Approaching the solving of constrained variational inequalities via penalty term-based dynamical systems

We investigate the existence and uniqueness of (locally) absolutely continuous trajectories of a penalty term-based dynamical system associated to a constrained variational inequality expressed as a monotone inclusion problem. Relying on Lyapunov analysis and on the ergodic continuous version of the...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 435; no. 2; pp. 1688 - 1700
Main Authors: Boţ, Radu Ioan, Csetnek, Ernö Robert
Format: Journal Article
Language:English
Published: Elsevier Inc 15.03.2016
Subjects:
ISSN:0022-247X, 1096-0813
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract We investigate the existence and uniqueness of (locally) absolutely continuous trajectories of a penalty term-based dynamical system associated to a constrained variational inequality expressed as a monotone inclusion problem. Relying on Lyapunov analysis and on the ergodic continuous version of the celebrated Opial Lemma we prove weak ergodic convergence of the orbits to a solution of the constrained variational inequality under investigation. If one of the operators involved satisfies stronger monotonicity properties, then strong convergence of the trajectories can be shown.
AbstractList We investigate the existence and uniqueness of (locally) absolutely continuous trajectories of a penalty term-based dynamical system associated to a constrained variational inequality expressed as a monotone inclusion problem. Relying on Lyapunov analysis and on the ergodic continuous version of the celebrated Opial Lemma we prove weak ergodic convergence of the orbits to a solution of the constrained variational inequality under investigation. If one of the operators involved satisfies stronger monotonicity properties, then strong convergence of the trajectories can be shown.
Author Boţ, Radu Ioan
Csetnek, Ernö Robert
Author_xml – sequence: 1
  givenname: Radu Ioan
  orcidid: 0000-0002-4469-314X
  surname: Boţ
  fullname: Boţ, Radu Ioan
  email: radu.bot@univie.ac.at
– sequence: 2
  givenname: Ernö Robert
  surname: Csetnek
  fullname: Csetnek, Ernö Robert
  email: ernoe.robert.csetnek@univie.ac.at
BookMark eNp9kM1qwzAQhEVJoUnaF-jJL2BXa1mWA72E0D8I9JJDb2ItrxsZ_6SSGsjb12566iGnXYb5lp1ZsFk_9MTYPfAEOOQPTdJ0iEnKQSYACRfpFZsDX-UxL0DM2JzzNI3TTH3csIX3DecAUsGc7deHgxvQ7G3_GYU9RX5oj9M-1JEZeh8c2p6q6IjOYrBDj200Cl_f2NpgyUdHi9GBRjmcokCui0v0o7869dhZM7r9yQfq_C27rrH1dPc3l2z3_LTbvMbb95e3zXobG5FlIUZlSpRCCZArzFVmsDIyr_hKUa5IVWAoo1yOv8tCiRKqTBZyJURZmjotSCxZej5r3OC9o1ofnO3QnTRwPVWlGz1VpaeqNIAeqxqh4h9kbPhNO8VvL6OPZ5TGTEdLTntjqTdUWUcm6Gqwl_AfWoGJpw
CitedBy_id crossref_primary_10_1007_s11228_017_0411_1
crossref_primary_10_1016_j_jmaa_2016_07_007
crossref_primary_10_1080_02331934_2021_1981892
crossref_primary_10_1137_16M1105682
crossref_primary_10_1137_15M1012657
crossref_primary_10_1007_s12346_022_00698_4
crossref_primary_10_1007_s11590_017_1158_1
crossref_primary_10_1007_s10013_017_0256_9
crossref_primary_10_1007_s00028_018_0441_7
crossref_primary_10_1109_LCSYS_2024_3401019
crossref_primary_10_1007_s11228_017_0409_8
crossref_primary_10_1080_02331934_2016_1181759
crossref_primary_10_1007_s40314_025_03147_5
crossref_primary_10_1080_02331934_2018_1452922
crossref_primary_10_1007_s10013_021_00544_1
crossref_primary_10_1080_10556788_2018_1556660
crossref_primary_10_1080_00036811_2016_1157589
Cites_doi 10.1007/s10013-013-0050-2
10.1007/s10957-013-0414-5
10.1007/s10957-014-0700-x
10.1023/B:JOTA.0000005445.21095.02
10.1007/978-1-4419-9467-7
10.1137/100789464
10.1080/02331934.2014.971412
10.1007/s10957-011-9936-x
10.1007/s11228-008-0093-9
10.1137/110820300
10.1137/100784114
10.1016/j.jde.2009.06.014
10.1023/A:1020639314056
10.1007/s11228-014-0274-7
10.1007/s10957-013-0296-6
ContentType Journal Article
Copyright 2015 Elsevier Inc.
Copyright_xml – notice: 2015 Elsevier Inc.
DBID AAYXX
CITATION
DOI 10.1016/j.jmaa.2015.11.032
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 1096-0813
EndPage 1700
ExternalDocumentID 10_1016_j_jmaa_2015_11_032
S0022247X15010707
GrantInformation_xml – fundername: FWF
  grantid: M 1682-N25
  funderid: http://dx.doi.org/10.13039/501100002428
– fundername: DFG
  grantid: BO 2516/4-1
  funderid: http://dx.doi.org/10.13039/501100001659
GroupedDBID --K
--M
--Z
-~X
.~1
0R~
0SF
1B1
1RT
1~.
4.4
457
4G.
5GY
6I.
71M
85S
8P~
9JN
AABNK
AACTN
AAEDT
AAEDW
AAFTH
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AASFE
AAXUO
ABAOU
ABJNI
ABMAC
ABVKL
ABYKQ
ACAZW
ACDAQ
ACGFS
ACRLP
ADBBV
ADEZE
AEBSH
AEKER
AENEX
AEXQZ
AFKWA
AFTJW
AGUBO
AGYEJ
AHHHB
AIEXJ
AIGVJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
ARUGR
AXJTR
BKOJK
BLXMC
CS3
DM4
EBS
EFBJH
EFLBG
EJD
EO8
EO9
EP2
EP3
F5P
FDB
FEDTE
FIRID
FNPLU
FYGXN
G-Q
GBLVA
HVGLF
IHE
IXB
J1W
KOM
LG5
M25
M41
MCRUF
MHUIS
MO0
N9A
NCXOZ
O-L
O9-
OAUVE
OK1
OZT
P-8
P-9
P2P
PC.
Q38
RIG
RNS
ROL
RPZ
SDF
SDG
SDP
SES
SPC
SPCBC
SSW
SSZ
T5K
TN5
TWZ
UPT
WH7
XPP
YQT
ZMT
ZU3
~G-
1~5
29L
5VS
6TJ
7-5
9DU
AAQFI
AAQXK
AATTM
AAXKI
AAYWO
AAYXX
ABDPE
ABEFU
ABFNM
ABUFD
ABWVN
ABXDB
ACLOT
ACRPL
ACVFH
ADCNI
ADFGL
ADIYS
ADMUD
ADNMO
ADVLN
ADXHL
AEIPS
AETEA
AEUPX
AFFNX
AFJKZ
AFPUW
AGHFR
AGQPQ
AI.
AIGII
AIIUN
AKBMS
AKRWK
AKYEP
ANKPU
APXCP
ASPBG
AVWKF
AZFZN
CAG
CITATION
COF
EFKBS
FGOYB
G-2
HZ~
H~9
MVM
OHT
R2-
SEW
VH1
VOH
WUQ
XOL
YYP
ZCG
~HD
ID FETCH-LOGICAL-c344t-a7cba5373159a674cadc56d097e67e7d1ce4e655715873b1d4585933bbcf28e3
ISICitedReferencesCount 24
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000367119200042&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0022-247X
IngestDate Sat Nov 29 02:56:17 EST 2025
Tue Nov 18 22:30:39 EST 2025
Fri Feb 23 02:28:59 EST 2024
IsDoiOpenAccess false
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 2
Keywords Lyapunov analysis
Penalty schemes
Monotone inclusions
Dynamical systems
Forward–backward algorithm
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c344t-a7cba5373159a674cadc56d097e67e7d1ce4e655715873b1d4585933bbcf28e3
ORCID 0000-0002-4469-314X
OpenAccessLink https://doi.org/10.1016/j.jmaa.2015.11.032
PageCount 13
ParticipantIDs crossref_primary_10_1016_j_jmaa_2015_11_032
crossref_citationtrail_10_1016_j_jmaa_2015_11_032
elsevier_sciencedirect_doi_10_1016_j_jmaa_2015_11_032
PublicationCentury 2000
PublicationDate 2016-03-15
PublicationDateYYYYMMDD 2016-03-15
PublicationDate_xml – month: 03
  year: 2016
  text: 2016-03-15
  day: 15
PublicationDecade 2010
PublicationTitle Journal of mathematical analysis and applications
PublicationYear 2016
Publisher Elsevier Inc
Publisher_xml – name: Elsevier Inc
References Zălinescu (br0330) 2002
Abbas, Attouch, Svaiter (br0020) 2014; 161
Brézis (br0230) 1973; vol. 5
Sontag (br0320) 1998; vol. 6
Burachik, Svaiter (br0250) 2002; 10
Simons (br0310) 2008
Haraux (br0270) 1991; vol. 17
Attouch, Czarnecki, Peypouquet (br0050) 2011; 21
Peypouquet (br0290) 2012; 153
Borwein (br0140) 2006; 13
Banert, Boţ (br0100) 2015
Boţ, Csetnek (br0180) 2015
Bolte (br0130) 2003; 119
Noun, Peypouquet (br0280) 2013; 158
Attouch, Czarnecki, Peypouquet (br0060) 2011; 21
Bauschke, McLaren, Sendov (br0120) 2006; 13
Boţ, Csetnek (br0170) 2008; 16
Boţ, Csetnek (br0200) 2014; 42
Fitzpatrick (br0260) 1988; vol. 20
Antipin (br0030) 1994; 30
Borwein, Vanderwerff (br0150) 2010
Boţ (br0160) 2010; vol. 637
Boţ, Csetnek (br0210) 2015
Abbas, Attouch (br0010) 2015; 64
Attouch, Svaiter (br0070) 2011; 49
Boţ, Csetnek (br0220) 2015
Bauschke, Combettes (br0110) 2011
Banert, Boţ (br0090) 2015; 166
Boţ, Csetnek (br0190) 2014; 22
Attouch, Czarnecki (br0040) 2010; 248
Banert (10.1016/j.jmaa.2015.11.032_br0100)
Peypouquet (10.1016/j.jmaa.2015.11.032_br0290) 2012; 153
Fitzpatrick (10.1016/j.jmaa.2015.11.032_br0260) 1988; vol. 20
Sontag (10.1016/j.jmaa.2015.11.032_br0320) 1998; vol. 6
Brézis (10.1016/j.jmaa.2015.11.032_br0230) 1973; vol. 5
Boţ (10.1016/j.jmaa.2015.11.032_br0190) 2014; 22
Noun (10.1016/j.jmaa.2015.11.032_br0280) 2013; 158
Antipin (10.1016/j.jmaa.2015.11.032_br0030) 1994; 30
Attouch (10.1016/j.jmaa.2015.11.032_br0070) 2011; 49
Banert (10.1016/j.jmaa.2015.11.032_br0090) 2015; 166
Bauschke (10.1016/j.jmaa.2015.11.032_br0110) 2011
Zălinescu (10.1016/j.jmaa.2015.11.032_br0330) 2002
Attouch (10.1016/j.jmaa.2015.11.032_br0040) 2010; 248
Boţ (10.1016/j.jmaa.2015.11.032_br0160) 2010; vol. 637
Boţ (10.1016/j.jmaa.2015.11.032_br0170) 2008; 16
Abbas (10.1016/j.jmaa.2015.11.032_br0010) 2015; 64
Abbas (10.1016/j.jmaa.2015.11.032_br0020) 2014; 161
Attouch (10.1016/j.jmaa.2015.11.032_br0050) 2011; 21
Bauschke (10.1016/j.jmaa.2015.11.032_br0120) 2006; 13
Burachik (10.1016/j.jmaa.2015.11.032_br0250) 2002; 10
Boţ (10.1016/j.jmaa.2015.11.032_br0210)
Boţ (10.1016/j.jmaa.2015.11.032_br0220)
Borwein (10.1016/j.jmaa.2015.11.032_br0150) 2010
Borwein (10.1016/j.jmaa.2015.11.032_br0140) 2006; 13
Haraux (10.1016/j.jmaa.2015.11.032_br0270) 1991; vol. 17
Bolte (10.1016/j.jmaa.2015.11.032_br0130) 2003; 119
Boţ (10.1016/j.jmaa.2015.11.032_br0180) 2015
Boţ (10.1016/j.jmaa.2015.11.032_br0200) 2014; 42
Attouch (10.1016/j.jmaa.2015.11.032_br0060) 2011; 21
Simons (10.1016/j.jmaa.2015.11.032_br0310) 2008
References_xml – volume: vol. 20
  start-page: 59
  year: 1988
  end-page: 65
  ident: br0260
  article-title: Representing monotone operators by convex functions
  publication-title: Workshop/Miniconference on Functional Analysis and Optimization
– volume: 42
  start-page: 451
  year: 2014
  end-page: 465
  ident: br0200
  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.
– volume: 30
  start-page: 1475
  year: 1994
  end-page: 1486
  ident: br0030
  article-title: Minimization of convex functions on convex sets by means of differential equations
  publication-title: Differ. Uravn.
– volume: 166
  start-page: 930
  year: 2015
  end-page: 948
  ident: br0090
  article-title: Backward penalty schemes for monotone inclusion problems
  publication-title: J. Optim. Theory Appl.
– volume: vol. 637
  year: 2010
  ident: br0160
  article-title: Conjugate Duality in Convex Optimization
  publication-title: Lecture Notes in Economics and Mathematical Systems
– volume: 13
  start-page: 561
  year: 2006
  end-page: 586
  ident: br0140
  article-title: Maximal monotonicity via convex analysis
  publication-title: J. Convex Anal.
– year: 2010
  ident: br0150
  article-title: Convex Functions: Constructions, Characterizations and Counterexamples
– volume: 158
  start-page: 787
  year: 2013
  end-page: 795
  ident: br0280
  article-title: Forward–backward penalty scheme for constrained convex minimization without inf-compactness
  publication-title: J. Optim. Theory Appl.
– year: 2008
  ident: br0310
  article-title: From Hahn–Banach to Monotonicity
– volume: 64
  start-page: 2223
  year: 2015
  end-page: 2252
  ident: br0010
  article-title: Dynamical systems and forward–backward algorithms associated with the sum of a convex subdifferential and a monotone cocoercive operator
  publication-title: Optimization
– volume: 161
  start-page: 331
  year: 2014
  end-page: 360
  ident: br0020
  article-title: Newton-like dynamics and forward–backward methods for structured monotone inclusions in Hilbert spaces
  publication-title: J. Optim. Theory Appl.
– volume: vol. 6
  year: 1998
  ident: br0320
  article-title: Mathematical Control Theory. Deterministic Finite-Dimensional Systems
  publication-title: Texts in Applied Mathematics
– year: 2002
  ident: br0330
  article-title: Convex Analysis in General Vector Spaces
– volume: 21
  start-page: 149
  year: 2011
  end-page: 173
  ident: br0050
  article-title: Prox-penalization and splitting methods for constrained variational problems
  publication-title: SIAM J. Optim.
– volume: 248
  start-page: 1315
  year: 2010
  end-page: 1344
  ident: br0040
  article-title: Asymptotic behavior of coupled dynamical systems with multiscale aspects
  publication-title: J. Differential Equations
– volume: 22
  start-page: 313
  year: 2014
  end-page: 331
  ident: br0190
  article-title: Forward–backward and Tseng's type penalty schemes for monotone inclusion problems
  publication-title: Set-Valued Var. Anal.
– year: 2015
  ident: br0220
  article-title: Convergence rates for forward–backward dynamical systems associated with strongly monotone inclusions
– volume: 13
  start-page: 499
  year: 2006
  end-page: 523
  ident: br0120
  article-title: Fitzpatrick functions: inequalities, examples and remarks on a problem by S. Fitzpatrick
  publication-title: J. Convex Anal.
– volume: 21
  start-page: 1251
  year: 2011
  end-page: 1274
  ident: br0060
  article-title: Coupling forward–backward with penalty schemes and parallel splitting for constrained variational inequalities
  publication-title: SIAM J. Optim.
– year: 2011
  ident: br0110
  article-title: Convex Analysis and Monotone Operator Theory in Hilbert Spaces
  publication-title: CMS Books in Mathematics
– volume: 49
  start-page: 574
  year: 2011
  end-page: 598
  ident: br0070
  article-title: A continuous dynamical Newton-like approach to solving monotone inclusions
  publication-title: SIAM J. Control Optim.
– year: 2015
  ident: br0210
  article-title: Second order forward–backward dynamical systems for monotone inclusion problems
– volume: vol. 5
  year: 1973
  ident: br0230
  article-title: Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert
  publication-title: Notas de Matemática (50), North-Holland Mathematics Studies
– year: 2015
  ident: br0180
  article-title: A dynamical system associated with the fixed points set of a nonexpansive operator
  publication-title: J. Dynam. Differential Equations
– volume: 153
  start-page: 123
  year: 2012
  end-page: 138
  ident: br0290
  article-title: Coupling the gradient method with a general exterior penalization scheme for convex minimization
  publication-title: J. Optim. Theory Appl.
– volume: 10
  start-page: 297
  year: 2002
  end-page: 316
  ident: br0250
  article-title: Maximal monotone operators, convex functions and a special family of enlargements
  publication-title: Set-Valued Anal.
– year: 2015
  ident: br0100
  article-title: A forward–backward–forward differential equation and its asymptotic properties
– volume: 119
  start-page: 235
  year: 2003
  end-page: 259
  ident: br0130
  article-title: Continuous gradient projection method in Hilbert spaces
  publication-title: J. Optim. Theory Appl.
– volume: 16
  start-page: 983
  year: 2008
  end-page: 997
  ident: br0170
  article-title: An application of the bivariate inf-convolution formula to enlargements of monotone operators
  publication-title: Set-Valued Anal.
– volume: vol. 17
  year: 1991
  ident: br0270
  article-title: Systèmes Dynamiques Dissipatifs et Applications
  publication-title: Rech. Math. Appl.
– volume: 42
  start-page: 451
  issue: 4
  year: 2014
  ident: 10.1016/j.jmaa.2015.11.032_br0200
  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: vol. 637
  year: 2010
  ident: 10.1016/j.jmaa.2015.11.032_br0160
  article-title: Conjugate Duality in Convex Optimization
– ident: 10.1016/j.jmaa.2015.11.032_br0210
– volume: 161
  start-page: 331
  issue: 2
  year: 2014
  ident: 10.1016/j.jmaa.2015.11.032_br0020
  article-title: Newton-like dynamics and forward–backward methods for structured monotone inclusions in Hilbert spaces
  publication-title: J. Optim. Theory Appl.
  doi: 10.1007/s10957-013-0414-5
– year: 2010
  ident: 10.1016/j.jmaa.2015.11.032_br0150
– ident: 10.1016/j.jmaa.2015.11.032_br0220
– volume: vol. 20
  start-page: 59
  year: 1988
  ident: 10.1016/j.jmaa.2015.11.032_br0260
  article-title: Representing monotone operators by convex functions
– ident: 10.1016/j.jmaa.2015.11.032_br0100
– volume: 166
  start-page: 930
  issue: 3
  year: 2015
  ident: 10.1016/j.jmaa.2015.11.032_br0090
  article-title: Backward penalty schemes for monotone inclusion problems
  publication-title: J. Optim. Theory Appl.
  doi: 10.1007/s10957-014-0700-x
– volume: 119
  start-page: 235
  issue: 2
  year: 2003
  ident: 10.1016/j.jmaa.2015.11.032_br0130
  article-title: Continuous gradient projection method in Hilbert spaces
  publication-title: J. Optim. Theory Appl.
  doi: 10.1023/B:JOTA.0000005445.21095.02
– year: 2011
  ident: 10.1016/j.jmaa.2015.11.032_br0110
  article-title: Convex Analysis and Monotone Operator Theory in Hilbert Spaces
  doi: 10.1007/978-1-4419-9467-7
– volume: 13
  start-page: 561
  issue: 3–4
  year: 2006
  ident: 10.1016/j.jmaa.2015.11.032_br0140
  article-title: Maximal monotonicity via convex analysis
  publication-title: J. Convex Anal.
– volume: vol. 17
  year: 1991
  ident: 10.1016/j.jmaa.2015.11.032_br0270
  article-title: Systèmes Dynamiques Dissipatifs et Applications
– volume: 21
  start-page: 149
  issue: 1
  year: 2011
  ident: 10.1016/j.jmaa.2015.11.032_br0050
  article-title: Prox-penalization and splitting methods for constrained variational problems
  publication-title: SIAM J. Optim.
  doi: 10.1137/100789464
– year: 2015
  ident: 10.1016/j.jmaa.2015.11.032_br0180
  article-title: A dynamical system associated with the fixed points set of a nonexpansive operator
  publication-title: J. Dynam. Differential Equations
– volume: 64
  start-page: 2223
  issue: 10
  year: 2015
  ident: 10.1016/j.jmaa.2015.11.032_br0010
  article-title: Dynamical systems and forward–backward algorithms associated with the sum of a convex subdifferential and a monotone cocoercive operator
  publication-title: Optimization
  doi: 10.1080/02331934.2014.971412
– volume: 153
  start-page: 123
  issue: 1
  year: 2012
  ident: 10.1016/j.jmaa.2015.11.032_br0290
  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
– year: 2008
  ident: 10.1016/j.jmaa.2015.11.032_br0310
– volume: vol. 5
  year: 1973
  ident: 10.1016/j.jmaa.2015.11.032_br0230
  article-title: Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert
– volume: 16
  start-page: 983
  issue: 7–8
  year: 2008
  ident: 10.1016/j.jmaa.2015.11.032_br0170
  article-title: An application of the bivariate inf-convolution formula to enlargements of monotone operators
  publication-title: Set-Valued Anal.
  doi: 10.1007/s11228-008-0093-9
– volume: vol. 6
  year: 1998
  ident: 10.1016/j.jmaa.2015.11.032_br0320
  article-title: Mathematical Control Theory. Deterministic Finite-Dimensional Systems
– volume: 13
  start-page: 499
  issue: 3–4
  year: 2006
  ident: 10.1016/j.jmaa.2015.11.032_br0120
  article-title: Fitzpatrick functions: inequalities, examples and remarks on a problem by S. Fitzpatrick
  publication-title: J. Convex Anal.
– volume: 21
  start-page: 1251
  issue: 4
  year: 2011
  ident: 10.1016/j.jmaa.2015.11.032_br0060
  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: 49
  start-page: 574
  issue: 2
  year: 2011
  ident: 10.1016/j.jmaa.2015.11.032_br0070
  article-title: A continuous dynamical Newton-like approach to solving monotone inclusions
  publication-title: SIAM J. Control Optim.
  doi: 10.1137/100784114
– volume: 30
  start-page: 1475
  issue: 9
  year: 1994
  ident: 10.1016/j.jmaa.2015.11.032_br0030
  article-title: Minimization of convex functions on convex sets by means of differential equations
  publication-title: Differ. Uravn.
– volume: 248
  start-page: 1315
  issue: 6
  year: 2010
  ident: 10.1016/j.jmaa.2015.11.032_br0040
  article-title: Asymptotic behavior of coupled dynamical systems with multiscale aspects
  publication-title: J. Differential Equations
  doi: 10.1016/j.jde.2009.06.014
– volume: 10
  start-page: 297
  issue: 4
  year: 2002
  ident: 10.1016/j.jmaa.2015.11.032_br0250
  article-title: Maximal monotone operators, convex functions and a special family of enlargements
  publication-title: Set-Valued Anal.
  doi: 10.1023/A:1020639314056
– year: 2002
  ident: 10.1016/j.jmaa.2015.11.032_br0330
– volume: 22
  start-page: 313
  year: 2014
  ident: 10.1016/j.jmaa.2015.11.032_br0190
  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: 158
  start-page: 787
  issue: 3
  year: 2013
  ident: 10.1016/j.jmaa.2015.11.032_br0280
  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
SSID ssj0011571
Score 2.3096077
Snippet We investigate the existence and uniqueness of (locally) absolutely continuous trajectories of a penalty term-based dynamical system associated to a...
SourceID crossref
elsevier
SourceType Enrichment Source
Index Database
Publisher
StartPage 1688
SubjectTerms Dynamical systems
Forward–backward algorithm
Lyapunov analysis
Monotone inclusions
Penalty schemes
Title Approaching the solving of constrained variational inequalities via penalty term-based dynamical systems
URI https://dx.doi.org/10.1016/j.jmaa.2015.11.032
Volume 435
WOSCitedRecordID wos000367119200042&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: 1096-0813
  dateEnd: 20180131
  omitProxy: false
  ssIdentifier: ssj0011571
  issn: 0022-247X
  databaseCode: AIEXJ
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV09b9swECXcpEM7FP1E06YFh2YSFFgiKVKja6RoCjTo4MGbQJE0GiORjdgR8lvya3NnUjKTpkEzdBEMwqI-3tPxjrx7JOQLG-Yzm9cqdUYPU24yl9YQaKWoJWYcM4JptdlsQp6cqOm0_DUYXHe1MO2ZbBp1dVUu_yvU0AZgY-nsI-DuO4UG-A2gwxFgh-M_AT8KKuFdHRRcrQ2pzQadQdwTArzMFoLkbiIQGnxxJYTNSXuqk6WDZnDP0W6nONDZxPqt67G8JBI5_9OtPe91YDcqBEHyZCMJG62V97MAi4OxOBixDdLaXibHiy1dxyu3blww1w0u6X8tQip4PFmRFZit5cs1o-KBnMtpbIA5ExHT8sicZoXf8y8MzagleK_Z9zMQ88P5uUYtqUwcojJrmDi9pbF9Z-zrMxK7ZLd5hX1U2AcERxX08YTs5lKUYDF3R8dH0x_9GlUmZNZp0eMjhZIsnz14907ud3siV2bykrwIYNGR584rMnDNa_L8Zw_c6g35HbGIQjsNLKKLGY1YRCMW0ZhFFFhEA4volkW0ZxENLHpLJt-OJuPvadiUIzWM83Wqpam1YJKBH6wLyY22RhR2WEpXSCctfOHcFQLejVCS1ZnlAiX1WF2bWa4ce0d2mkXj3hM647l0xmlu1ZAXolYQrIP3qCyuDDJZ7pGse2WVCYL1-HRn1d_B2iNJf87Sy7U8-G_RIVEFh9M7khUQ64HzPjzqKh_Js-2nsE921heX7hN5atr16eric2DVDbJxpZ8
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=Approaching+the+solving+of+constrained+variational+inequalities+via+penalty+term-based+dynamical+systems&rft.jtitle=Journal+of+mathematical+analysis+and+applications&rft.au=Bo%C5%A3%2C+Radu+Ioan&rft.au=Csetnek%2C+Ern%C3%B6+Robert&rft.date=2016-03-15&rft.issn=0022-247X&rft.volume=435&rft.issue=2&rft.spage=1688&rft.epage=1700&rft_id=info:doi/10.1016%2Fj.jmaa.2015.11.032&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_jmaa_2015_11_032
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0022-247X&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0022-247X&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0022-247X&client=summon