Generalized forward–backward splitting with penalization for monotone inclusion problems

We introduce a generalized forward–backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of another maximally monotone operator. We show weak ergodic co...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Journal of global optimization Ročník 73; číslo 4; s. 825 - 847
Hlavní autori: Nimana, Nimit, Petrot, Narin
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 15.04.2019
Springer
Springer Nature B.V
Predmet:
ISSN:0925-5001, 1573-2916
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Abstract We introduce a generalized forward–backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of another maximally monotone operator. We show weak ergodic convergence of the generated sequence of iterates to a solution of the considered monotone inclusion problem, provided that the condition corresponding to the Fitzpatrick function of the operator describing the set of the normal cone is fulfilled. Under strong monotonicity of an operator, we show strong convergence of the iterates. Furthermore, we utilize the proposed method for minimizing a large-scale hierarchical minimization problem concerning the sum of differentiable and nondifferentiable convex functions subject to the set of minima of another differentiable convex function. We illustrate the functionality of the method through numerical experiments addressing constrained elastic net and generalized Heron location problems.
AbstractList We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of another maximally monotone operator. We show weak ergodic convergence of the generated sequence of iterates to a solution of the considered monotone inclusion problem, provided that the condition corresponding to the Fitzpatrick function of the operator describing the set of the normal cone is fulfilled. Under strong monotonicity of an operator, we show strong convergence of the iterates. Furthermore, we utilize the proposed method for minimizing a large-scale hierarchical minimization problem concerning the sum of differentiable and nondifferentiable convex functions subject to the set of minima of another differentiable convex function. We illustrate the functionality of the method through numerical experiments addressing constrained elastic net and generalized Heron location problems.
Audience Academic
Author Petrot, Narin
Nimana, Nimit
Author_xml – sequence: 1
  givenname: Nimit
  surname: Nimana
  fullname: Nimana, Nimit
  organization: Department of Mathematics, Faculty of Science, Khon Kaen University
– sequence: 2
  givenname: Narin
  orcidid: 0000-0001-6539-7107
  surname: Petrot
  fullname: Petrot, Narin
  email: narinp@nu.ac.th
  organization: Department of Mathematics, Faculty of Science, Naresuan University, Center of Excellence in Nonlinear Analysis and Optimization, Faculty of Science, Naresuan University
BookMark eNp9UM1KAzEYDFLBtvoCnhY8b02yP8keS9EqFLzoxUtIs0lN3U3WJKXoyXfwDX0Ss11B8FBCSBhmvplvJmBkrJEAXCI4QxCSa48grWgKUbyQZDAtTsAYFSRLcYXKERjDChdpASE6AxPvtxDCihZ4DJ6X0kjHG_0h60RZt-eu_v78WnPx2n8T3zU6BG02yV6Hl6STpufyoK3p6UlrjQ0xS6KNaHa-hztn141s_Tk4Vbzx8uL3nYKn25vHxV26eljeL-arVGQFDSmCCtOyRFjmtOSSc07xmiqUYyUiQkpV1TnBElWiJLhWucJcxfw0w5jKrM6m4GqYG43fdtIHtrU7F3N6hhGlFJUFKSJrNrA2vJFMG2WD4yKeWrZaxA2UjvicIJrjnGRVFOBBIJz13knFOqdb7t4ZgqwvnQ2ls1g6O5TOehf6TyR0OLQV3XRzXJoNUh99zEa6vzWOqH4AAFWaZw
CitedBy_id crossref_primary_10_1080_10556788_2018_1556660
crossref_primary_10_3390_su14127511
crossref_primary_10_1080_02331934_2020_1846188
Cites_doi 10.1080/00401706.1970.10488634
10.1007/s10957-011-9936-x
10.1137/130942954
10.1137/110820300
10.1137/15M1046095
10.1137/15M1018253
10.1007/s10013-017-0256-9
10.1137/120872802
10.1007/s11075-015-0007-5
10.1016/j.jde.2009.06.014
10.1007/BF03007664
10.1007/s10444-011-9254-8
10.1007/s10957-013-0296-6
10.1007/s11228-011-0191-y
10.1016/0022-247X(79)90234-8
10.1007/978-1-4419-9467-7
10.1007/s10107-016-1030-6
10.1080/02331934.2016.1181759
10.1137/140957639
10.1007/s10957-014-0700-x
10.1111/j.1467-9868.2005.00503.x
10.1137/100789464
10.1007/s11590-017-1158-1
10.1137/16M1080173
10.1142/5021
10.1137/140980910
10.1007/s11228-014-0274-7
10.1016/j.compbiolchem.2012.12.008
10.1007/s10013-013-0050-2
10.1111/j.2517-6161.1996.tb02080.x
ContentType Journal Article
Copyright Springer Science+Business Media, LLC, part of Springer Nature 2018
COPYRIGHT 2019 Springer
Journal of Global Optimization is a copyright of Springer, (2018). All Rights Reserved.
Copyright_xml – notice: Springer Science+Business Media, LLC, part of Springer Nature 2018
– notice: COPYRIGHT 2019 Springer
– notice: Journal of Global Optimization is a copyright of Springer, (2018). All Rights Reserved.
DBID AAYXX
CITATION
3V.
7SC
7WY
7WZ
7XB
87Z
88I
8AL
8AO
8FD
8FE
8FG
8FK
8FL
8G5
ABJCF
ABUWG
AFKRA
ARAPS
AZQEC
BENPR
BEZIV
BGLVJ
CCPQU
DWQXO
FRNLG
F~G
GNUQQ
GUQSH
HCIFZ
JQ2
K60
K6~
K7-
L.-
L6V
L7M
L~C
L~D
M0C
M0N
M2O
M2P
M7S
MBDVC
P5Z
P62
PHGZM
PHGZT
PKEHL
PQBIZ
PQBZA
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
Q9U
DOI 10.1007/s10898-018-00730-5
DatabaseName CrossRef
ProQuest Central (Corporate)
Computer and Information Systems Abstracts
ABI/INFORM Collection
ABI/INFORM Global (PDF only)
ProQuest Central (purchase pre-March 2016)
ABI/INFORM Collection
Science Database (Alumni Edition)
Computing Database (Alumni Edition)
ProQuest Pharma Collection
Technology Research Database
ProQuest SciTech Collection
ProQuest Technology Collection
ProQuest Central (Alumni) (purchase pre-March 2016)
ABI/INFORM Collection (Alumni)
Research Library (Alumni)
ProQuest Materials Science & Engineering
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
Advanced Technologies & Computer Science Collection
ProQuest Central Essentials
ProQuest Central
Business Premium Collection
Technology Collection
ProQuest One
ProQuest Central
Business Premium Collection (Alumni)
ABI/INFORM Global (Corporate)
ProQuest Central Student
ProQuest Research Library
SciTech Premium Collection
ProQuest Computer Science Collection
ProQuest Business Collection (Alumni Edition)
ProQuest Business Collection
Computer Science Database
ABI/INFORM Professional Advanced
ProQuest Engineering Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
ABI/INFORM Global
Computing Database
Research Library
Science Database
Engineering Database
Research Library (Corporate)
ProQuest advanced technologies & aerospace journals
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Premium
ProQuest One Academic (New)
ProQuest One Academic Middle East (New)
ProQuest One Business (UW System Shared)
ProQuest One Business (Alumni)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Applied & Life Sciences
ProQuest One Academic (retired)
ProQuest One Academic UKI Edition
ProQuest Central China
Engineering Collection
ProQuest Central Basic
DatabaseTitle CrossRef
ProQuest Business Collection (Alumni Edition)
Research Library Prep
Computer Science Database
ProQuest Central Student
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
ProQuest Computer Science Collection
Computer and Information Systems Abstracts
SciTech Premium Collection
ProQuest Central China
ABI/INFORM Complete
ProQuest One Applied & Life Sciences
ProQuest Central (New)
Engineering Collection
Advanced Technologies & Aerospace Collection
Business Premium Collection
ABI/INFORM Global
Engineering Database
ProQuest Science Journals (Alumni Edition)
ProQuest One Academic Eastern Edition
ProQuest Technology Collection
ProQuest Business Collection
ProQuest One Academic UKI Edition
ProQuest One Academic
ProQuest One Academic (New)
ABI/INFORM Global (Corporate)
ProQuest One Business
Technology Collection
Technology Research Database
Computer and Information Systems Abstracts – Academic
ProQuest One Academic Middle East (New)
ProQuest Central (Alumni Edition)
ProQuest One Community College
Research Library (Alumni Edition)
ProQuest Pharma Collection
ProQuest Central
ABI/INFORM Professional Advanced
ProQuest Engineering Collection
ProQuest Central Korea
ProQuest Research Library
Advanced Technologies Database with Aerospace
ABI/INFORM Complete (Alumni Edition)
ProQuest Computing
ABI/INFORM Global (Alumni Edition)
ProQuest Central Basic
ProQuest Science Journals
ProQuest Computing (Alumni Edition)
ProQuest SciTech Collection
Computer and Information Systems Abstracts Professional
Advanced Technologies & Aerospace Database
Materials Science & Engineering Collection
ProQuest One Business (Alumni)
ProQuest Central (Alumni)
Business Premium Collection (Alumni)
DatabaseTitleList
ProQuest Business Collection (Alumni Edition)

Database_xml – sequence: 1
  dbid: BENPR
  name: ProQuest Central
  url: https://www.proquest.com/central
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
Mathematics
Sciences (General)
Computer Science
EISSN 1573-2916
EndPage 847
ExternalDocumentID A718424739
10_1007_s10898_018_00730_5
GrantInformation_xml – fundername: Thailand Research Fund
  grantid: RSA5880028
  funderid: http://dx.doi.org/10.13039/501100004396
GroupedDBID -52
-57
-5G
-BR
-EM
-~C
.4S
.86
.DC
.VR
06D
0R~
0VY
199
1N0
203
29K
2J2
2JN
2JY
2KG
2LR
2~H
30V
4.4
406
408
409
40D
40E
5GY
5VS
67Z
6NX
78A
7WY
88I
8AO
8FE
8FG
8FL
8G5
8TC
8UJ
95-
95.
95~
96X
AAAVM
AABHQ
AACDK
AAHNG
AAIAL
AAJBT
AAJKR
AANZL
AARTL
AASML
AATNV
AATVU
AAUYE
AAWCG
AAYIU
AAYQN
AAYZH
ABAKF
ABBBX
ABBXA
ABDZT
ABECU
ABFTV
ABHLI
ABHQN
ABJCF
ABJNI
ABJOX
ABKCH
ABKTR
ABMNI
ABMQK
ABNWP
ABQBU
ABSXP
ABTEG
ABTHY
ABTKH
ABTMW
ABUWG
ABWNU
ABXPI
ACAOD
ACDTI
ACGFS
ACGOD
ACHSB
ACHXU
ACIWK
ACKNC
ACMDZ
ACMLO
ACOKC
ACOMO
ACPIV
ACZOJ
ADHHG
ADHIR
ADIMF
ADINQ
ADKNI
ADKPE
ADRFC
ADTPH
ADURQ
ADYFF
ADZKW
AEFQL
AEGAL
AEGNC
AEJHL
AEJRE
AEMSY
AENEX
AEOHA
AEPYU
AESKC
AETLH
AEVLU
AEXYK
AFBBN
AFKRA
AFLOW
AFQWF
AFWTZ
AFZKB
AGAYW
AGDGC
AGJBK
AGMZJ
AGQEE
AGQMX
AGRTI
AGWIL
AGWZB
AGYKE
AHAVH
AHBYD
AHKAY
AHSBF
AHYZX
AIAKS
AIGIU
AIIXL
AILAN
AITGF
AJRNO
AJZVZ
ALMA_UNASSIGNED_HOLDINGS
ALWAN
AMKLP
AMXSW
AMYLF
AMYQR
AOCGG
ARAPS
ARCSS
ARMRJ
ASPBG
AVWKF
AXYYD
AYQZM
AZFZN
AZQEC
B-.
BA0
BAPOH
BDATZ
BENPR
BEZIV
BGLVJ
BGNMA
BPHCQ
BSONS
CCPQU
CS3
CSCUP
D-I
DDRTE
DL5
DNIVK
DPUIP
DU5
DWQXO
EBLON
EBS
EDO
EIOEI
EJD
ESBYG
FEDTE
FERAY
FFXSO
FIGPU
FINBP
FNLPD
FRNLG
FRRFC
FSGXE
FWDCC
GGCAI
GGRSB
GJIRD
GNUQQ
GNWQR
GQ6
GQ7
GQ8
GROUPED_ABI_INFORM_COMPLETE
GUQSH
GXS
HCIFZ
HF~
HG5
HG6
HMJXF
HQYDN
HRMNR
HVGLF
HZ~
I09
IAO
IHE
IJ-
IKXTQ
ITC
ITM
IWAJR
IXC
IZIGR
IZQ
I~X
I~Z
J-C
J0Z
JBSCW
JCJTX
JZLTJ
K60
K6V
K6~
K7-
KDC
KOV
L6V
LAK
LLZTM
M0C
M0N
M2O
M2P
M4Y
M7S
MA-
N9A
NB0
NPVJJ
NQJWS
NU0
O93
O9G
O9I
O9J
OAM
P19
P2P
P62
P9M
PF0
PQBIZ
PQBZA
PQQKQ
PROAC
PT4
PT5
PTHSS
Q2X
QOK
QOS
R89
R9I
RHV
RNS
ROL
RPX
RSV
S16
S27
S3B
SAP
SBE
SDD
SDH
SDM
SHX
SISQX
SJYHP
SNE
SNPRN
SNX
SOHCF
SOJ
SPISZ
SRMVM
SSLCW
STPWE
SZN
T13
TN5
TSG
TSK
TSV
TUC
TUS
U2A
UG4
UOJIU
UTJUX
UZXMN
VC2
VFIZW
W23
W48
WK8
YLTOR
Z45
Z5O
Z7R
Z7X
Z7Z
Z81
Z83
Z86
Z88
Z8M
Z8N
Z8T
Z8U
Z8W
Z92
ZMTXR
~EX
-Y2
1SB
2.D
28-
2P1
2VQ
5QI
AAPKM
AARHV
AAYTO
AAYXX
ABBRH
ABDBE
ABFSG
ABQSL
ABRTQ
ABULA
ACBXY
ACSTC
ADHKG
AEBTG
AEFIE
AEKMD
AEZWR
AFDZB
AFEXP
AFFHD
AFGCZ
AFHIU
AFOHR
AGGDS
AGQPQ
AHPBZ
AHWEU
AI.
AIXLP
AJBLW
AMVHM
ATHPR
AYFIA
BBWZM
CAG
CITATION
COF
H13
KOW
N2Q
NDZJH
O9-
OVD
PHGZM
PHGZT
PQGLB
R4E
RNI
RZC
RZE
RZK
S1Z
S26
S28
SCLPG
T16
TEORI
VH1
ZWQNP
ZY4
3V.
7SC
7XB
8AL
8FD
8FK
JQ2
L.-
L7M
L~C
L~D
MBDVC
PKEHL
PQEST
PQUKI
PRINS
Q9U
ID FETCH-LOGICAL-c358t-10f286612e486aeaaa82b8f142fc48676f9d472e19c672df4f2af00083228e3d3
IEDL.DBID K7-
ISICitedReferencesCount 4
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000462013800007&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0925-5001
IngestDate Tue Nov 04 22:33:07 EST 2025
Sat Nov 29 10:09:48 EST 2025
Tue Nov 18 21:58:25 EST 2025
Sat Nov 29 01:59:35 EST 2025
Fri Feb 21 02:42:28 EST 2025
IsPeerReviewed true
IsScholarly true
Issue 4
Keywords Monotone inclusion
65K05
90C25
65K10
Monotone operator
Hierarchical optimization
47H05
Forward–backward algorithm
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c358t-10f286612e486aeaaa82b8f142fc48676f9d472e19c672df4f2af00083228e3d3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0001-6539-7107
PQID 2188816575
PQPubID 29930
PageCount 23
ParticipantIDs proquest_journals_2188816575
gale_infotracacademiconefile_A718424739
crossref_primary_10_1007_s10898_018_00730_5
crossref_citationtrail_10_1007_s10898_018_00730_5
springer_journals_10_1007_s10898_018_00730_5
PublicationCentury 2000
PublicationDate 20190415
PublicationDateYYYYMMDD 2019-04-15
PublicationDate_xml – month: 4
  year: 2019
  text: 20190415
  day: 15
PublicationDecade 2010
PublicationPlace New York
PublicationPlace_xml – name: New York
– name: Dordrecht
PublicationSubtitle An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering
PublicationTitle Journal of global optimization
PublicationTitleAbbrev J Glob Optim
PublicationYear 2019
Publisher Springer US
Springer
Springer Nature B.V
Publisher_xml – name: Springer US
– name: Springer
– name: Springer Nature B.V
References Bauschke, Combettes (CR7) 2011
Boţ, Csetnek (CR11) 2016; 71
Hoerl, Kennard (CR20) 1970; 12
Raguet, Landrieu (CR29) 2015; 8
Zou, Hastie (CR35) 2005; 67
CR19
Passty (CR25) 1979; 72
CR15
Noun, Peypouquet (CR23) 2013; 158
Boţ, Csetnek (CR9) 2014; 42
Boţ, Csetnek (CR12) 2017; 66
Czarnecki, Noun, Peypouquet (CR18) 2016; 23
Schmidt, Le Roux, Bach (CR30) 2017; 162
Zălinescu (CR34) 2002
Attouch, Czarnecki (CR1) 2010; 248
Attouch, Peypouquet (CR4) 2016; 26
Mairal (CR22) 2015; 25
Boţ, Csetnek (CR10) 2014; 22
Tibshirani (CR33) 1996; 58
Attouch, Czarnecki, Peypouquet (CR2) 2011; 21
Shalev-Schwartz, Zhang (CR32) 2013; 14
Chen, Ma, Yang (CR16) 2015; 25
Baillon, Haddad (CR5) 1977; 26
Ochs, Chen, Brox, Pock (CR24) 2014; 7
Combettes, Pesquet (CR17) 2012; 20
Huang, Gong, Yang, He (CR21) 2013; 43
Polyak (CR27) 1987
Bottou, Curtis, Nocedal (CR8) 2018; 60
Vũ (CR31) 2013; 38
Boţ, Csetnek, Nimana (CR14) 2018; 46
Attouch, Czarnecki, Peypouquet (CR3) 2011; 21
Banert, Boţ (CR6) 2015; 166
Peypouquet (CR26) 2012; 153
Boţ, Csetnek, Nimana (CR13) 2018; 12
Raguet, Fadili, Peyré (CR28) 2013; 6
J-B Baillon (730_CR5) 1977; 26
J Peypouquet (730_CR26) 2012; 153
H Attouch (730_CR3) 2011; 21
GB Passty (730_CR25) 1979; 72
RI Boţ (730_CR11) 2016; 71
J Mairal (730_CR22) 2015; 25
H Raguet (730_CR29) 2015; 8
S Banert (730_CR6) 2015; 166
RI Boţ (730_CR14) 2018; 46
T Huang (730_CR21) 2013; 43
N Noun (730_CR23) 2013; 158
H Attouch (730_CR4) 2016; 26
BT Polyak (730_CR27) 1987
S Shalev-Schwartz (730_CR32) 2013; 14
730_CR15
C Zălinescu (730_CR34) 2002
730_CR19
L Bottou (730_CR8) 2018; 60
P Ochs (730_CR24) 2014; 7
RI Boţ (730_CR13) 2018; 12
PL Combettes (730_CR17) 2012; 20
HH Bauschke (730_CR7) 2011
RI Boţ (730_CR9) 2014; 42
M Schmidt (730_CR30) 2017; 162
C Chen (730_CR16) 2015; 25
AE Hoerl (730_CR20) 1970; 12
H Attouch (730_CR2) 2011; 21
M-O Czarnecki (730_CR18) 2016; 23
BC Vũ (730_CR31) 2013; 38
R Tibshirani (730_CR33) 1996; 58
RI Boţ (730_CR12) 2017; 66
H Attouch (730_CR1) 2010; 248
RI Boţ (730_CR10) 2014; 22
H Raguet (730_CR28) 2013; 6
H Zou (730_CR35) 2005; 67
References_xml – volume: 12
  start-page: 55
  year: 1970
  end-page: 67
  ident: CR20
  article-title: Ridge regression: biased estimation for nonorthogonal problems
  publication-title: Technometrics
  doi: 10.1080/00401706.1970.10488634
– volume: 153
  start-page: 123
  issue: 1
  year: 2012
  end-page: 138
  ident: CR26
  article-title: Coupling the gradient method with a general exterior penalization scheme for convex minimization
  publication-title: J. Optim. Theory Appl.
  doi: 10.1007/s10957-011-9936-x
– volume: 7
  start-page: 1388
  issue: 2
  year: 2014
  end-page: 1419
  ident: CR24
  article-title: iPiano: inertial proximal algorithm for non-convex optimization
  publication-title: SIAM J. Imaging Sci.
  doi: 10.1137/130942954
– volume: 21
  start-page: 1251
  issue: 4
  year: 2011
  end-page: 1274
  ident: CR3
  article-title: Coupling forward–backward with penalty schemes and parallel splitting for constrained variational inequalities
  publication-title: SIAM J. Optim.
  doi: 10.1137/110820300
– volume: 26
  start-page: 1824
  year: 2016
  end-page: 1834
  ident: CR4
  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
– volume: 8
  start-page: 2706
  year: 2015
  end-page: 2739
  ident: CR29
  article-title: Preconditioning of a generalized forward–backward splitting and application to optimization on graphs
  publication-title: SIAM J. Imaging Sci.
  doi: 10.1137/15M1018253
– volume: 46
  start-page: 53
  issue: 1
  year: 2018
  end-page: 71
  ident: CR14
  article-title: An inertial proximal-gradient penalization scheme for constrained convex optimization problems
  publication-title: Vietnam J. Math.
  doi: 10.1007/s10013-017-0256-9
– volume: 6
  start-page: 1199
  year: 2013
  end-page: 1226
  ident: CR28
  article-title: A generalized forward–backward splitting: SIAM
  publication-title: J. Imaging Sci.
  doi: 10.1137/120872802
– volume: 71
  start-page: 519
  year: 2016
  end-page: 540
  ident: CR11
  article-title: An inertial forward–backward–forward primal–dual splitting algorithm for solving monotone inclusion problems
  publication-title: Numer. Algorithms
  doi: 10.1007/s11075-015-0007-5
– volume: 248
  start-page: 1315
  issue: 6
  year: 2010
  end-page: 1344
  ident: CR1
  article-title: Asymptotic behavior of coupled dynamical systems with multiscale aspects
  publication-title: J. Differ. Equ.
  doi: 10.1016/j.jde.2009.06.014
– volume: 26
  start-page: 137
  year: 1977
  end-page: 150
  ident: CR5
  article-title: Quelques propriétés des opérateurs angle-bornés et -cycliquement monotones
  publication-title: Israel J. Math.
  doi: 10.1007/BF03007664
– volume: 38
  start-page: 667
  year: 2013
  end-page: 681
  ident: CR31
  article-title: A splitting algorithm for dual monotone inclusions involving cocoercive operators
  publication-title: Adv. Comput. Math.
  doi: 10.1007/s10444-011-9254-8
– volume: 158
  start-page: 787
  issue: 3
  year: 2013
  end-page: 795
  ident: CR23
  article-title: Forward–backward penalty scheme for constrained convex minimization without inf-compactness
  publication-title: J. Optim. Theory Appl.
  doi: 10.1007/s10957-013-0296-6
– volume: 14
  start-page: 567
  year: 2013
  end-page: 599
  ident: CR32
  article-title: Stochastic dual coordinate ascent methods for regularized loss minimization
  publication-title: J. Mach. Learn. Res.
– volume: 58
  start-page: 267
  year: 1996
  end-page: 288
  ident: CR33
  article-title: Regression shrinkage and selection via the lasso
  publication-title: J. R. Stat. Soc. Ser. B Stat. Methodol.
– volume: 20
  start-page: 307
  year: 2012
  end-page: 330
  ident: CR17
  article-title: Primal–dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators
  publication-title: Set-Valued Var. Anal.
  doi: 10.1007/s11228-011-0191-y
– volume: 72
  start-page: 383
  year: 1979
  end-page: 390
  ident: CR25
  article-title: Ergodic convergence to a zero of the sum of monotone operators in Hilbert space
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/0022-247X(79)90234-8
– year: 2011
  ident: CR7
  publication-title: Convex Analysis and Monotone Operator Theory in Hilbert Spaces
  doi: 10.1007/978-1-4419-9467-7
– volume: 23
  start-page: 531
  year: 2016
  end-page: 565
  ident: CR18
  article-title: Splitting forward–backward penalty scheme for constrained variational problems
  publication-title: J. Convex Anal.
– volume: 162
  start-page: 83
  issue: 1
  year: 2017
  end-page: 112
  ident: CR30
  article-title: Minimizing finite sums with the stochastic average gradient
  publication-title: Math. Program.
  doi: 10.1007/s10107-016-1030-6
– volume: 66
  start-page: 965
  year: 2017
  end-page: 982
  ident: CR12
  article-title: Penalty schemes with inertial effects for monotone inclusion problems
  publication-title: Optimization
  doi: 10.1080/02331934.2016.1181759
– ident: CR19
– volume: 25
  start-page: 829
  issue: 2
  year: 2015
  end-page: 855
  ident: CR22
  article-title: Incremental majorization–minimization optimization with application to large-scale machine learning
  publication-title: SIAM J. Optim.
  doi: 10.1137/140957639
– volume: 166
  start-page: 930
  issue: 3
  year: 2015
  end-page: 948
  ident: CR6
  article-title: Backward penalty schemes for monotone inclusion problems
  publication-title: J. Optim. Theory Appl.
  doi: 10.1007/s10957-014-0700-x
– volume: 67
  start-page: 301
  year: 2005
  end-page: 320
  ident: CR35
  article-title: Regularization and variable selection via the elastic net
  publication-title: J. R. Stat. Soc. Ser. B Stat. Methodol.
  doi: 10.1111/j.1467-9868.2005.00503.x
– volume: 21
  start-page: 149
  issue: 1
  year: 2011
  end-page: 173
  ident: CR2
  article-title: Prox-penalization and splitting methods for constrained variational problems
  publication-title: SIAM J. Optim.
  doi: 10.1137/100789464
– ident: CR15
– volume: 12
  start-page: 17
  issue: 1
  year: 2018
  end-page: 33
  ident: CR13
  article-title: Gradient-type penalty method with inertial effects for solving constrained convex optimization problems with smooth data
  publication-title: Optim. Lett.
  doi: 10.1007/s11590-017-1158-1
– volume: 60
  start-page: 223
  issue: 2
  year: 2018
  end-page: 311
  ident: CR8
  article-title: Optimization methods for large-scale machine learning
  publication-title: SIAM Rev.
  doi: 10.1137/16M1080173
– year: 2002
  ident: CR34
  publication-title: Convex Analysis in General Vector Spaces
  doi: 10.1142/5021
– volume: 25
  start-page: 2120
  issue: 4
  year: 2015
  end-page: 2142
  ident: CR16
  article-title: A general inertial proximal point algorithm for mixed variational inequality problem
  publication-title: SIAM J. Optim.
  doi: 10.1137/140980910
– volume: 22
  start-page: 313
  year: 2014
  end-page: 331
  ident: CR10
  article-title: Forward–backward and Tseng’s type penalty schemes for monotone inclusion problems
  publication-title: Set-Valued Var. Anal.
  doi: 10.1007/s11228-014-0274-7
– volume: 43
  start-page: 46
  year: 2013
  end-page: 54
  ident: CR21
  article-title: ProteinLasso: a Lasso regression approach to protein inference problem in shotgun proteomics
  publication-title: Comp. Biol. Chem.
  doi: 10.1016/j.compbiolchem.2012.12.008
– year: 1987
  ident: CR27
  publication-title: Introduction to Optimization (Translated from the Russian). Translations Series in Mathematics and Engineering
– volume: 42
  start-page: 451
  issue: 4
  year: 2014
  end-page: 465
  ident: CR9
  article-title: A Tseng’s type penalty scheme for solving inclusion problems involving linearly composed and parallel-sum type monotone operators
  publication-title: Vietnam J. Math.
  doi: 10.1007/s10013-013-0050-2
– volume: 7
  start-page: 1388
  issue: 2
  year: 2014
  ident: 730_CR24
  publication-title: SIAM J. Imaging Sci.
  doi: 10.1137/130942954
– volume: 6
  start-page: 1199
  year: 2013
  ident: 730_CR28
  publication-title: J. Imaging Sci.
  doi: 10.1137/120872802
– volume: 26
  start-page: 137
  year: 1977
  ident: 730_CR5
  publication-title: Israel J. Math.
  doi: 10.1007/BF03007664
– volume: 38
  start-page: 667
  year: 2013
  ident: 730_CR31
  publication-title: Adv. Comput. Math.
  doi: 10.1007/s10444-011-9254-8
– volume: 21
  start-page: 149
  issue: 1
  year: 2011
  ident: 730_CR2
  publication-title: SIAM J. Optim.
  doi: 10.1137/100789464
– volume: 22
  start-page: 313
  year: 2014
  ident: 730_CR10
  publication-title: Set-Valued Var. Anal.
  doi: 10.1007/s11228-014-0274-7
– volume-title: Convex Analysis in General Vector Spaces
  year: 2002
  ident: 730_CR34
  doi: 10.1142/5021
– volume: 46
  start-page: 53
  issue: 1
  year: 2018
  ident: 730_CR14
  publication-title: Vietnam J. Math.
  doi: 10.1007/s10013-017-0256-9
– volume: 23
  start-page: 531
  year: 2016
  ident: 730_CR18
  publication-title: J. Convex Anal.
– volume: 21
  start-page: 1251
  issue: 4
  year: 2011
  ident: 730_CR3
  publication-title: SIAM J. Optim.
  doi: 10.1137/110820300
– volume: 60
  start-page: 223
  issue: 2
  year: 2018
  ident: 730_CR8
  publication-title: SIAM Rev.
  doi: 10.1137/16M1080173
– volume: 25
  start-page: 2120
  issue: 4
  year: 2015
  ident: 730_CR16
  publication-title: SIAM J. Optim.
  doi: 10.1137/140980910
– volume: 43
  start-page: 46
  year: 2013
  ident: 730_CR21
  publication-title: Comp. Biol. Chem.
  doi: 10.1016/j.compbiolchem.2012.12.008
– volume: 158
  start-page: 787
  issue: 3
  year: 2013
  ident: 730_CR23
  publication-title: J. Optim. Theory Appl.
  doi: 10.1007/s10957-013-0296-6
– volume: 58
  start-page: 267
  year: 1996
  ident: 730_CR33
  publication-title: J. R. Stat. Soc. Ser. B Stat. Methodol.
  doi: 10.1111/j.2517-6161.1996.tb02080.x
– volume-title: Introduction to Optimization (Translated from the Russian). Translations Series in Mathematics and Engineering
  year: 1987
  ident: 730_CR27
– volume: 72
  start-page: 383
  year: 1979
  ident: 730_CR25
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/0022-247X(79)90234-8
– volume: 25
  start-page: 829
  issue: 2
  year: 2015
  ident: 730_CR22
  publication-title: SIAM J. Optim.
  doi: 10.1137/140957639
– volume: 153
  start-page: 123
  issue: 1
  year: 2012
  ident: 730_CR26
  publication-title: J. Optim. Theory Appl.
  doi: 10.1007/s10957-011-9936-x
– volume: 67
  start-page: 301
  year: 2005
  ident: 730_CR35
  publication-title: J. R. Stat. Soc. Ser. B Stat. Methodol.
  doi: 10.1111/j.1467-9868.2005.00503.x
– volume: 42
  start-page: 451
  issue: 4
  year: 2014
  ident: 730_CR9
  publication-title: Vietnam J. Math.
  doi: 10.1007/s10013-013-0050-2
– volume: 71
  start-page: 519
  year: 2016
  ident: 730_CR11
  publication-title: Numer. Algorithms
  doi: 10.1007/s11075-015-0007-5
– volume: 162
  start-page: 83
  issue: 1
  year: 2017
  ident: 730_CR30
  publication-title: Math. Program.
  doi: 10.1007/s10107-016-1030-6
– volume-title: Convex Analysis and Monotone Operator Theory in Hilbert Spaces
  year: 2011
  ident: 730_CR7
  doi: 10.1007/978-1-4419-9467-7
– volume: 12
  start-page: 17
  issue: 1
  year: 2018
  ident: 730_CR13
  publication-title: Optim. Lett.
  doi: 10.1007/s11590-017-1158-1
– ident: 730_CR15
– volume: 14
  start-page: 567
  year: 2013
  ident: 730_CR32
  publication-title: J. Mach. Learn. Res.
– ident: 730_CR19
– volume: 8
  start-page: 2706
  year: 2015
  ident: 730_CR29
  publication-title: SIAM J. Imaging Sci.
  doi: 10.1137/15M1018253
– volume: 166
  start-page: 930
  issue: 3
  year: 2015
  ident: 730_CR6
  publication-title: J. Optim. Theory Appl.
  doi: 10.1007/s10957-014-0700-x
– volume: 12
  start-page: 55
  year: 1970
  ident: 730_CR20
  publication-title: Technometrics
  doi: 10.1080/00401706.1970.10488634
– volume: 26
  start-page: 1824
  year: 2016
  ident: 730_CR4
  publication-title: SIAM J. Optim.
  doi: 10.1137/15M1046095
– volume: 248
  start-page: 1315
  issue: 6
  year: 2010
  ident: 730_CR1
  publication-title: J. Differ. Equ.
  doi: 10.1016/j.jde.2009.06.014
– volume: 20
  start-page: 307
  year: 2012
  ident: 730_CR17
  publication-title: Set-Valued Var. Anal.
  doi: 10.1007/s11228-011-0191-y
– volume: 66
  start-page: 965
  year: 2017
  ident: 730_CR12
  publication-title: Optimization
  doi: 10.1080/02331934.2016.1181759
SSID ssj0009852
Score 2.2361019
Snippet We introduce a generalized forward–backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of...
We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of...
SourceID proquest
gale
crossref
springer
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 825
SubjectTerms Computer Science
Convergence
Mathematical analysis
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Operators (mathematics)
Optimization
Real Functions
Splitting
SummonAdditionalLinks – databaseName: SpringerLINK Contemporary 1997-Present
  dbid: RSV
  link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Lb9QwEB6VhQM9UHahauhS-YBUEI20cZzEPq4qKg6lQvShiosVO7a0UrWtmt0eeuI_8A_5Jcx4nd3yqkRveThjy55XPJ5vAN5YV_vSSpUqk0n8QfGj1PiySa3hhSlVLl3Y0D87rI6O5Pm5-hyTwtrutHsXkgya-k6ym6R0MCRJ4aVRWjyCx2juJInjl-OzFdSuDHV2RooXaYFaOKbK_J3GL-bod6X8R3Q0GJ2DjYcN9zk8i04mGy-4og9rbjqAja6AA4vyPID1O2iEePdpCeHaDqAfW7XsbYSmfvcCvsbLya1rGLq7dOT2x7fvhjYB8ZK16NKGg9SM9nfZlSM3f5HoSc0Z8vwloX-zydRezGmjjsWKNu1LOD34cLL_MY3VGVKbF3KG-ttzidadOyHL2tV1LbmRPhPcW4LxK71qRMVdpmxZ8cYLz2sfXD7OpcubfBN6U-xxC1jhfJMbJQxSFEKVRlT4yNfO5wZ5Jk8g6xZJ2whdThU0LvQKdJlmW-Ns6zDbukjg_fKbqwVwx72td2ntNUk1UrZ1TE7A8RE-lh6jCRdcVLlKYNixh47i3mr0k6TMKIaVwF7HDqvX_-731f8134an6LCFaFZWDKE3u5671_DE3swm7fVOEIOfcfkCcw
  priority: 102
  providerName: Springer Nature
Title Generalized forward–backward splitting with penalization for monotone inclusion problems
URI https://link.springer.com/article/10.1007/s10898-018-00730-5
https://www.proquest.com/docview/2188816575
Volume 73
WOSCitedRecordID wos000462013800007&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: PRVAVX
  databaseName: Springer LINK
  customDbUrl:
  eissn: 1573-2916
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0009852
  issn: 0925-5001
  databaseCode: RSV
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22
  providerName: Springer Nature
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3NbhQxDLZoywEO0BYQC2WVAxIgiNjJJDPJCZWqFRKwrFoopZdokkmklart0tly4MQ78IY8CXY22-VH9MLFGs1PEsmO7bHjzwAPfWhi5bXhxhUaf1DigLtYtdw7oVxlSh1SQP_wTT0c6qMjM8oBty4fq1zoxKSo21NPMfLnaIq0LihN8GL6mVPXKMqu5hYaK7BWCFGQnL-u-RJ0V6eOOwMjFFeoj3PRTC6d01RchgukZNWAq98M05_q-a88aTI_ezf_d-HrcCM7nmx7LikbcCVMNuH6L3CEm7CRN3rHHmc06ie34Dhfjr-GlqGHS6dsf3z77ijuh5esQy82nZ1mFNJl00Ce_by2k15nOP0pAX6z8cSfnFNsjuUmNt1t-LC3-37nFc8NGbgvlZ6hyo5Co0EXQeqqCU3TaOF0LKSInpD7qmhaWYtQGF_Voo0yiiYmL08IHcq2vAOrE5zxLjAVYls6Ix2OKKWpnKzxVmxCLB2KSdmDYsEN6zNaOTXNOLFLnGXioEUO2sRBq3rw9OKb6Ryr49K3HxGTLW1kHNk3uR4B10eQWHYbrbYUsi5ND7YWnLV5h3d2ydYePFvIxvLxv-e9d_lo9-Ea-mQpYVWoLVidnZ2HB3DVf5mNu7M-rNQfP_Vh7eXucLTfT9KO9O1gh6h4l-iIaH2AdKSOke4fHP4EDcoJ0A
linkProvider ProQuest
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3NbtQwEB6VggQcWlpAbH_ABxAgiNg4TmIfqqoqVK26rDgUVPViYseWVqq2S7Nt1Z76DrwHD8WTMON1WH5Ebz1wi_LjJPbnmfGM5xuAp9ZVvrBSJcqkEhcovpsYX9SJNTw3hcqkCw79T72y35f7--rDDHxrc2FoW2UrE4Ogro8s-cjfoCqSMqUwwfroS0JVoyi62pbQmMBi152f4ZKtWdt5i-P7jPOtd3ub20msKpDYLJdjlDueS9RK3AlZVK6qKsmN9Kng3hL9XOFVLUruUmWLktdeeF75YKpwLl1WZ9juDbgpBE4H2irY3ZyS_MpQ4aereJ7kKP9jkk5M1ZOUzIYdQsGxbpL_pgj_VAd_xWWDutua_9866h7MRcOabUxmwgLMuOEi3P2FbnERFqIga9iLyLb98j4cxMPBhasZWvC0i_j75VdDfk08ZA1a6WFvOCOXNRs5WrlMclfpdoa_e0SE5mwwtIcn5HtksUhP8wA-XssfP4TZIb7xEbDc-TozShhsUQhVGFHiKV85nxmcBlkH0nb0tY1s7FQU5FBPeaQJMRoRowNidN6BVz-fGU24SK68-zmBSpOgwpZtFfMt8PuI8ktvoFUiuCgz1YGVFkk6SrBGT2HUgdctFqeX__3epatbewK3t_fe93Rvp7-7DHfQ_gzBuTRfgdnx8YlbhVv2dDxojh-HucXg83Vj9AdlQF0T
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3LbtQwFL0qBaGyAFpAHSjgBQgQRJ04dmIvEKooI6pWo1kAqrpxY8eWRqqmQzMFwYp_4G_4HL6Eez0Ow0N01wW7KA_ndXyfvucCPHC-DqVTOtM2V-ighH5mQ9lkznJpS10oHwP67_aq4VDt7-vREnzramFoWWUnE6Ogbo4dxcg3URUplVOaYDOkZRGj7cGL6fuMOkhRprVrpzGHyK7_9BHdt_b5zjb-64ecD169efk6Sx0GMldINUMZFLhCDcW9UGXt67pW3KqQCx4cUdGVQTei4j7Xrqx4E0TgdYhmC-fKF02B416AixX6mOT4jeTBgvBXxW4_fc1lJlEXpIKdVLanqLANPw4lyvqZ_E0p_qka_srRRtU3uPY_f7TrcDUZ3GxrPkNWYclP1uDKLzSMa7CaBFzLHicW7ic34CBtjj_7hqFlT6uLv3_5aineiZusRes9rhlnFMpmU08ezbymlU5n-LrHRHTOxhN3dEoxSZaa97Q34e25vPEtWJ7gHdeBSR-awmphcUQhdGlFhbtC7UNhcXoUPcg7JBiXWNqpWciRWfBLE3oMosdE9BjZg6c_r5nOOUrOPPsRAcyQAMORXZ3qMPD5iArMbKG1IrioCt2DjQ5VJkm21iwg1YNnHS4Xh_9939tnj3YfLiM0zd7OcPcOrKBZGnN2udyA5dnJqb8Ll9yH2bg9uRenGYPD84boD4_9ZiQ
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=Generalized+forward%E2%80%93backward+splitting+with+penalization+for+monotone+inclusion+problems&rft.jtitle=Journal+of+global+optimization&rft.au=Nimana%2C+Nimit&rft.au=Petrot%2C+Narin&rft.date=2019-04-15&rft.pub=Springer+Nature+B.V&rft.issn=0925-5001&rft.eissn=1573-2916&rft.volume=73&rft.issue=4&rft.spage=825&rft.epage=847&rft_id=info:doi/10.1007%2Fs10898-018-00730-5&rft.externalDBID=HAS_PDF_LINK
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0925-5001&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0925-5001&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0925-5001&client=summon