Exponential convergence of distributed primal–dual convex optimization algorithm without strong convexity

This paper establishes exponential convergence rates for a class of primal–dual gradient algorithms in distributed optimization without strong convexity. The convergence analysis is based on a carefully constructed Lyapunov function. By evaluating metric subregularity of the primal–dual gradient map...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Automatica (Oxford) Jg. 105; S. 298 - 306
Hauptverfasser: Liang, Shu, Wang, Le Yi, Yin, George
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.07.2019
Schlagworte:
ISSN:0005-1098, 1873-2836
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Abstract This paper establishes exponential convergence rates for a class of primal–dual gradient algorithms in distributed optimization without strong convexity. The convergence analysis is based on a carefully constructed Lyapunov function. By evaluating metric subregularity of the primal–dual gradient map, we present a general criterion under which the algorithm achieves exponential convergence. To facilitate practical applications of this criterion, several simplified sufficient conditions are derived. We also prove that although these results are developed for the continuous-time algorithms, they carry over in a parallel manner to the discrete-time algorithms constructed by using Euler’s approximation method.
AbstractList This paper establishes exponential convergence rates for a class of primal–dual gradient algorithms in distributed optimization without strong convexity. The convergence analysis is based on a carefully constructed Lyapunov function. By evaluating metric subregularity of the primal–dual gradient map, we present a general criterion under which the algorithm achieves exponential convergence. To facilitate practical applications of this criterion, several simplified sufficient conditions are derived. We also prove that although these results are developed for the continuous-time algorithms, they carry over in a parallel manner to the discrete-time algorithms constructed by using Euler’s approximation method.
Author Wang, Le Yi
Liang, Shu
Yin, George
Author_xml – sequence: 1
  givenname: Shu
  surname: Liang
  fullname: Liang, Shu
  email: sliang@ustb.edu.cn
  organization: Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education, School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China
– sequence: 2
  givenname: Le Yi
  surname: Wang
  fullname: Wang, Le Yi
  email: lywang@wayne.edu
  organization: Department of Electrical and Computer Engineering, Wayne State University, Detroit, MI 48202, USA
– sequence: 3
  givenname: George
  surname: Yin
  fullname: Yin, George
  email: gyin@math.wayne.edu
  organization: Department of Mathematics, Wayne State University, Detroit, MI 48202, USA
BookMark eNqNkEtOwzAQhi1UJNrCHXyBBNtxg7NBgqo8pEpsYG059qS4JHHluKVlxR24ISfBfSAkNrDxyNL838x8A9RrXQsIYUpSSmh-Pk_VMrhGBatVyggtUsJTQvgR6lNxkSVMZHkP9Qkho4SSQpygQdfN45dTwfroZbJeRGAbrKqxdu0K_AxaDdhV2NgueFsuAxi88LZR9ef7h1l-N66xWwTb2Lc427VY1TPnbXhu8Gt83TLgmHbt7NBsw-YUHVeq7uDsUIfo6WbyOL5Lpg-39-OraaKzXIREqELzkTGZFmWVjxStQDCaQ8lzTQTklPGs5EVhKlUZBgJEyYBxUXJFMq5ENkSXe672rus8VFLbsFsyeGVrSYncqpNz-aNObtVJwmUUEwHiF2B3vt_8J3q9j0I8cGXBy07brVBjPeggjbN_Q74AZ76X4Q
CitedBy_id crossref_primary_10_1016_j_automatica_2023_111346
crossref_primary_10_1109_TAC_2021_3103865
crossref_primary_10_1109_TAC_2023_3339439
crossref_primary_10_1007_s12555_024_0424_0
crossref_primary_10_1109_TCNS_2020_3029996
crossref_primary_10_1109_TSIPN_2024_3430492
crossref_primary_10_1016_j_jfranklin_2019_06_026
crossref_primary_10_1049_gtd2_12142
crossref_primary_10_1109_TCNS_2024_3469048
crossref_primary_10_1080_10556788_2025_2517174
crossref_primary_10_1016_j_automatica_2023_111508
crossref_primary_10_1109_TAC_2021_3075666
crossref_primary_10_1109_TCSII_2023_3324187
crossref_primary_10_1016_j_ifacol_2020_12_383
crossref_primary_10_1016_j_automatica_2021_109585
crossref_primary_10_1007_s00521_022_07003_z
crossref_primary_10_1007_s43684_022_00024_4
crossref_primary_10_1109_TCNS_2024_3371550
crossref_primary_10_3390_pr11051416
crossref_primary_10_1016_j_automatica_2022_110492
crossref_primary_10_1016_j_jfranklin_2025_108014
crossref_primary_10_1007_s11768_020_00018_8
crossref_primary_10_1109_TNNLS_2023_3330017
crossref_primary_10_1007_s11590_022_01910_9
crossref_primary_10_1109_TAC_2022_3152720
crossref_primary_10_1109_TNSE_2022_3178107
crossref_primary_10_1109_TNSE_2025_3527466
crossref_primary_10_1016_j_amc_2021_126794
crossref_primary_10_1016_j_neunet_2021_11_013
crossref_primary_10_1007_s00245_023_10102_5
crossref_primary_10_1016_j_jfranklin_2023_11_017
crossref_primary_10_1002_rnc_5451
crossref_primary_10_1177_01423312241297730
crossref_primary_10_1109_TCSII_2022_3149749
crossref_primary_10_1016_j_ifacol_2023_10_115
crossref_primary_10_1109_TAC_2022_3176527
crossref_primary_10_1109_TAC_2023_3312137
crossref_primary_10_1002_asjc_3555
crossref_primary_10_1016_j_automatica_2022_110358
crossref_primary_10_1016_j_neunet_2023_11_025
crossref_primary_10_1109_ACCESS_2023_3341295
crossref_primary_10_1109_JIOT_2025_3578363
crossref_primary_10_1016_j_automatica_2023_111328
crossref_primary_10_1016_j_jfranklin_2022_03_046
crossref_primary_10_1016_j_automatica_2020_109407
crossref_primary_10_1109_TAC_2023_3301289
crossref_primary_10_1109_TNNLS_2022_3208086
crossref_primary_10_1109_TAC_2024_3394128
crossref_primary_10_1016_j_automatica_2025_112575
crossref_primary_10_1080_02331934_2023_2253813
crossref_primary_10_1016_j_automatica_2022_110590
crossref_primary_10_1007_s12555_023_0015_5
crossref_primary_10_1002_asjc_3467
crossref_primary_10_1016_j_automatica_2023_111059
crossref_primary_10_1109_TAC_2021_3108501
crossref_primary_10_1016_j_automatica_2022_110547
crossref_primary_10_1109_TCNS_2021_3068352
crossref_primary_10_1109_TAC_2023_3266018
crossref_primary_10_1016_j_automatica_2021_109899
crossref_primary_10_1016_j_neucom_2024_129022
crossref_primary_10_1007_s43684_024_00063_z
Cites_doi 10.1137/16M1084316
10.1016/j.automatica.2015.02.038
10.1109/TAC.2016.2610945
10.1016/j.automatica.2016.02.019
10.1137/14096668X
10.1109/TAC.1977.1101561
10.1109/TSP.2014.2304432
10.1007/s10107-011-0472-0
10.1137/070708111
10.1016/j.automatica.2016.01.055
10.1109/TCYB.2017.2759141
10.1137/140978259
10.1109/TAC.2016.2612819
10.1109/TAC.2008.2009515
10.1016/j.automatica.2016.08.007
10.1109/TAC.2013.2278132
10.1109/TAC.2016.2628807
10.1016/j.automatica.2010.08.011
10.1109/TAC.2017.2677879
10.1007/s10107-018-1232-1
10.1109/TNNLS.2016.2549566
10.1016/j.automatica.2017.07.064
10.1073/pnas.1614734113
10.1109/TCSI.2004.834493
10.1007/s11432-016-9173-8
10.1016/j.automatica.2015.03.001
10.1109/TNNLS.2015.2480419
10.1016/j.automatica.2016.07.003
10.1016/j.automatica.2017.01.004
ContentType Journal Article
Copyright 2019 Elsevier Ltd
Copyright_xml – notice: 2019 Elsevier Ltd
DBID AAYXX
CITATION
DOI 10.1016/j.automatica.2019.04.004
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 1873-2836
EndPage 306
ExternalDocumentID 10_1016_j_automatica_2019_04_004
S0005109819301645
GroupedDBID --K
--M
-~X
.DC
.~1
0R~
1B1
1~.
1~5
23N
3R3
4.4
457
4G.
5GY
5VS
6TJ
7-5
71M
8P~
9JN
9JO
AAAKF
AAAKG
AABNK
AACTN
AAEDT
AAEDW
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AARIN
AAXUO
ABDEX
ABFNM
ABFRF
ABJNI
ABMAC
ABUCO
ABXDB
ABYKQ
ACBEA
ACDAQ
ACGFO
ACGFS
ACNNM
ACRLP
ADBBV
ADEZE
ADIYS
ADMUD
ADTZH
AEBSH
AECPX
AEFWE
AEKER
AENEX
AFFNX
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHJVU
AHPGS
AI.
AIEXJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
APLSM
ASPBG
AVWKF
AXJTR
AZFZN
BJAXD
BKOJK
BLXMC
CS3
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
F5P
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
GBLVA
HAMUX
HLZ
HVGLF
HZ~
H~9
IHE
J1W
JJJVA
K-O
KOM
LG9
LY7
M41
MO0
N9A
O-L
O9-
OAUVE
OZT
P-8
P-9
P2P
PC.
Q38
R2-
RIG
ROL
RPZ
RXW
SBC
SDF
SDG
SDP
SES
SET
SEW
SPC
SPCBC
SSB
SSD
SST
SSZ
T5K
T9H
TAE
TN5
VH1
WH7
WUQ
X6Y
XFK
XPP
ZMT
~G-
77I
9DU
AATTM
AAXKI
AAYWO
AAYXX
ABUFD
ABWVN
ACLOT
ACRPL
ACVFH
ADCNI
ADNMO
AEIPS
AEUPX
AFJKZ
AFPUW
AGQPQ
AIGII
AIIUN
AKBMS
AKRWK
AKYEP
ANKPU
APXCP
CITATION
EFKBS
~HD
ID FETCH-LOGICAL-c368t-8a9c45dd3c8bf65a1fe8216eb46c08e61243b499dfafd2e8e8b2e248b4a034a83
ISICitedReferencesCount 73
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000476963500030&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0005-1098
IngestDate Tue Nov 18 22:43:14 EST 2025
Sat Nov 29 07:31:00 EST 2025
Fri Feb 23 02:23:46 EST 2024
IsDoiOpenAccess false
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Keywords Exponential convergence
Metric subregularity
Variational analysis
Distributed optimization
Convex optimization without strong convexity
Rate of convergence
Primal–dual algorithm
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c368t-8a9c45dd3c8bf65a1fe8216eb46c08e61243b499dfafd2e8e8b2e248b4a034a83
OpenAccessLink https://www.sciencedirect.com/science/article/am/pii/S0005109819301645
PageCount 9
ParticipantIDs crossref_citationtrail_10_1016_j_automatica_2019_04_004
crossref_primary_10_1016_j_automatica_2019_04_004
elsevier_sciencedirect_doi_10_1016_j_automatica_2019_04_004
PublicationCentury 2000
PublicationDate July 2019
2019-07-00
PublicationDateYYYYMMDD 2019-07-01
PublicationDate_xml – month: 07
  year: 2019
  text: July 2019
PublicationDecade 2010
PublicationTitle Automatica (Oxford)
PublicationYear 2019
Publisher Elsevier Ltd
Publisher_xml – name: Elsevier Ltd
References Necoara, I., Nesterov, Y., & Glineur, F. (n.d.). Linear convergence of first order methods for non-strongly convex optimization. Mathematical Programming.
Facchinei, Pang (b7) 2003
Mateos-Nunez, Cortés (b19) 2016; 54
Qiu, Liu, Xie (b26) 2016; 68
Dontchev, Rockafellar (b6) 2014
Yuan, Ho, Xu (b36) 2016; 27
Ljung (b16) 1977; 22
Bertsekas (b2) 2011; 129
Nedić, Olshevsky, Shi (b22) 2017; 27
Wang, Elia (b31) 2011
Nedić, Ozdaglar (b24) 2009; 54
Cherukuri, Cortés (b4) 2016; 74
Brockett (b3) 1988
Deng, Liang, Hong (b5) 2018; 48
Lou, Hong, Wang (b17) 2016; 69
Shi, Ling, Yuan, Wu, Yin (b30) 2014; 62
Feijer, Paganini (b8) 2010; 46
Gharesifard, Cortés (b10) 2014; 59
Makhdoumi, Ozdaglar (b18) 2017; 62
Godsil, Royle (b11) 2001; Vol. 207
Wang, Lin, Hong (b32) 2018; 61
Arrow, Hurwicz, Uzawa (b1) 1958
Kia, Cortés, Martínez (b13) 2015; 55
Necoara, Nedelcu (b20) 2015; 55
Nesterov (b25) 2004; Vol. 87
Yang, Liu, Wang (b34) 2017; 62
Liang, Yi, Hong (b14) 2017; 85
Wibisono, Wilson, Jordan (b33) 2016; 113
Nedić, Ozdaglar (b23) 2009; 19
Shi, Ling, Wu, Yin (b29) 2015; 25
.
Shi, Anderson, Helmke (b28) 2017; 62
Forti, Nistri, Quincampoix (b9) 2004; 51
Liu, Yang, Wang (b15) 2017; 28
Zhang, Deng, Hong (b38) 2017; 79
Zeng, Yi, Hong (b37) 2017; 62
Rockafellar, Wets (b27) 1998; Vol. 317
Ioffe (b12) 2017
Yi, Hong, Liu (b35) 2016; 74
Zhang (10.1016/j.automatica.2019.04.004_b38) 2017; 79
Wang (10.1016/j.automatica.2019.04.004_b32) 2018; 61
Liang (10.1016/j.automatica.2019.04.004_b14) 2017; 85
Shi (10.1016/j.automatica.2019.04.004_b30) 2014; 62
Wang (10.1016/j.automatica.2019.04.004_b31) 2011
Zeng (10.1016/j.automatica.2019.04.004_b37) 2017; 62
10.1016/j.automatica.2019.04.004_b21
Liu (10.1016/j.automatica.2019.04.004_b15) 2017; 28
Cherukuri (10.1016/j.automatica.2019.04.004_b4) 2016; 74
Necoara (10.1016/j.automatica.2019.04.004_b20) 2015; 55
Godsil (10.1016/j.automatica.2019.04.004_b11) 2001; Vol. 207
Mateos-Nunez (10.1016/j.automatica.2019.04.004_b19) 2016; 54
Yi (10.1016/j.automatica.2019.04.004_b35) 2016; 74
Shi (10.1016/j.automatica.2019.04.004_b28) 2017; 62
Makhdoumi (10.1016/j.automatica.2019.04.004_b18) 2017; 62
Feijer (10.1016/j.automatica.2019.04.004_b8) 2010; 46
Brockett (10.1016/j.automatica.2019.04.004_b3) 1988
Facchinei (10.1016/j.automatica.2019.04.004_b7) 2003
Rockafellar (10.1016/j.automatica.2019.04.004_b27) 1998; Vol. 317
Deng (10.1016/j.automatica.2019.04.004_b5) 2018; 48
Nedić (10.1016/j.automatica.2019.04.004_b23) 2009; 19
Dontchev (10.1016/j.automatica.2019.04.004_b6) 2014
Ljung (10.1016/j.automatica.2019.04.004_b16) 1977; 22
Nedić (10.1016/j.automatica.2019.04.004_b22) 2017; 27
Yuan (10.1016/j.automatica.2019.04.004_b36) 2016; 27
Arrow (10.1016/j.automatica.2019.04.004_b1) 1958
Kia (10.1016/j.automatica.2019.04.004_b13) 2015; 55
Shi (10.1016/j.automatica.2019.04.004_b29) 2015; 25
Gharesifard (10.1016/j.automatica.2019.04.004_b10) 2014; 59
Nedić (10.1016/j.automatica.2019.04.004_b24) 2009; 54
Forti (10.1016/j.automatica.2019.04.004_b9) 2004; 51
Wibisono (10.1016/j.automatica.2019.04.004_b33) 2016; 113
Qiu (10.1016/j.automatica.2019.04.004_b26) 2016; 68
Lou (10.1016/j.automatica.2019.04.004_b17) 2016; 69
Bertsekas (10.1016/j.automatica.2019.04.004_b2) 2011; 129
Yang (10.1016/j.automatica.2019.04.004_b34) 2017; 62
Nesterov (10.1016/j.automatica.2019.04.004_b25) 2004; Vol. 87
Ioffe (10.1016/j.automatica.2019.04.004_b12) 2017
References_xml – volume: Vol. 317
  year: 1998
  ident: b27
  publication-title: Variational analysis
– volume: 62
  start-page: 5082
  year: 2017
  end-page: 5095
  ident: b18
  article-title: Convergence rate of distributed ADMM over networks
  publication-title: IEEE Transactions on Automatic Control
– volume: 46
  start-page: 1974
  year: 2010
  end-page: 1981
  ident: b8
  article-title: Stability of primal–dual gradient dynamics and applications to network optimization
  publication-title: Automatica
– volume: 74
  start-page: 259
  year: 2016
  end-page: 269
  ident: b35
  article-title: Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and its application to economic dispatch of power systems
  publication-title: Automatica
– volume: 28
  start-page: 1747
  year: 2017
  end-page: 1758
  ident: b15
  article-title: A collective neurodynamic approach to distributed constrained optimization
  publication-title: IEEE Transactions on Neural Networks and Learning Systems
– volume: 74
  start-page: 183
  year: 2016
  end-page: 193
  ident: b4
  article-title: Initialization-free distributed coordination for economic dispatch under varying loads and generator commitment
  publication-title: Automatica
– volume: 22
  start-page: 551
  year: 1977
  end-page: 575
  ident: b16
  article-title: Analysis of recursive stochastic algorithms
  publication-title: IEEE Transactions on Automatic Control
– volume: 62
  start-page: 2659
  year: 2017
  end-page: 2674
  ident: b28
  article-title: Network flows that solve linear equations
  publication-title: IEEE Transactions on Automatic Control
– volume: 62
  start-page: 5227
  year: 2017
  end-page: 5233
  ident: b37
  article-title: Distributed continuous-time algorithm for constrained convex optimizations via nonsmooth analysis approach
  publication-title: IEEE Transactions on Automatic Control
– volume: 129
  start-page: 163
  year: 2011
  end-page: 195
  ident: b2
  article-title: Incremental proximal methods for large scale convex optimization
  publication-title: Mathematical Programming
– volume: 25
  start-page: 944
  year: 2015
  end-page: 966
  ident: b29
  article-title: Extra: an exact first-order algorithm for decentralized consensus optimization
  publication-title: SIAM Journal on Optimization
– start-page: 3800
  year: 2011
  end-page: 3805
  ident: b31
  article-title: A control perspective for centralized and distributed convex optimization
  publication-title: The 50th IEEE conference on decision and control and european control conference
– volume: 54
  start-page: 48
  year: 2009
  end-page: 61
  ident: b24
  article-title: Distributed subgradient methods for multi-agent optimization
  publication-title: IEEE Transactions on Automatic Control
– volume: Vol. 87
  year: 2004
  ident: b25
  publication-title: Introductory lectures on convex optimization: a basic course
– volume: 48
  start-page: 3116
  year: 2018
  end-page: 3125
  ident: b5
  article-title: Distributed continuous-time algorithms for resource allocation problems over weight-balanced digraphs
  publication-title: IEEE Transactions on Cybernetics
– volume: 59
  start-page: 781
  year: 2014
  end-page: 786
  ident: b10
  article-title: Distributed continuous-time convex optimization on weight-balanced digraphs
  publication-title: IEEE Transactions on Automatic Control
– volume: 61
  year: 2018
  ident: b32
  article-title: Distributed regression estimation with incomplete data in multi-agent networks
  publication-title: Science China. Information Sciences
– year: 2017
  ident: b12
  publication-title: Variational analysis of regular mappings: theory and applications
– start-page: 799
  year: 1988
  end-page: 803
  ident: b3
  article-title: Dynamical systems that sort lists, diagonalize matrices and solve linear programming problems
  publication-title: The 27th IEEE conference on decision and control
– volume: 51
  start-page: 1741
  year: 2004
  end-page: 1754
  ident: b9
  article-title: Generalized neural network for nonsmooth nonlinear programming problems
  publication-title: IEEE Transactions on Circuits and Systems. I. Regular Papers
– year: 2003
  ident: b7
  article-title: Finite-dimensional variational inequalities and complementarity problems, operations research
– reference: Necoara, I., Nesterov, Y., & Glineur, F. (n.d.). Linear convergence of first order methods for non-strongly convex optimization. Mathematical Programming.
– volume: Vol. 207
  year: 2001
  ident: b11
  publication-title: Algebraic graph theory
– volume: 69
  start-page: 289
  year: 2016
  end-page: 297
  ident: b17
  article-title: Distributed continuous-time approximate projection protocols for shortest distance optimization problems
  publication-title: Automatica
– year: 2014
  ident: b6
  article-title: Implicit functions and solution mappings: a view from variational analysis, operations research and financial engineering
– volume: 79
  start-page: 207
  year: 2017
  end-page: 213
  ident: b38
  article-title: Distributed optimal coordination for multiple heterogeneous Euler–Lagrangian systems
  publication-title: Automatica
– reference: .
– volume: 55
  start-page: 254
  year: 2015
  end-page: 264
  ident: b13
  article-title: Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication
  publication-title: Automatica
– volume: 113
  start-page: E7351
  year: 2016
  end-page: E7358
  ident: b33
  article-title: A variational perspective on accelerated methods in optimization
  publication-title: Proceedings of the National Academy of Sciences
– volume: 27
  start-page: 2597
  year: 2017
  end-page: 2633
  ident: b22
  article-title: Achieving geometric convergence for distributed optimization over time-varying graphs
  publication-title: SIAM Journal on Optimization
– volume: 85
  start-page: 179
  year: 2017
  end-page: 185
  ident: b14
  article-title: Distributed Nash equilibrium seeking for aggregative games with coupled constraints
  publication-title: Automatica
– volume: 27
  start-page: 284
  year: 2016
  end-page: 294
  ident: b36
  article-title: Zeroth-order method for distributed optimization with approximate projections
  publication-title: IEEE Transactions on Neural Networks & Learning Systems
– volume: 62
  start-page: 1750
  year: 2014
  end-page: 1761
  ident: b30
  article-title: On the linear convergence of the admm in decentralized consensus optimization
  publication-title: IEEE Tranactions on Signal Processing
– volume: 54
  start-page: 266
  year: 2016
  end-page: 290
  ident: b19
  article-title: Noise-to-state exponentially stable distributed convex optimization on weight-balanced digraphs
  publication-title: SIAM Journal on Control and Optimization
– year: 1958
  ident: b1
  article-title: Studies in linear and non-linear programming
– volume: 55
  start-page: 209
  year: 2015
  end-page: 216
  ident: b20
  article-title: On linear convergence of a distributed dual gradient algorithm for linearly constrained separable convex problems
  publication-title: Automatica
– volume: 68
  start-page: 209
  year: 2016
  end-page: 215
  ident: b26
  article-title: Distributed constrained optimal consensus of multi-agent systems
  publication-title: Automatica
– volume: 19
  start-page: 1757
  year: 2009
  end-page: 1780
  ident: b23
  article-title: Approximate primal solutions and rate analysis for dual subgradient methods
  publication-title: SIAM Journal on Optimization
– volume: 62
  start-page: 3461
  year: 2017
  end-page: 3467
  ident: b34
  article-title: A multi-agent system with a proportional-integral protocol for distributed constrained optimization
  publication-title: IEEE Transactions on Automatic Control
– volume: 27
  start-page: 2597
  issue: 4
  year: 2017
  ident: 10.1016/j.automatica.2019.04.004_b22
  article-title: Achieving geometric convergence for distributed optimization over time-varying graphs
  publication-title: SIAM Journal on Optimization
  doi: 10.1137/16M1084316
– volume: Vol. 317
  year: 1998
  ident: 10.1016/j.automatica.2019.04.004_b27
– year: 2014
  ident: 10.1016/j.automatica.2019.04.004_b6
– volume: 55
  start-page: 209
  issue: 5
  year: 2015
  ident: 10.1016/j.automatica.2019.04.004_b20
  article-title: On linear convergence of a distributed dual gradient algorithm for linearly constrained separable convex problems
  publication-title: Automatica
  doi: 10.1016/j.automatica.2015.02.038
– year: 2003
  ident: 10.1016/j.automatica.2019.04.004_b7
– volume: 62
  start-page: 3461
  issue: 7
  year: 2017
  ident: 10.1016/j.automatica.2019.04.004_b34
  article-title: A multi-agent system with a proportional-integral protocol for distributed constrained optimization
  publication-title: IEEE Transactions on Automatic Control
  doi: 10.1109/TAC.2016.2610945
– volume: 69
  start-page: 289
  issue: 7
  year: 2016
  ident: 10.1016/j.automatica.2019.04.004_b17
  article-title: Distributed continuous-time approximate projection protocols for shortest distance optimization problems
  publication-title: Automatica
  doi: 10.1016/j.automatica.2016.02.019
– volume: 25
  start-page: 944
  issue: 2
  year: 2015
  ident: 10.1016/j.automatica.2019.04.004_b29
  article-title: Extra: an exact first-order algorithm for decentralized consensus optimization
  publication-title: SIAM Journal on Optimization
  doi: 10.1137/14096668X
– volume: 22
  start-page: 551
  issue: 4
  year: 1977
  ident: 10.1016/j.automatica.2019.04.004_b16
  article-title: Analysis of recursive stochastic algorithms
  publication-title: IEEE Transactions on Automatic Control
  doi: 10.1109/TAC.1977.1101561
– year: 2017
  ident: 10.1016/j.automatica.2019.04.004_b12
– volume: 62
  start-page: 1750
  issue: 7
  year: 2014
  ident: 10.1016/j.automatica.2019.04.004_b30
  article-title: On the linear convergence of the admm in decentralized consensus optimization
  publication-title: IEEE Tranactions on Signal Processing
  doi: 10.1109/TSP.2014.2304432
– volume: 129
  start-page: 163
  issue: 2
  year: 2011
  ident: 10.1016/j.automatica.2019.04.004_b2
  article-title: Incremental proximal methods for large scale convex optimization
  publication-title: Mathematical Programming
  doi: 10.1007/s10107-011-0472-0
– volume: 19
  start-page: 1757
  issue: 4
  year: 2009
  ident: 10.1016/j.automatica.2019.04.004_b23
  article-title: Approximate primal solutions and rate analysis for dual subgradient methods
  publication-title: SIAM Journal on Optimization
  doi: 10.1137/070708111
– volume: Vol. 87
  year: 2004
  ident: 10.1016/j.automatica.2019.04.004_b25
– volume: 68
  start-page: 209
  year: 2016
  ident: 10.1016/j.automatica.2019.04.004_b26
  article-title: Distributed constrained optimal consensus of multi-agent systems
  publication-title: Automatica
  doi: 10.1016/j.automatica.2016.01.055
– volume: 48
  start-page: 3116
  issue: 11
  year: 2018
  ident: 10.1016/j.automatica.2019.04.004_b5
  article-title: Distributed continuous-time algorithms for resource allocation problems over weight-balanced digraphs
  publication-title: IEEE Transactions on Cybernetics
  doi: 10.1109/TCYB.2017.2759141
– volume: 54
  start-page: 266
  issue: 1
  year: 2016
  ident: 10.1016/j.automatica.2019.04.004_b19
  article-title: Noise-to-state exponentially stable distributed convex optimization on weight-balanced digraphs
  publication-title: SIAM Journal on Control and Optimization
  doi: 10.1137/140978259
– volume: 62
  start-page: 2659
  issue: 6
  year: 2017
  ident: 10.1016/j.automatica.2019.04.004_b28
  article-title: Network flows that solve linear equations
  publication-title: IEEE Transactions on Automatic Control
  doi: 10.1109/TAC.2016.2612819
– start-page: 799
  year: 1988
  ident: 10.1016/j.automatica.2019.04.004_b3
  article-title: Dynamical systems that sort lists, diagonalize matrices and solve linear programming problems
– volume: 54
  start-page: 48
  issue: 1
  year: 2009
  ident: 10.1016/j.automatica.2019.04.004_b24
  article-title: Distributed subgradient methods for multi-agent optimization
  publication-title: IEEE Transactions on Automatic Control
  doi: 10.1109/TAC.2008.2009515
– volume: 74
  start-page: 259
  issue: 12
  year: 2016
  ident: 10.1016/j.automatica.2019.04.004_b35
  article-title: Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and its application to economic dispatch of power systems
  publication-title: Automatica
  doi: 10.1016/j.automatica.2016.08.007
– volume: 59
  start-page: 781
  issue: 3
  year: 2014
  ident: 10.1016/j.automatica.2019.04.004_b10
  article-title: Distributed continuous-time convex optimization on weight-balanced digraphs
  publication-title: IEEE Transactions on Automatic Control
  doi: 10.1109/TAC.2013.2278132
– volume: 62
  start-page: 5227
  issue: 10
  year: 2017
  ident: 10.1016/j.automatica.2019.04.004_b37
  article-title: Distributed continuous-time algorithm for constrained convex optimizations via nonsmooth analysis approach
  publication-title: IEEE Transactions on Automatic Control
  doi: 10.1109/TAC.2016.2628807
– volume: 46
  start-page: 1974
  issue: 12
  year: 2010
  ident: 10.1016/j.automatica.2019.04.004_b8
  article-title: Stability of primal–dual gradient dynamics and applications to network optimization
  publication-title: Automatica
  doi: 10.1016/j.automatica.2010.08.011
– volume: 62
  start-page: 5082
  issue: 10
  year: 2017
  ident: 10.1016/j.automatica.2019.04.004_b18
  article-title: Convergence rate of distributed ADMM over networks
  publication-title: IEEE Transactions on Automatic Control
  doi: 10.1109/TAC.2017.2677879
– ident: 10.1016/j.automatica.2019.04.004_b21
  doi: 10.1007/s10107-018-1232-1
– volume: Vol. 207
  year: 2001
  ident: 10.1016/j.automatica.2019.04.004_b11
– volume: 28
  start-page: 1747
  issue: 8
  year: 2017
  ident: 10.1016/j.automatica.2019.04.004_b15
  article-title: A collective neurodynamic approach to distributed constrained optimization
  publication-title: IEEE Transactions on Neural Networks and Learning Systems
  doi: 10.1109/TNNLS.2016.2549566
– volume: 85
  start-page: 179
  issue: 11
  year: 2017
  ident: 10.1016/j.automatica.2019.04.004_b14
  article-title: Distributed Nash equilibrium seeking for aggregative games with coupled constraints
  publication-title: Automatica
  doi: 10.1016/j.automatica.2017.07.064
– year: 1958
  ident: 10.1016/j.automatica.2019.04.004_b1
– volume: 113
  start-page: E7351
  issue: 47
  year: 2016
  ident: 10.1016/j.automatica.2019.04.004_b33
  article-title: A variational perspective on accelerated methods in optimization
  publication-title: Proceedings of the National Academy of Sciences
  doi: 10.1073/pnas.1614734113
– volume: 51
  start-page: 1741
  issue: 9
  year: 2004
  ident: 10.1016/j.automatica.2019.04.004_b9
  article-title: Generalized neural network for nonsmooth nonlinear programming problems
  publication-title: IEEE Transactions on Circuits and Systems. I. Regular Papers
  doi: 10.1109/TCSI.2004.834493
– volume: 61
  issue: 9
  year: 2018
  ident: 10.1016/j.automatica.2019.04.004_b32
  article-title: Distributed regression estimation with incomplete data in multi-agent networks
  publication-title: Science China. Information Sciences
  doi: 10.1007/s11432-016-9173-8
– volume: 55
  start-page: 254
  issue: 5
  year: 2015
  ident: 10.1016/j.automatica.2019.04.004_b13
  article-title: Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication
  publication-title: Automatica
  doi: 10.1016/j.automatica.2015.03.001
– start-page: 3800
  year: 2011
  ident: 10.1016/j.automatica.2019.04.004_b31
  article-title: A control perspective for centralized and distributed convex optimization
– volume: 27
  start-page: 284
  issue: 2
  year: 2016
  ident: 10.1016/j.automatica.2019.04.004_b36
  article-title: Zeroth-order method for distributed optimization with approximate projections
  publication-title: IEEE Transactions on Neural Networks & Learning Systems
  doi: 10.1109/TNNLS.2015.2480419
– volume: 74
  start-page: 183
  issue: 12
  year: 2016
  ident: 10.1016/j.automatica.2019.04.004_b4
  article-title: Initialization-free distributed coordination for economic dispatch under varying loads and generator commitment
  publication-title: Automatica
  doi: 10.1016/j.automatica.2016.07.003
– volume: 79
  start-page: 207
  issue: 5
  year: 2017
  ident: 10.1016/j.automatica.2019.04.004_b38
  article-title: Distributed optimal coordination for multiple heterogeneous Euler–Lagrangian systems
  publication-title: Automatica
  doi: 10.1016/j.automatica.2017.01.004
SSID ssj0004182
Score 2.5888143
Snippet This paper establishes exponential convergence rates for a class of primal–dual gradient algorithms in distributed optimization without strong convexity. The...
SourceID crossref
elsevier
SourceType Enrichment Source
Index Database
Publisher
StartPage 298
SubjectTerms Convex optimization without strong convexity
Distributed optimization
Exponential convergence
Metric subregularity
Primal–dual algorithm
Rate of convergence
Variational analysis
Title Exponential convergence of distributed primal–dual convex optimization algorithm without strong convexity
URI https://dx.doi.org/10.1016/j.automatica.2019.04.004
Volume 105
WOSCitedRecordID wos000476963500030&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVESC
  databaseName: Elsevier SD Freedom Collection Journals 2021
  customDbUrl:
  eissn: 1873-2836
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0004182
  issn: 0005-1098
  databaseCode: AIEXJ
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lj9MwELbKLgc4IJ5ieckHblVQ4jiJI04VKgK0WiGxSOUU2bGzm902qbpplSNH7vxDfgnjRx4LK7EIcYlaK24Sz5fR-OvMNwi9pL4UwufCI4VisEGRyksjkngxFypREcn9oDDNJpKjI7ZYpB8nk29dLcxumVQVa9t0_V9NDWNgbF06-xfm7n8UBuAzGB2OYHY4Xsvw83ZdVzoHyCh_VDtbXmmoAalVcnWDK6XFAcoVX3a5DqEpyTKnt9Ma3MjK1WdO-fKk3pTN6cpQtjqL-UKz5yfu5LK59L_wbNvURgSWGx3T1qbO92TDYdnR06fbgcq3Q4dq-qXsnZCVNrCM_ZiZMMVQY2aiL5kZ8pOsC9bSp7b19CtlvS5LQg_inPiSW_ajsWPtJphvoVEp-N39WybiTCf_uIfVyXupEbO1XY5_Edf-ZGJYuBuIY7XYWHQD7ZMkSsFj7s_ezxcfhhrbgFnleXf7LivM5gpefb2rQ51R-HJ8F91x-w48s3i5hyaquo9uj9QoH6DzEXLwCDm4LvAIOdgi58fX7xoz9sQWjzGDe8xghxlsMYN7zDxEn9_Oj9-881wvDi8PY9Z4jKc5jaQMcyaKOOIBvNokiJWgce4zBXEyDQXsnmXBC0kUU0wQRSgTlPsh5Sx8hPYqeIbHCOeE5b4ofKnJiEAIRrkkgnGiJEniKDpASbdsWe6E6nW_lGXWZSSeZcOCZ3rBM59msOAHKOhnrq1YyzXmvO4sk7mg0waTGYDqj7Of_NPsp-jW8N48Q3vNZqueo5v5rikvNi8cAn8Ce-uzHA
linkProvider Elsevier
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Exponential+convergence+of+distributed+primal%E2%80%93dual+convex+optimization+algorithm+without+strong+convexity&rft.jtitle=Automatica+%28Oxford%29&rft.au=Liang%2C+Shu&rft.au=Wang%2C+Le+Yi&rft.au=Yin%2C+George&rft.date=2019-07-01&rft.pub=Elsevier+Ltd&rft.issn=0005-1098&rft.eissn=1873-2836&rft.volume=105&rft.spage=298&rft.epage=306&rft_id=info:doi/10.1016%2Fj.automatica.2019.04.004&rft.externalDocID=S0005109819301645
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0005-1098&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0005-1098&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0005-1098&client=summon