10.1007/s40314-016-0371-3
10.1007/s10589-013-9564-5
10.1137/100814494
10.1007/s11075-018-0618-8
10.3934/jimo.2021174
10.1017/CBO9780511801389
10.1016/j.amc.2012.11.093
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Keywords Convergence rate
Primal–dual hybrid gradient method
Global convergence
90C30
90C25
Convex programming
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References You, Jiang (CR8) 2023; 19
He, Xu, Yuan (CR13) 2022; 64
Rockafellar (CR14) 1970
Cai, Gu, He (CR18) 2014; 57
Ma, Bi, Gao (CR9) 2019; 82
Zhu, Chan (CR5) 2008
You, Fu, He (CR7) 2014; 10
CR4
Ma, Ni (CR19) 2018; 37
CR3
He (CR16) 2009; 42
Hou (CR17) 2013; 219
CR15
Chambolle, Pock (CR11) 2011; 40
CR10
Facchinei, Pang (CR20) 2003
He (CR6) 2016; 38
He, Yuan, Zhang (CR1) 2013; 56
He (CR2) 2015; 3
He, Yuan (CR12) 2012; 5
M Zhu (778_CR5) 2008
LS Hou (778_CR17) 2013; 219
BS He (778_CR1) 2013; 56
YF You (778_CR7) 2014; 10
BS He (778_CR2) 2015; 3
YF You (778_CR8) 2023; 19
778_CR4
F Ma (778_CR9) 2019; 82
A Chambolle (778_CR11) 2011; 40
RT Rockafellar (778_CR14) 1970
BS He (778_CR12) 2012; 5
778_CR3
F Ma (778_CR19) 2018; 37
F Facchinei (778_CR20) 2003
BS He (778_CR6) 2016; 38
BS He (778_CR16) 2009; 42
778_CR10
BS He (778_CR13) 2022; 64
778_CR15
XJ Cai (778_CR18) 2014; 57
References_xml – year: 1970
  ident: CR14
  publication-title: Convex Analysis
  doi: 10.1515/9781400873173
– volume: 64
  start-page: 662
  issue: 6
  year: 2022
  end-page: 671
  ident: CR13
  article-title: On convergence of the Arrow-Hurwicz method for saddle point problems
  publication-title: J. Math. Imaging Vis.
  doi: 10.1007/s10851-022-01089-9
– ident: CR3
– ident: CR4
– ident: CR15
– year: 2003
  ident: CR20
  publication-title: Finite-Dimensional Variational Inequalities and Complementarity Problems
– volume: 40
  start-page: 120
  year: 2011
  end-page: 145
  ident: CR11
  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: 3
  start-page: 391
  year: 2015
  end-page: 420
  ident: CR2
  article-title: PPA-like contraction methods for convex optimization: a framework using variation inequality approach
  publication-title: J. Oper. Res. Soc. China
  doi: 10.1007/s40305-015-0108-9
– ident: CR10
– volume: 42
  start-page: 195
  year: 2009
  end-page: 212
  ident: CR16
  article-title: Parallel splitting augmented Lagrangian methods for monotone structured variational inequalities
  publication-title: Comput. Optim. Appl.
  doi: 10.1007/s10589-007-9109-x
– volume: 219
  start-page: 5862
  year: 2013
  end-page: 5869
  ident: CR17
  article-title: On the (1/ ) convergence rate of the parallel descent-like method and parallel splitting augmented Lagrangian method for solving a class of variational inequalities
  publication-title: Appl. Math. Comput.
– volume: 37
  start-page: 896
  issue: 2
  year: 2018
  end-page: 911
  ident: CR19
  article-title: A class of customized proximal point algorithms for linearly constrained convex optimization
  publication-title: Comput. Appl. Math.
  doi: 10.1007/s40314-016-0371-3
– volume: 56
  start-page: 559
  year: 2013
  end-page: 572
  ident: CR1
  article-title: A customized proximal point algorithm for convex minimization with linear constraints
  publication-title: Comput. Optimiz. Appl.
  doi: 10.1007/s10589-013-9564-5
– year: 2008
  ident: CR5
  publication-title: An Efficient Primal-dual Hybrid Gradient Algorithm for Total Variation Image Restoration, CAM Report 08–34
– volume: 38
  start-page: 74
  issue: 1
  year: 2016
  end-page: 96
  ident: CR6
  article-title: From the projection and contraction methods for variational inequalities to the splitting contraction methods for convex optimization
  publication-title: Numer. Math. J. Chin. Univ.
– volume: 10
  start-page: 199
  year: 2014
  end-page: 213
  ident: CR7
  article-title: Lagrangian-PPA based contraction methods for linearly constrained convex optimization
  publication-title: Pacific J. Optimiz.
– volume: 5
  start-page: 119
  issue: 1
  year: 2012
  end-page: 149
  ident: CR12
  article-title: Convergence analysis of primal-dual algorithms for a saddle-point problem: from contraction perspective
  publication-title: SIAM J. Imag. Sci.
  doi: 10.1137/100814494
– volume: 57
  start-page: 339
  year: 2014
  end-page: 363
  ident: CR18
  article-title: On the (1/ ) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators
  publication-title: Comput. Appl. Math.
– volume: 82
  start-page: 641
  year: 2019
  end-page: 662
  ident: CR9
  article-title: A prediction-correction-based primal-dual hybrid gradient method for linearly constrained convex minimization
  publication-title: Numeric. Algorithms
  doi: 10.1007/s11075-018-0618-8
– volume: 19
  start-page: 56
  issue: 1
  year: 2023
  end-page: 68
  ident: CR8
  article-title: Improved Lagrangian-PPA based prediction correction method for linearly constrained convex optimization
  publication-title: J. Ind. Manage. Optimiz.
  doi: 10.3934/jimo.2021174
– volume-title: Finite-Dimensional Variational Inequalities and Complementarity Problems
  year: 2003
  ident: 778_CR20
– ident: 778_CR15
– ident: 778_CR3
  doi: 10.1017/CBO9780511801389
– volume: 56
  start-page: 559
  year: 2013
  ident: 778_CR1
  publication-title: Comput. Optimiz. Appl.
  doi: 10.1007/s10589-013-9564-5
– volume-title: An Efficient Primal-dual Hybrid Gradient Algorithm for Total Variation Image Restoration, CAM Report 08–34
  year: 2008
  ident: 778_CR5
– ident: 778_CR10
– volume: 38
  start-page: 74
  issue: 1
  year: 2016
  ident: 778_CR6
  publication-title: Numer. Math. J. Chin. Univ.
– volume: 3
  start-page: 391
  year: 2015
  ident: 778_CR2
  publication-title: J. Oper. Res. Soc. China
  doi: 10.1007/s40305-015-0108-9
– volume: 42
  start-page: 195
  year: 2009
  ident: 778_CR16
  publication-title: Comput. Optim. Appl.
  doi: 10.1007/s10589-007-9109-x
– volume: 219
  start-page: 5862
  year: 2013
  ident: 778_CR17
  publication-title: Appl. Math. Comput.
  doi: 10.1016/j.amc.2012.11.093
– volume: 40
  start-page: 120
  year: 2011
  ident: 778_CR11
  publication-title: J. Math. Imaging Vis.
  doi: 10.1007/s10851-010-0251-1
– volume: 57
  start-page: 339
  year: 2014
  ident: 778_CR18
  publication-title: Comput. Appl. Math.
– volume: 19
  start-page: 56
  issue: 1
  year: 2023
  ident: 778_CR8
  publication-title: J. Ind. Manage. Optimiz.
  doi: 10.3934/jimo.2021174
– ident: 778_CR4
– volume: 10
  start-page: 199
  year: 2014
  ident: 778_CR7
  publication-title: Pacific J. Optimiz.
– volume-title: Convex Analysis
  year: 1970
  ident: 778_CR14
  doi: 10.1515/9781400873173
– volume: 82
  start-page: 641
  year: 2019
  ident: 778_CR9
  publication-title: Numeric. Algorithms
  doi: 10.1007/s11075-018-0618-8
– volume: 5
  start-page: 119
  issue: 1
  year: 2012
  ident: 778_CR12
  publication-title: SIAM J. Imag. Sci.
  doi: 10.1137/100814494
– volume: 37
  start-page: 896
  issue: 2
  year: 2018
  ident: 778_CR19
  publication-title: Comput. Appl. Math.
  doi: 10.1007/s40314-016-0371-3
– volume: 64
  start-page: 662
  issue: 6
  year: 2022
  ident: 778_CR13
  publication-title: J. Math. Imaging Vis.
  doi: 10.1007/s10851-022-01089-9
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Mathematics and Statistics
Original Paper
Title Two Convergent Primal–Dual Hybrid Gradient Type Methods for Convex Programming with Linear Constraints
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