Second-Order Optimality Conditions for Infinite-Dimensional Quadratic Programs

Second-order necessary and sufficient optimality conditions for local solutions and locally unique solutions of generalized quadratic programming problems in Banach spaces are established in this paper. Since the decomposition procedures using orthogonality relations in Euclidean spaces and the comp...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of optimization theory and applications Jg. 192; H. 2; S. 426 - 442
1. Verfasser: An, Duong Thi Viet
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.02.2022
Springer Nature B.V
Schlagworte:
Applications of Mathematics
Banach spaces
Calculus of Variations and Optimal Control; Optimization
Engineering
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Orthogonality
Quadratic programming
Theory of Computation
90C20
generalized quadratic programming problem
generalized polyhedral convex set
second-order optimality condition
90C30
90C46
locally unique solution
90C48
Banach space
49K27
ISSN:0022-3239, 1573-2878
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Abstract Second-order necessary and sufficient optimality conditions for local solutions and locally unique solutions of generalized quadratic programming problems in Banach spaces are established in this paper. Since the decomposition procedures using orthogonality relations in Euclidean spaces and the compactness of finite-dimensional unit spheres, which worked well for finite-dimensional quadratic programs, cannot be applied to the Banach space setting, a series of new constructions and arguments are proposed. These results give a comprehensive extension of the corresponding theorems on finite-dimensional quadratic programs.
AbstractList Second-order necessary and sufficient optimality conditions for local solutions and locally unique solutions of generalized quadratic programming problems in Banach spaces are established in this paper. Since the decomposition procedures using orthogonality relations in Euclidean spaces and the compactness of finite-dimensional unit spheres, which worked well for finite-dimensional quadratic programs, cannot be applied to the Banach space setting, a series of new constructions and arguments are proposed. These results give a comprehensive extension of the corresponding theorems on finite-dimensional quadratic programs.
Author An, Duong Thi Viet
Author_xml – sequence: 1
  givenname: Duong Thi Viet
  orcidid: 0000-0003-1822-4929
  surname: An
  fullname: An, Duong Thi Viet
  email: andtv@tnus.edu.vn
  organization: Department of Mathematics and Informatics, Thai Nguyen University of Sciences, Institute of Mathematics, Vietnam Academy of Science and Technology
BookMark eNp9kM1KAzEQgINUsK2-gKcFz9FJ0k02R6l_hUIV9Ryyu9mSss3WJD20T-Oz-GSmriB46GlgZr75-UZo4DpnELokcE0AxE0gIHOBgRIMRHKB9ydoSHLBMC1EMUBDAEoxo0yeoVEIKwCQhZgM0eLVVJ2r8cLXxmeLTbRr3dq4y6Ypa6PtXMiazn99zlxjnY0G39m1cSEVdJu9bHXtdbRV9uy7pdfrcI5OG90Gc_Ebx-j94f5t-oTni8fZ9HaOK0ZkxJUpiazqCW-AalrmJWOiIcxwDUXNa0JLJrnhrAbKBCcTmgMHzbSsQZqy0WyMrvq5G999bE2IatVtfbopKMqpAOAFsNRF-67KdyF406iNTw_6nSKgDuJUL04lcepHnNonqPgHVTbqg4rotW2Po6xHQ9rjlsb_XXWE-gY19YaD
CitedBy_id crossref_primary_10_1137_22M1512454
crossref_primary_10_1007_s11117_024_01091_y
Cites_doi 10.1007/s10898-021-01011-4
10.1007/s40306-017-0237-9
10.1007/BF00934107
10.1080/02331934.2019.1614179
10.1007/BF01585095
10.1007/BF01581641
10.1007/s10898-010-9573-1
10.1137/0115056
10.1007/s10957-018-1296-3
10.1515/9781400841059
10.1007/978-1-4612-1394-9
10.11650/tjm.20.2016.6936
10.1007/BF01584097
10.1137/110852528
10.1080/01630563.2017.1387863
10.1007/BF01396705
10.1137/S0363012996311095
10.1007/BF01582222
ContentType Journal Article
Copyright The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021
The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021.
Copyright_xml – notice: The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021
– notice: The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021.
DBID AAYXX
CITATION
3V.
7SC
7TB
7WY
7WZ
7XB
87Z
88I
8AO
8FD
8FE
8FG
8FK
8FL
8G5
ABJCF
ABUWG
AFKRA
ARAPS
AZQEC
BENPR
BEZIV
BGLVJ
CCPQU
DWQXO
FR3
FRNLG
F~G
GNUQQ
GUQSH
HCIFZ
JQ2
K60
K6~
K7-
KR7
L.-
L6V
L7M
L~C
L~D
M0C
M2O
M2P
M7S
MBDVC
P5Z
P62
PHGZM
PHGZT
PKEHL
PQBIZ
PQBZA
PQEST
PQGLB
PQQKQ
PQUKI
PTHSS
Q9U
DOI 10.1007/s10957-021-01967-z
DatabaseName CrossRef
ProQuest Central (Corporate)
Computer and Information Systems Abstracts
Mechanical & Transportation Engineering Abstracts
ProQuest ABI/INFORM Collection
ABI/INFORM Global (PDF only)
ProQuest Central (purchase pre-March 2016)
ABI/INFORM Collection
Science 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
ProQuest Materials Science & Engineering
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
Advanced Technologies & Computer Science Collection
ProQuest Central Essentials
ProQuest Central
Business Premium Collection (Proquest)
Technology Collection
ProQuest One Community College
ProQuest Central
Engineering Research Database
Business Premium Collection (Alumni)
ABI/INFORM Global (Corporate)
ProQuest Central Student
Research Library Prep
SciTech Premium Collection
ProQuest Computer Science Collection
ProQuest Business Collection (Alumni Edition)
ProQuest Business Collection
Computer Science Database
Civil Engineering Abstracts
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
Proquest Research Library
Science Database
Engineering Database
Research Library (Corporate)
Advanced Technologies & Aerospace Database
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Premium
ProQuest One Academic (New)
ProQuest One Academic Middle East (New)
ProQuest One Business (OCUL)
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
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
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
Engineering Research Database
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)
Mechanical & Transportation Engineering Abstracts
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)
Civil Engineering Abstracts
ABI/INFORM Global (Alumni Edition)
ProQuest Central Basic
ProQuest Science Journals
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
EISSN 1573-2878
EndPage 442
ExternalDocumentID 10_1007_s10957_021_01967_z
GrantInformation_xml – fundername: Simons Foundation Grant Targeted for Institute of Mathematics, Vietnam Academy of Science and Technology
GroupedDBID -52
-5D
-5G
-BR
-EM
-Y2
-~C
-~X
.4S
.86
.DC
.VR
06D
0R~
0VY
199
1N0
1SB
2.D
203
28-
29L
2J2
2JN
2JY
2KG
2KM
2LR
2P1
2VQ
2~H
30V
3V.
4.4
406
408
409
40D
40E
5GY
5QI
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
AARHV
AARTL
AASML
AATNV
AATVU
AAUYE
AAWCG
AAYIU
AAYQN
AAYTO
AAYZH
ABAKF
ABBBX
ABBXA
ABDPE
ABDZT
ABECU
ABFTV
ABHLI
ABHQN
ABJCF
ABJNI
ABJOX
ABKCH
ABKTR
ABMNI
ABMQK
ABNWP
ABQBU
ABQSL
ABSXP
ABTAH
ABTEG
ABTHY
ABTKH
ABTMW
ABULA
ABUWG
ABWNU
ABXPI
ACAOD
ACBXY
ACDTI
ACGFS
ACGOD
ACHSB
ACHXU
ACIWK
ACKNC
ACMDZ
ACMLO
ACOKC
ACOMO
ACPIV
ACZOJ
ADHHG
ADHIR
ADINQ
ADKNI
ADKPE
ADRFC
ADTPH
ADURQ
ADYFF
ADZKW
AEBTG
AEFIE
AEFQL
AEGAL
AEGNC
AEJHL
AEJRE
AEKMD
AEMSY
AENEX
AEOHA
AEPYU
AESKC
AETLH
AEVLU
AEXYK
AFBBN
AFEXP
AFGCZ
AFKRA
AFLOW
AFQWF
AFWTZ
AFZKB
AGAYW
AGDGC
AGGDS
AGJBK
AGMZJ
AGQEE
AGQMX
AGRTI
AGWIL
AGWZB
AGYKE
AHAVH
AHBYD
AHKAY
AHSBF
AHYZX
AI.
AIAKS
AIGIU
AIIXL
AILAN
AITGF
AJBLW
AJRNO
AJZVZ
ALMA_UNASSIGNED_HOLDINGS
ALWAN
AMKLP
AMXSW
AMYLF
AMYQR
AOCGG
ARAPS
ARCSS
ARMRJ
ASPBG
AVWKF
AXYYD
AYJHY
AZFZN
AZQEC
B-.
BA0
BAPOH
BBWZM
BDATZ
BENPR
BEZIV
BGLVJ
BGNMA
BPHCQ
BSONS
CAG
CCPQU
COF
CS3
CSCUP
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
GROUPED_ABI_INFORM_RESEARCH
GUQSH
GXS
H13
HCIFZ
HF~
HG5
HG6
HMJXF
HQYDN
HRMNR
HVGLF
H~9
I-F
I09
IHE
IJ-
IKXTQ
ITM
IWAJR
IXC
IZIGR
IZQ
I~X
I~Z
J-C
J0Z
JBSCW
JCJTX
JZLTJ
K60
K6V
K6~
K7-
KDC
KOV
KOW
L6V
LAK
LLZTM
M0C
M2O
M2P
M4Y
M7S
MA-
N2Q
N9A
NB0
NDZJH
NPVJJ
NQJWS
NU0
O93
O9G
O9I
O9J
OAM
OVD
P19
P2P
P62
P9R
PF0
PKN
PQBIZ
PQBZA
PQQKQ
PROAC
PT4
PT5
PTHSS
Q2X
QOK
QOS
R4E
R89
R9I
RHV
RNI
RNS
ROL
RPX
RSV
RZC
RZE
RZK
S16
S1Z
S26
S27
S28
S3B
SAP
SCLPG
SDD
SDH
SDM
SHX
SISQX
SJYHP
SMT
SNE
SNPRN
SNX
SOHCF
SOJ
SPISZ
SRMVM
SSLCW
STPWE
SZN
T13
T16
TEORI
TN5
TSG
TSK
TSV
TUC
TUS
TWZ
U2A
UG4
UOJIU
UTJUX
UZXMN
VC2
VFIZW
VH1
VOH
W23
W48
WH7
WK8
YLTOR
YQT
Z45
Z7R
Z7S
Z7U
Z7X
Z7Y
Z7Z
Z81
Z83
Z86
Z88
Z8M
Z8N
Z8R
Z8S
Z8T
Z8U
Z8W
Z92
ZCG
ZMTXR
ZWQNP
ZY4
~EX
AAPKM
AAYXX
ABBRH
ABDBE
ABFSG
ABRTQ
ACSTC
ADHKG
ADXHL
AEZWR
AFDZB
AFFHD
AFHIU
AFOHR
AGQPQ
AHPBZ
AHWEU
AIXLP
AMVHM
ATHPR
AYFIA
CITATION
PHGZM
PHGZT
PQGLB
7SC
7TB
7XB
8FD
8FK
FR3
JQ2
KR7
L.-
L7M
L~C
L~D
MBDVC
PKEHL
PQEST
PQUKI
Q9U
ID FETCH-LOGICAL-c319t-ceb19cd46f02a2b5b337f13e6a08d6d12b396e63d023761425060a3a9d09ebfa3
IEDL.DBID M2P
ISICitedReferencesCount 3
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000722805200002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0022-3239
IngestDate Wed Nov 05 04:14:36 EST 2025
Sat Nov 29 06:02:31 EST 2025
Tue Nov 18 22:23:58 EST 2025
Fri Feb 21 02:47:36 EST 2025
IsPeerReviewed true
IsScholarly true
Issue 2
Keywords 90C20
generalized quadratic programming problem
generalized polyhedral convex set
second-order optimality condition
90C30
90C46
locally unique solution
90C48
Banach space
49K27
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c319t-ceb19cd46f02a2b5b337f13e6a08d6d12b396e63d023761425060a3a9d09ebfa3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0003-1822-4929
PQID 2627006803
PQPubID 48247
PageCount 17
ParticipantIDs proquest_journals_2627006803
crossref_primary_10_1007_s10957_021_01967_z
crossref_citationtrail_10_1007_s10957_021_01967_z
springer_journals_10_1007_s10957_021_01967_z
PublicationCentury 2000
PublicationDate 20220200
2022-02-00
20220201
PublicationDateYYYYMMDD 2022-02-01
PublicationDate_xml – month: 2
  year: 2022
  text: 20220200
PublicationDecade 2020
PublicationPlace New York
PublicationPlace_xml – name: New York
PublicationTitle Journal of optimization theory and applications
PublicationTitleAbbrev J Optim Theory Appl
PublicationYear 2022
Publisher Springer US
Springer Nature B.V
Publisher_xml – name: Springer US
– name: Springer Nature B.V
References Lee, Tam, Yen (CR12) 2005
Majthay (CR16) 1971; 1
Bonnans, Shapiro (CR4) 2000
CR19
Mangasarian (CR17) 1980; 19
Chieu, Lee, Yen (CR5) 2017; 1
McCormick (CR18) 1967; 15
Luan, Yen (CR14) 2020; 69
CR13
Ruszczynski (CR24) 2006
Luenberger (CR15) 1969
An, Yen (CR1) 2021; 8
Yen, Yang (CR25) 2018; 178
Rudin (CR23) 1991
Dong, Tam (CR8) 2016; 20
CR6
Le Thi, Tao, Yen (CR11) 2011; 49
CR7
Dong, Tam (CR9) 2018; 43
CR22
CR21
Ioffe, Tihomirov (CR10) 1979
Ben-Tal (CR2) 1980; 31
Mordukhovich, Rockafellar (CR20) 2012; 22
Ben-Tal, Zowe (CR3) 1982; 24
GM Lee (1967_CR12) 2005
1967_CR22
VV Dong (1967_CR9) 2018; 43
1967_CR21
JF Bonnans (1967_CR4) 2000
David G Luenberger (1967_CR15) 1969
A Ruszczynski (1967_CR24) 2006
AD Ioffe (1967_CR10) 1979
OL Mangasarian (1967_CR17) 1980; 19
BS Mordukhovich (1967_CR20) 2012; 22
A Ben-Tal (1967_CR2) 1980; 31
W Rudin (1967_CR23) 1991
Garth P McCormick (1967_CR18) 1967; 15
1967_CR6
1967_CR13
1967_CR7
A Ben-Tal (1967_CR3) 1982; 24
1967_CR19
NN Luan (1967_CR14) 2020; 69
NH Chieu (1967_CR5) 2017; 1
VV Dong (1967_CR8) 2016; 20
DTV An (1967_CR1) 2021; 8
ND Yen (1967_CR25) 2018; 178
HA Le Thi (1967_CR11) 2011; 49
A Majthay (1967_CR16) 1971; 1
References_xml – ident: CR22
– volume: 8
  start-page: 351
  issue: 1
  year: 2021
  end-page: 365
  ident: CR1
  article-title: Optimality conditions based on the Fréchet second-order subdifferential
  publication-title: J. Global Optim.
  doi: 10.1007/s10898-021-01011-4
– volume: 43
  start-page: 155
  year: 2018
  end-page: 174
  ident: CR9
  article-title: On the solution existence of nonconvex quadratic programming problems in Hilbert spaces
  publication-title: Acta Math. Vietnam.
  doi: 10.1007/s40306-017-0237-9
– ident: CR6
– volume: 31
  start-page: 143
  year: 1980
  end-page: 165
  ident: CR2
  article-title: Second-order and related extremality conditions in nonlinear programming
  publication-title: J. Optim. Theory Appl.
  doi: 10.1007/BF00934107
– volume: 69
  start-page: 471
  year: 2020
  end-page: 492
  ident: CR14
  article-title: A representation of generalized convex polyhedra and applications
  publication-title: Optimization
  doi: 10.1080/02331934.2019.1614179
– volume: 24
  start-page: 70
  year: 1982
  end-page: 91
  ident: CR3
  article-title: Necessary and sufficient optimality conditions for a class of nonsmooth minimization problems
  publication-title: Math. Program.
  doi: 10.1007/BF01585095
– year: 2005
  ident: CR12
  publication-title: Quadratic Programming and Affine Variational Inequalities. A Qualitative Study
– volume: 19
  start-page: 200
  year: 1980
  end-page: 212
  ident: CR17
  article-title: Locally unique solutions of quadratic programs, linear and nonlinear complementarity problems
  publication-title: Math. Program.
  doi: 10.1007/BF01581641
– volume: 49
  start-page: 481
  year: 2011
  end-page: 495
  ident: CR11
  article-title: Properties of two DC algorithms in quadratic programming
  publication-title: J. Global Optim.
  doi: 10.1007/s10898-010-9573-1
– volume: 15
  start-page: 641
  year: 1967
  end-page: 652
  ident: CR18
  article-title: Second order conditions for constrained minima
  publication-title: SIAM J. Appl. Math.
  doi: 10.1137/0115056
– ident: CR21
– volume: 178
  start-page: 36
  year: 2018
  end-page: 55
  ident: CR25
  article-title: Affine variational inequalities on normed spaces
  publication-title: J. Optim. Theory Appl.
  doi: 10.1007/s10957-018-1296-3
– ident: CR19
– year: 2006
  ident: CR24
  publication-title: Nonlinear Optimization
  doi: 10.1515/9781400841059
– year: 2000
  ident: CR4
  publication-title: Perturbation Analysis of Optimization Problems
  doi: 10.1007/978-1-4612-1394-9
– volume: 20
  start-page: 1417
  year: 2016
  end-page: 1436
  ident: CR8
  article-title: On the solution existence of convex quadratic programming problems in Hilbert spaces
  publication-title: Taiwanese J. Math.
  doi: 10.11650/tjm.20.2016.6936
– year: 1979
  ident: CR10
  publication-title: Theory of Extremal Problems
– volume: 1
  start-page: 461
  year: 2017
  end-page: 476
  ident: CR5
  article-title: Second-order subdifferentials and optimality conditions for -smooth optimization problems
  publication-title: Appl. Anal. Optim.
– ident: CR13
– year: 1969
  ident: CR15
  publication-title: Optimization by Vector Space Methods
– volume: 1
  start-page: 359
  year: 1971
  end-page: 365
  ident: CR16
  article-title: Optimality conditions for quadratic programming
  publication-title: Math. Program.
  doi: 10.1007/BF01584097
– year: 1991
  ident: CR23
  publication-title: Functional Analysis
– ident: CR7
– volume: 22
  start-page: 953
  year: 2012
  end-page: 986
  ident: CR20
  article-title: Second-order subdifferential calculus with applications to tilt stability in optimization
  publication-title: SIAM J. Optim.
  doi: 10.1137/110852528
– volume: 1
  start-page: 461
  year: 2017
  ident: 1967_CR5
  publication-title: Appl. Anal. Optim.
– volume-title: Theory of Extremal Problems
  year: 1979
  ident: 1967_CR10
– ident: 1967_CR19
– ident: 1967_CR7
– volume: 49
  start-page: 481
  year: 2011
  ident: 1967_CR11
  publication-title: J. Global Optim.
  doi: 10.1007/s10898-010-9573-1
– volume: 1
  start-page: 359
  year: 1971
  ident: 1967_CR16
  publication-title: Math. Program.
  doi: 10.1007/BF01584097
– volume: 69
  start-page: 471
  year: 2020
  ident: 1967_CR14
  publication-title: Optimization
  doi: 10.1080/02331934.2019.1614179
– volume-title: Quadratic Programming and Affine Variational Inequalities. A Qualitative Study
  year: 2005
  ident: 1967_CR12
– volume: 178
  start-page: 36
  year: 2018
  ident: 1967_CR25
  publication-title: J. Optim. Theory Appl.
  doi: 10.1007/s10957-018-1296-3
– volume-title: Perturbation Analysis of Optimization Problems
  year: 2000
  ident: 1967_CR4
  doi: 10.1007/978-1-4612-1394-9
– volume: 24
  start-page: 70
  year: 1982
  ident: 1967_CR3
  publication-title: Math. Program.
  doi: 10.1007/BF01585095
– volume: 43
  start-page: 155
  year: 2018
  ident: 1967_CR9
  publication-title: Acta Math. Vietnam.
  doi: 10.1007/s40306-017-0237-9
– ident: 1967_CR13
  doi: 10.1080/01630563.2017.1387863
– volume-title: Optimization by Vector Space Methods
  year: 1969
  ident: 1967_CR15
– volume: 8
  start-page: 351
  issue: 1
  year: 2021
  ident: 1967_CR1
  publication-title: J. Global Optim.
  doi: 10.1007/s10898-021-01011-4
– volume: 19
  start-page: 200
  year: 1980
  ident: 1967_CR17
  publication-title: Math. Program.
  doi: 10.1007/BF01581641
– volume: 22
  start-page: 953
  year: 2012
  ident: 1967_CR20
  publication-title: SIAM J. Optim.
  doi: 10.1137/110852528
– volume: 31
  start-page: 143
  year: 1980
  ident: 1967_CR2
  publication-title: J. Optim. Theory Appl.
  doi: 10.1007/BF00934107
– ident: 1967_CR6
  doi: 10.1007/BF01396705
– volume: 20
  start-page: 1417
  year: 2016
  ident: 1967_CR8
  publication-title: Taiwanese J. Math.
  doi: 10.11650/tjm.20.2016.6936
– volume-title: Nonlinear Optimization
  year: 2006
  ident: 1967_CR24
  doi: 10.1515/9781400841059
– volume-title: Functional Analysis
  year: 1991
  ident: 1967_CR23
– volume: 15
  start-page: 641
  year: 1967
  ident: 1967_CR18
  publication-title: SIAM J. Appl. Math.
  doi: 10.1137/0115056
– ident: 1967_CR22
  doi: 10.1137/S0363012996311095
– ident: 1967_CR21
  doi: 10.1007/BF01582222
SSID ssj0009874
Score 2.3335514
Snippet Second-order necessary and sufficient optimality conditions for local solutions and locally unique solutions of generalized quadratic programming problems in...
SourceID proquest
crossref
springer
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 426
SubjectTerms Applications of Mathematics
Banach spaces
Calculus of Variations and Optimal Control; Optimization
Engineering
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Orthogonality
Quadratic programming
Theory of Computation
SummonAdditionalLinks – databaseName: Springer Nature - Connect here FIRST to enable access
  dbid: RSV
  link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3NTsMwDI5gcIAD_4jBQD1wg0hp06bNEQ0mkGAbDNBuVZqk0iTo0Lpx2NPwLDwZcX_WgQAJjlXTqHJs57Nsf0bo2NGaxpwBTyWFAIUSHEQacq5CmiAo8gKZkbhe--120O_zbtEUlpbV7mVKMvPUc81u3PMxlBQAp4uPp4toyVx3AQxsuOs9VlS7Qcm97GDqUF60yny_x-frqMKYX9Ki2W3TWv_ff26gtQJdWme5OmyiBZ1sodU5zkHzdDMjak23UacHAbHCHWDgtDrGfzxnwNxqDiGXDTppGVj7_naVxAOAp_gcxgHkVB7W7UQo0CBpdfMyr3QHPbQu7puXuJixgKUxvjGWxldzqVwWE0c4kRdR6sc21UyQQDFlOxHlTDOqCJTP2MbCCSOCCq4I11Es6C6qJcNE7yGLcmrb3ISXgsWuy1VkS9cjdmwglIhN5FlHdinqUBYE5DAH4ymsqJNBdKERXZiJLpzW0cnsm5ecfuPX1Y3yBMPCFNPQYZBbZwGhdXRanlj1-ufd9v-2_ACtOKByWUV3A9XGo4k-RMvydTxIR0eZin4AQK_gKw
  priority: 102
  providerName: Springer Nature
Title Second-Order Optimality Conditions for Infinite-Dimensional Quadratic Programs
URI https://link.springer.com/article/10.1007/s10957-021-01967-z
https://www.proquest.com/docview/2627006803
Volume 192
WOSCitedRecordID wos000722805200002&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 Nature - Connect here FIRST to enable access
  customDbUrl:
  eissn: 1573-2878
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0009874
  issn: 0022-3239
  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/eLvHCXMwpV1LT9wwEB7x6IEeWqBU3fJQDtyKVT82TnyqYAtqBbubsm15XCLHdqSVyi6QpQd-PZ6sQ2ilcullJCsPRZnx-BvP-BuAXe6cKJVEnkqBAYqgJC0c5ly18UFQEaemJnE9SQaD9PxcZWHDrQpllY1PrB21nRrcI__IJaZIZUrFp-sbgl2jMLsaWmgswrJHNgxLuvo8a0l304aFmRPBhQqHZsLRORUnBAsUkCEmIfd_Lkwt2vwrQVqvO0ev__eLV-FVQJzR_txE1mDBTdbh5RMeQj_qP5K3Vm9gMMIg2ZIhsnJGQ-9TrmqwHvWmmN9GO4081I2-TsoxIlbyGTsEzNk9om932qJRmSibV35VG_Dj6PB77wsJbReI8fNxRox338rYriwp17yICyGSkgknNU2ttIwXQkknhaVYUcP8pKeSaqGVpcoVpRZvYWkynbh3EAklGFM-4tSy7HaVLZjpxpSVHlXp0gejHWDNP89N4CTH1hi_8pZNGfWUez3ltZ7y-w58eHzmes7I8ezdW41y8jA7q7zVTAf2GvW2l__9tvfPv20TVjjaWl3UvQVLs9s7tw0vzO_ZuLrdgcXk7GIHlg8OB9mpHx0nxMs-7aHkw1pmKJORl1l86eXp6OcDAo_wPA
linkProvider ProQuest
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1LT9wwEB5RqNT2APQllkfxoT21Vh07ceIDQghYsWJZtiqVuKWO7UhIJUvJ0gp-FL8RTx6krcTeOPQYJRkp8TfjGc_MNwDvuXMiVxJ5KgUGKILRJHOYc9XGB0FZlJiKxHUYj0bJ6akaz8Ft2wuDZZWtTawMtZ0YPCP_zCWmSGXCxPbFT4pTozC72o7QqGFx6K5_-5Ct3Brs-fX9wHl__2T3gDZTBajxcJtS462TMjaUOeOaZ1EmRJwHwknNEittwDOhpJPCMiwYCTymmWRaaGWZclmuhZf7BBZCZBbDUkE-7kh-k5b1mVPBhWqadJpWPRXFFAsikJEmpjd_b4Sdd_tPQrba5_pL_9sfWobFxqMmO7UKvIQ5V7yCF3_wLPqro3ty2vI1jL7iIYClx8g6So69zTyvghGyO8H8Peoh8a48GRT5GXrkdA8nINTsJeTLlbaoNIaM68q28g18e5TPewvzxaRwK0CEEkGgfEStZR6GymaBCSMW5N5r1LkPtnsQtGucmoZzHUd__Eg7tmjERepxkVa4SG968PH-nYuacWTm0-stGNLG-pRph4QefGrh1N1-WNrqbGmb8Ozg5GiYDgejwzV4zhHnVQH7OsxPL6_cBjw1v6Zn5eW7Si8IfH9smN0BLe1EOw
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1LT9wwEB5RWlXlQB-06vKqD-2ptXDsjRMfEEJsV6ygyyJaCXEJjh8SUrsLZKEqP41fhycPApXKjUOPURJLib8Zz3g-fwPwkTsnvJKoUykwQRGMprnDmqs2IQnK49SUIq67yXCYHh6q0QxcN2dhkFbZ-MTSUduJwT3yNS6xRCpTJtZ8TYsY9fobp2cUO0hhpbVpp1FBZMf9-R3St2J90Atz_Ynz_tfvW9u07jBATYDelJrgqZSxXekZ1zyPcyESHwknNUuttBHPhZJOCsuQPBIFfDPJtNDKMuVyr0UY9wk8TUKOiXTCUXzUCv6mjQI0p4ILVR_YqY_tqTihSI5AdZqEXt1fFNtI96_ibLnm9V_-z3_rFczXkTbZrEzjNcy48RuYu6O_GK6-3YrWFgswPMDNAUv3UI2U7AVf-qtMUsjWBOv6aJ8khPhkMPYnGKnTHnZGqFRNyP6FtmhMhowqxlvxFn48yue9g9nxZOzeAxFKRJEKmbaWvttVNo9MN2aRD9Gk9iEJ70DUzHdmai12bAnyM2tVpBEjWcBIVmIku-rA59t3TislkgefXm6AkdVeqchaVHTgSwOt9va_R1t8eLQP8DygK9sdDHeW4AVHyJe89mWYnZ5fuBV4Zi6nJ8X5amkiBI4fG2U3nklNJw
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=Second-Order+Optimality+Conditions+for+Infinite-Dimensional+Quadratic+Programs&rft.jtitle=Journal+of+optimization+theory+and+applications&rft.au=An+Duong+Thi+Viet&rft.date=2022-02-01&rft.pub=Springer+Nature+B.V&rft.issn=0022-3239&rft.eissn=1573-2878&rft.volume=192&rft.issue=2&rft.spage=426&rft.epage=442&rft_id=info:doi/10.1007%2Fs10957-021-01967-z&rft.externalDBID=HAS_PDF_LINK
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0022-3239&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0022-3239&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0022-3239&client=summon