An alternating direction method of multipliers for the eigenvalue complementarity problem

We introduce an Alternating Direction Method of Multipliers (ADMM) for finding a solution of the nonsymmetric Eigenvalue Complementarity Problem (EiCP). A simpler version of this method is proposed for the symmetric EiCP, that is, for the computation of a Stationary Point (SP) of a Standard Fraction...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Optimization Methods and Software Ročník 36; číslo 2-3; s. 337 - 370
Hlavní autori: Júdice, Joaquim J., Fukushima, Masao, Iusem, Alfredo, Martinez, J. M., Sessa, Valentina
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Abingdon Taylor & Francis 04.05.2021
Informa UK Limited
Taylor & Francis Ltd
Predmet:
[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]
[MATH.APPL]Mathematics [math]/Applied mathematics
[MATH.APPL]Mathematics [math]/domain_math.appl
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Algorithms
Applied mathematics
Complementarity problems
Computer Science
Data Structures and Algorithms
eigenvalue problems
Eigenvalues
global optimization
Mathematics
Multipliers
Newton methods
nonlinear programming
Optimization and Control
ISSN:1055-6788, 1029-4937
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Abstract We introduce an Alternating Direction Method of Multipliers (ADMM) for finding a solution of the nonsymmetric Eigenvalue Complementarity Problem (EiCP). A simpler version of this method is proposed for the symmetric EiCP, that is, for the computation of a Stationary Point (SP) of a Standard Fractional Quadratic Program. The algorithm is also extended for the computation of an SP of a Standard Quadratic Program (StQP). Convergence analyses of these three versions of ADMM are presented. The main computational effort of ADMM is the solution of a Strictly Convex StQP, which can be efficiently solved by a Block Principal Pivoting algorithm. Furthermore, this algorithm provides a stopping criterion for ADMM that improves very much its efficacy to compute an accurate solution of the EiCP. Numerical results indicate that ADMM is in general very efficient for solving symmetric EiCPs in terms of the number of iterations and computational effort, but is less efficient for the solution of nonsymmetric EiCPs. However, ADMM is able to provide a good initial point for a fast second-order method, such as the so-called Semismooth Newton method. The resulting hybrid ADMM and SN algorithm seems to be quite efficient in practice for the solution of nonsymmetric EiCPs.
AbstractList We introduce an Alternating Direction Method of Multipliers (ADMM) for finding a solution of the nonsymmetric Eigenvalue Complementarity Problem (EiCP). A simpler version of this method is proposed for the symmetric EiCP, that is, for the computation of a Stationary Point (SP) of a Standard Fractional Quadratic Program. The algorithm is also extended for the computation of an SP of a Standard Quadratic Program (StQP). Convergence analyses of these three versions of ADMM are presented. The main computational effort of ADMM is the solution of a Strictly Convex StQP, which can be efficiently solved by a Block Principal Pivoting algorithm. Furthermore, this algorithm provides a stopping criterion for ADMM that improves very much its efficacy to compute an accurate solution of the EiCP. Numerical results indicate that ADMM is in general very efficient for solving symmetric EiCPs in terms of the number of iterations and computational effort, but is less efficient for the solution of nonsymmetric EiCPs. However, ADMM is able to provide a good initial point for a fast second-order method, such as the so-called Semismooth Newton method. The resulting hybrid ADMM and SN algorithm seems to be quite efficient in practice for the solution of nonsymmetric EiCPs.
Author Fukushima, Masao
Martinez, J. M.
Sessa, Valentina
Júdice, Joaquim J.
Iusem, Alfredo
Author_xml – sequence: 1
  givenname: Joaquim J.
  surname: Júdice
  fullname: Júdice, Joaquim J.
  organization: Instituto Telecomunicações
– sequence: 2
  givenname: Masao
  surname: Fukushima
  fullname: Fukushima, Masao
  organization: Faculty of Science and Technology, Nanzan University
– sequence: 3
  givenname: Alfredo
  surname: Iusem
  fullname: Iusem, Alfredo
  organization: Instituto de Matemática Pura e Aplicada (IMPA)
– sequence: 4
  givenname: J. M.
  orcidid: 0000-0003-3331-368X
  surname: Martinez
  fullname: Martinez, J. M.
  organization: Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas
– sequence: 5
  givenname: Valentina
  orcidid: 0000-0002-0083-2515
  surname: Sessa
  fullname: Sessa, Valentina
  email: sessa.valentina@gmail.com
  organization: MINES ParisTech, PSL Research University, CMA Centre de Mathématiques Appliquées
BackLink https://cir.nii.ac.jp/crid/1870583642992682368$$DView record in CiNii
https://minesparis-psl.hal.science/hal-02503981$$DView record in HAL
BookMark eNqFUU1v1DAUtFCRaLf8BCRLcOGQYj9_xBEXVhVQpJV6oYeeLMdxuq4ce3G8RfvvcZT2wgEutt9o5s174wt0FlN0CL2j5IoSRT5RIoRslboCAhVqGVeEv0LnlEDX8I61Z8tbiGYhvUEX8_xICOGUy3N0v43YhOJyNMXHBzz47GzxKeLJlX0acBrxdAzFH4J3ecZjyrjsHXb-wcUnE44O2zQdgptcLCb7csKHnPpaX6LXowmze_t8b9Ddt68_r2-a3e33H9fbXWO5bEszSO4MEDmM0NvegVSGKgEtbYF11FIqne0q0I0SesKhA-o4SAF9ywmzwDbo49p3b4I-ZD-ZfNLJeH2z3ekFIyAI6xR9opX7fuXWGX8d3Vz0YzrW1cOsQQBUH1qbbtDnlWVzmufsRm19MUsoJRsfNCV6yV2_5K6X3PVz7lUt_lK_DPU_3YdVF72vhstJVUuEYrJu3dVggElVaV9Wmo_1LybzO-Uw6GJOIeUxm2j9rNm_nf4AbzOkeg
CitedBy_id crossref_primary_10_1007_s10898_024_01423_y
crossref_primary_10_1007_s10957_022_02019_w
crossref_primary_10_1007_s11075_025_02176_9
crossref_primary_10_1007_s10589_020_00226_7
crossref_primary_10_1016_j_jmaa_2023_127320
Cites_doi 10.1016/j.laa.2017.03.029
10.1007/s10898-014-0165-3
10.1007/s10107-017-1167-y
10.1016/j.amc.2016.09.005
10.1007/s10107-004-0559-y
10.1016/j.laa.2017.12.021
10.1090/S0025-5718-03-01614-4
10.1007/s10589-010-9388-5
10.1016/j.cam.2016.01.041
10.1007/s10898-014-0260-5
10.1016/j.laa.2009.03.031
10.1080/10556780903102592
10.1137/17M1111401
10.1016/j.cma.2003.09.013
10.1137/100801780
10.1016/S0024-3795(03)00553-6
10.1007/s10957-014-0645-0
10.1137/140998135
10.1007/s10589-009-9297-7
10.1080/10556788.2011.645543
10.1561/2200000016
10.1080/10556788.2018.1479408
10.1016/S0024-3795(99)00004-X
10.1007/s10898-007-9225-2
10.13001/1081-3810.1472
10.1007/s10957-017-1100-9
10.1007/s11075-008-9194-7
10.1016/0305-0548(94)90106-6
10.1007/s11075-018-0522-2
10.1007/s10589-008-9167-8
10.1016/j.jmaa.2015.02.064
ContentType Journal Article
Contributor Instituto de Matemática, Estatística e Computação Científica [Brésil] (IMECC) ; Universidade Estadual de Campinas (UNICAMP)
CMUC, Departamento de Matemática, Universidade de Coimbra, Coimbra - Portugal
CMUC, Departamento de Matemática, Universidade de Coimbra, Coimbra - Portugal ; Universidade de Coimbra [Coimbra]
Instituto Nacional de Matemática Pura e Aplicada (IMPA)
Instituto de Matemática, Estatística e Computação Científica Brésil (IMECC)
Faculty of Science and Technology, Nanzan University,Nagoya
Centre de Mathématiques Appliquées (CMA) ; MINES ParisTech - École nationale supérieure des mines de Paris ; Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Universidade de Coimbra Coimbra
Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Instituto de Matemática, Estatística e Computação Científica [Brésil] (IMECC) ; Universidade Estadual de Campinas = University of Campinas (UNICAMP)
Centre de Mathématiques Appliquées (CMA)
Contributor_xml – sequence: 1
  fullname: CMUC, Departamento de Matemática, Universidade de Coimbra, Coimbra - Portugal ; Universidade de Coimbra [Coimbra]
– sequence: 2
  fullname: Faculty of Science and Technology, Nanzan University,Nagoya
– sequence: 3
  fullname: Instituto Nacional de Matemática Pura e Aplicada (IMPA)
– sequence: 4
  fullname: Instituto de Matemática, Estatística e Computação Científica [Brésil] (IMECC) ; Universidade Estadual de Campinas = University of Campinas (UNICAMP)
– sequence: 5
  fullname: Centre de Mathématiques Appliquées (CMA) ; Mines Paris - PSL (École nationale supérieure des mines de Paris) ; Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)
– sequence: 6
  fullname: Instituto Nacional de Matemática Pura e Aplicada (IMPA) ; Instituto Nacional de matematica pura e aplicada
– sequence: 7
  fullname: Instituto de Matemática, Estatística e Computação Científica [Brésil] (IMECC) ; Universidade Estadual de Campinas (UNICAMP)
– sequence: 8
  fullname: Centre de Mathématiques Appliquées (CMA) ; MINES ParisTech - École nationale supérieure des mines de Paris ; Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
– sequence: 9
  fullname: Instituto de Matemática, Estatística e Computação Científica [Brésil] (IMECC) ; Universidade Estadual de Campinas = University of Campinas (UNICAMP)
– sequence: 10
  fullname: Centre de Mathématiques Appliquées (CMA) ; Mines Paris - PSL (École nationale supérieure des mines de Paris) ; Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
– sequence: 11
  fullname: CMUC, Departamento de Matemática, Universidade de Coimbra, Coimbra - Portugal
– sequence: 12
  fullname: Universidade de Coimbra Coimbra
– sequence: 13
  fullname: Instituto de Matemática, Estatística e Computação Científica Brésil (IMECC)
– sequence: 14
  fullname: Universidade Estadual de Campinas = University of Campinas (UNICAMP)
– sequence: 15
  fullname: Centre de Mathématiques Appliquées (CMA)
– sequence: 16
  fullname: Mines Paris - PSL (École nationale supérieure des mines de Paris)
– sequence: 17
  fullname: Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Copyright 2020 Informa UK Limited, trading as Taylor & Francis Group 2020
2020 Informa UK Limited, trading as Taylor & Francis Group
Distributed under a Creative Commons Attribution 4.0 International License
Copyright_xml – notice: 2020 Informa UK Limited, trading as Taylor & Francis Group 2020
– notice: 2020 Informa UK Limited, trading as Taylor & Francis Group
– notice: Distributed under a Creative Commons Attribution 4.0 International License
DBID RYH
AAYXX
CITATION
7SC
8FD
JQ2
L7M
L~C
L~D
1XC
DOI 10.1080/10556788.2020.1734804
DatabaseName CiNii Complete
CrossRef
Computer and Information Systems Abstracts
Technology Research Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
Hyper Article en Ligne (HAL)
DatabaseTitle CrossRef
Computer and Information Systems Abstracts
Technology Research Database
Computer and Information Systems Abstracts – Academic
Advanced Technologies Database with Aerospace
ProQuest Computer Science Collection
Computer and Information Systems Abstracts Professional
DatabaseTitleList
Computer and Information Systems Abstracts
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
Mathematics
Computer Science
EISSN 1029-4937
EndPage 370
ExternalDocumentID oai:HAL:hal-02503981v1
10_1080_10556788_2020_1734804
1734804
Genre Research Article
GroupedDBID .4S
.7F
.DC
.QJ
0BK
0R~
123
29N
30N
4.4
AAENE
AAGDL
AAHIA
AAJMT
AALDU
AAMIU
AAPUL
AAQRR
ABCCY
ABDBF
ABFIM
ABHAV
ABJNI
ABLIJ
ABPAQ
ABPEM
ABTAI
ABXUL
ABXYU
ACGEJ
ACGFS
ACIWK
ACTIO
ACUHS
ADCVX
ADGTB
ADXPE
AEISY
AENEX
AEOZL
AEPSL
AEYOC
AFKVX
AFRVT
AGDLA
AGMYJ
AHDZW
AIJEM
AIYEW
AJWEG
AKBVH
AKOOK
ALMA_UNASSIGNED_HOLDINGS
ALQZU
AMVHM
AQRUH
AQTUD
ARCSS
AVBZW
AWYRJ
BLEHA
CCCUG
CE4
CS3
DGEBU
DKSSO
DU5
EAP
EBS
EDO
EMK
EPL
EST
ESX
E~A
E~B
F5P
GTTXZ
H13
HF~
HZ~
H~P
I-F
IPNFZ
J.P
KYCEM
LJTGL
M4Z
NA5
NY~
O9-
P2P
PQQKQ
RIG
RNANH
ROSJB
RTWRZ
S-T
SNACF
TASJS
TBQAZ
TDBHL
TEJ
TFL
TFT
TFW
TTHFI
TUROJ
TUS
TWF
UT5
UU3
ZGOLN
~S~
RYH
AAYXX
CITATION
7SC
8FD
JQ2
L7M
L~C
L~D
1XC
ID FETCH-LOGICAL-c467t-d64ea206df2bcbe268a18527172391c116ec98529f62b042921e42652b7403c23
IEDL.DBID TFW
ISICitedReferencesCount 6
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000519334200001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 1055-6788
IngestDate Tue Oct 14 20:34:28 EDT 2025
Wed Aug 13 02:48:07 EDT 2025
Sat Nov 29 02:36:07 EST 2025
Tue Nov 18 22:12:03 EST 2025
Mon Nov 10 09:05:10 EST 2025
Mon Oct 20 23:47:56 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 2-3
Language English
License Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c467t-d64ea206df2bcbe268a18527172391c116ec98529f62b042921e42652b7403c23
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0002-0083-2515
0000-0003-3331-368X
0000-0003-3331-368x
PQID 2522985140
PQPubID 186278
PageCount 34
ParticipantIDs informaworld_taylorfrancis_310_1080_10556788_2020_1734804
hal_primary_oai_HAL_hal_02503981v1
proquest_journals_2522985140
crossref_citationtrail_10_1080_10556788_2020_1734804
crossref_primary_10_1080_10556788_2020_1734804
nii_cinii_1870583642992682368
PublicationCentury 2000
PublicationDate 2021-05-04
PublicationDateYYYYMMDD 2021-05-04
PublicationDate_xml – month: 05
  year: 2021
  text: 2021-05-04
  day: 04
PublicationDecade 2020
PublicationPlace Abingdon
PublicationPlace_xml – name: Abingdon
PublicationTitle Optimization Methods and Software
PublicationYear 2021
Publisher Taylor & Francis
Informa UK Limited
Taylor & Francis Ltd
Publisher_xml – name: Taylor & Francis
– name: Informa UK Limited
– name: Taylor & Francis Ltd
References Brás C. (CIT0006) 2012; 8
Iusem A.N. (CIT0018) 2017; 13
CIT0030
CIT0010
CIT0032
CIT0031
CIT0034
CIT0011
CIT0033
Murty K. (CIT0025) 1988
CIT0014
CIT0036
CIT0013
CIT0035
CIT0038
CIT0015
CIT0037
CIT0017
CIT0039
Facchinei F. (CIT0012) 2003
CIT0019
CIT0041
Chen Z.M. (CIT0009) 2015; 165
CIT0040
CIT0021
CIT0020
CIT0001
CIT0023
CIT0022
Nocedal J. (CIT0027) 2006
CIT0003
CIT0002
CIT0024
CIT0005
Golub G. (CIT0016) 1996
CIT0004
CIT0026
CIT0007
CIT0029
CIT0028
CIT0008
References_xml – ident: CIT0014
  doi: 10.1016/j.laa.2017.03.029
– ident: CIT0013
  doi: 10.1007/s10898-014-0165-3
– ident: CIT0015
  doi: 10.1007/s10107-017-1167-y
– ident: CIT0008
  doi: 10.1016/j.amc.2016.09.005
– ident: CIT0038
  doi: 10.1007/s10107-004-0559-y
– ident: CIT0034
  doi: 10.1016/j.laa.2017.12.021
– ident: CIT0011
– volume-title: Linear Complementarity, Linear and Nonlinear Programming
  year: 1988
  ident: CIT0025
– ident: CIT0031
  doi: 10.1090/S0025-5718-03-01614-4
– ident: CIT0023
  doi: 10.1007/s10589-010-9388-5
– ident: CIT0030
  doi: 10.1016/j.cam.2016.01.041
– ident: CIT0007
  doi: 10.1007/s10898-014-0260-5
– ident: CIT0041
  doi: 10.1016/j.laa.2009.03.031
– ident: CIT0021
  doi: 10.1080/10556780903102592
– ident: CIT0040
  doi: 10.1137/17M1111401
– volume-title: Finite-Dimensional Variational Inequalities and Complementarity Problems
  year: 2003
  ident: CIT0012
– volume: 8
  start-page: 197
  year: 2012
  ident: CIT0006
  publication-title: Pacific J. Opt.
– ident: CIT0028
  doi: 10.1016/j.cma.2003.09.013
– volume-title: Matrix Computations
  year: 1996
  ident: CIT0016
– ident: CIT0033
  doi: 10.1137/100801780
– ident: CIT0035
  doi: 10.1016/S0024-3795(03)00553-6
– ident: CIT0002
  doi: 10.1007/s10957-014-0645-0
– ident: CIT0010
– ident: CIT0024
  doi: 10.1137/140998135
– ident: CIT0003
  doi: 10.1007/s10589-009-9297-7
– ident: CIT0026
  doi: 10.1080/10556788.2011.645543
– ident: CIT0004
  doi: 10.1561/2200000016
– volume: 13
  start-page: 475
  year: 2017
  ident: CIT0018
  publication-title: Pacific J. Opt.
– volume: 165
  start-page: 583
  year: 2015
  ident: CIT0009
  publication-title: Comput. Opt. Appl.
– ident: CIT0019
  doi: 10.1080/10556788.2018.1479408
– ident: CIT0032
  doi: 10.1016/S0024-3795(99)00004-X
– ident: CIT0036
  doi: 10.1007/s10898-007-9225-2
– ident: CIT0037
  doi: 10.13001/1081-3810.1472
– ident: CIT0005
– ident: CIT0001
  doi: 10.1007/s10957-017-1100-9
– ident: CIT0022
  doi: 10.1007/s11075-008-9194-7
– ident: CIT0020
  doi: 10.1016/0305-0548(94)90106-6
– ident: CIT0039
  doi: 10.1007/s11075-018-0522-2
– ident: CIT0029
  doi: 10.1007/s10589-008-9167-8
– ident: CIT0017
  doi: 10.1016/j.jmaa.2015.02.064
– volume-title: Numerical Optimization
  year: 2006
  ident: CIT0027
SSID ssj0004146
ssib005901287
Score 2.288017
Snippet We introduce an Alternating Direction Method of Multipliers (ADMM) for finding a solution of the nonsymmetric Eigenvalue Complementarity Problem (EiCP). A...
SourceID hal
proquest
crossref
nii
informaworld
SourceType Open Access Repository
Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 337
SubjectTerms [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]
[MATH.APPL]Mathematics [math]/Applied mathematics
[MATH.APPL]Mathematics [math]/domain_math.appl
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Algorithms
Applied mathematics
Complementarity problems
Computer Science
Data Structures and Algorithms
eigenvalue problems
Eigenvalues
global optimization
Mathematics
Multipliers
Newton methods
nonlinear programming
Optimization and Control
Title An alternating direction method of multipliers for the eigenvalue complementarity problem
URI https://www.tandfonline.com/doi/abs/10.1080/10556788.2020.1734804
https://cir.nii.ac.jp/crid/1870583642992682368
https://www.proquest.com/docview/2522985140
https://minesparis-psl.hal.science/hal-02503981
Volume 36
WOSCitedRecordID wos000519334200001&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: PRVAWR
  databaseName: Taylor & Francis Online Journals
  customDbUrl:
  eissn: 1029-4937
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0004146
  issn: 1055-6788
  databaseCode: TFW
  dateStart: 19920101
  isFulltext: true
  titleUrlDefault: https://www.tandfonline.com
  providerName: Taylor & Francis
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3NS8MwFA86POjBb3G6SRCv1SZts_Y4xOFhDA8T5ykkWaoD6WSd-_t9L03nRGQHvfQQmoa8JO8j_b3fI-QqVkKose4EWmNKTkeZQKWJCmyiDIstMoA7ntl-ZzBIR6PswaMJSw-rxBg6r4ginK7Gw610WSPiblxNRwjdILrj0IT8LI4RFDx7BPUNe09fmZE-vwh6BNilzuH57SvfrNPmq8NGrjKYQmMxmfzQ284Y9fb-YRr7ZNd7orRbbZ0DsmGLQ7Kzwk94RJ67BXW_0_HKsHihlf2DlaRV4Wk6zalHJGJFbQozoOBQUosUn0gjbqmDrFcIdSyTR30Bm2Py2Lsb3t4HvhZDYECVzoOxiK3ioRjnXBttuUgVpl1DMMijjBnGhDUZNGS54BqNHGcWjH_CdScOI8OjE9IopoU9JTQ0Js6NjpSyOgaFkqrcYtgCkVMyDpOwSeJ6DaTxROVYL-NNMs9nWktOouSkl1yTXC-7vVdMHes6XMICL99Fnu37bl9iGzqGUZayBWuSbHX95dzdo-RV0RMZrRmgDZsF5oBPBooxSSOB9h-kxyORNkmr3kbSa45ScnCIQZAQ9579Yehzss0RfIPIzLhFGvPZh22TLbOYT8rZhTsjn9EDB6E
linkProvider Taylor & Francis
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3PT9swFH5igDR2gG0MrYNu1sQ1I3YSJzlWE1URWU9FlJNlu85WaQqIlv79e89xWBFCHOCSgxXH8rP9fjjvfR_Acaql1DOTR8ZQSU6ubaSLTEcu05anjhDAPc5slY_HxXRartfCUFolxdB1CxThdTUdbrqM7lLiTjypI8ZuGN4JbCKAFoIE3SJ2OgrAJsPL_7WRocIIu0TUp6vieeozD-zTmz8-O3IdwxQbm_n8keb25mi49xoTeQ-7wRllg3b3fIAN13yEd2sQhftwNWiY_6NOt4bNb9aaQFxM1nJPs-uahaREItVmOAWGPiVzhPJJSOKO-az1NkmdmPJY4LD5BBfD08nPURToGCKL2nQZzWTqtIjlrBbGGidkoanyGuNBkZTcci6dLbGhrKUwZOcEd2j_M2HyNE6sSA5gs7lu3GdgsbVpbU2itTMp6pRC144iFwyeslmcxT1Iu0VQNmCVE2XGX8UDpGknOUWSU0FyPfhx3-2mBet4rsN3XOH7dwlqezSoFLWRb5iUBV_xHpTrG0At_VVK3fKeqOSZAfq4W3AO9OSoG7MikeQCoPREIoseHHX7SAXlsVACfWIUJIa-X14w9Dd4O5r8qlR1Nj4_hB1BuTiUqJkeweby9s71YduulvPF7Vd_YP4BfU4LxA
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3NT9swFH9iBU3sAPtgooNu1rRrtthJ3ORYjVWgVVUPRbCTZTsOVJrSqi39-3nPcVjRNHFglxysOJaf7ffh_N7vAXxJtZS6NP3IGErJ6Wsb6TzTkcu05akjBnDPMzvqj8f59XUxCWjCVYBVUgxdNUQRXlfT4V6UVYuI--ZrOmLohtGdwCbiZyFG0F10nTPa2NPh1Z_UyJBghF0i6tMm8fzrM4_M04tbD47cpjDFxno2-0txe2s0PPwP83gNB8EVZYNm77yBHVe_hVdbBIXv4NegZv5_Ot0Z1jesMYC4lKypPM3mFQuQRCqpzXAGDD1K5ojjk3jEHfOY9QaiTnXyWKhgcwSXwx_T7-dRKMYQWdSl66iUqdMilmUljDVOyFxT3jVGgyIpuOVcOltgQ1FJYcjKCe7Q-mfC9NM4sSJ5D516XrtjYLG1aWVNorUzKWqUXFeO4hYMnbIyzuIupO0aKBuYyqlgxm_FA6FpKzlFklNBcl34-tBt0VB1PNXhMy7ww7tEtH0-GClqI88wKXK-4V0ottdfrf1FStVUPVHJEwP0cLPgHOjJUTNmeSLJAUDpiUTmXThtt5EKqmOlBHrEKEgMfD88Y-hP8HJyNlSji_HPE9gXBMQhlGZ6Cp318s71YM9u1rPV8qM_Lvc5Mgp2
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=An+alternating+direction+method+of+multipliers+for+the+eigenvalue+complementarity+problem&rft.jtitle=Optimization+methods+%26+software&rft.au=Judice%2C+Joaquim&rft.au=Fukushima%2C+Masao&rft.au=Iusem%2C+Alfredo&rft.au=Martinez%2C+J.+M.&rft.date=2021-05-04&rft.pub=Taylor+%26+Francis&rft.issn=1055-6788&rft.eissn=1029-4937&rft.spage=1&rft.epage=34&rft_id=info:doi/10.1080%2F10556788.2020.1734804&rft.externalDBID=HAS_PDF_LINK&rft.externalDocID=oai%3AHAL%3Ahal-02503981v1
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1055-6788&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1055-6788&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1055-6788&client=summon