Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions

In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(/)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and b...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of optimization theory and applications Jg. 123; H. 2; S. 409 - 429
Hauptverfasser: Ruan, G. Z., Wang, S. Y., Yamamoto, Y., Zhu, S. S.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY Springer 01.11.2004
Springer Nature B.V
Schlagworte:
Applied sciences
Decision making
Exact sciences and technology
Game theory
Investigations
Linear programming
Mathematical programming
Mathematics
Operational research and scientific management
Operational research. Management science
Optimization
Studies
Systems science
Variables
multilevel programming
Decision support system
Decision making
Optimality condition
Bilevel programming
Linear programming
Optimality criterion
connectedness
Objective function
upper semicontinuity
Semi continuous function
Semicontinuous
ISSN:0022-3239, 1573-2878
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Abstract In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(/)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(/) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems.
AbstractList In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(/)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(/) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems.
In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems. [PUBLICATION ABSTRACT]
In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems.
Author Zhu, S. S.
Wang, S. Y.
Ruan, G. Z.
Yamamoto, Y.
Author_xml – sequence: 1
  givenname: G. Z.
  surname: Ruan
  fullname: Ruan, G. Z.
– sequence: 2
  givenname: S. Y.
  surname: Wang
  fullname: Wang, S. Y.
– sequence: 3
  givenname: Y.
  surname: Yamamoto
  fullname: Yamamoto, Y.
– sequence: 4
  givenname: S. S.
  surname: Zhu
  fullname: Zhu, S. S.
BackLink http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=16310575$$DView record in Pascal Francis
BookMark eNqFksGOFCEQholZE2dXH8AbMdFba9E0DRzN6K4mY8aDngnQ9MqEhhHoNZP48HY7m5jswT1VpfL9VVD1X6KLmKJD6CWBtwSAvysEJOMNQNcwwvrm9ARtCOO0aQUXF2gD0LYNbal8hi5LOQCAFLzboN_7Y_WTDr6e8DbFwVefYsE6DvjGpcnV7C3-mtPR5epdwWnEGu98dDrjL3OoPrg7F1biNutp8vF2zU1wE_7l6w_8IS01Xd2A9-bgbPV3Dl_P0f4d8xw9HXUo7sV9vELfrz9-235qdvubz9v3u8ZSIWvDZC8BBB1tb4ZOEqrt6OgwCjtIJqyREmSrOR2M5kYS15qOwtAbOkojLGh6hd6c-x5z-jm7UtXki3Uh6OjSXFQrWU-A08dBITq6PGYBXz0AD2nOcfmEIrLviZCMPQIxwUF2C_T6HtLF6jBmHa0v6piXq-STIj0lwPjajJw5m1Mp2Y3_EFCrBdTZAmqxgFotoE6Lhj_QWF_1uvqatQ__Uf4B1mS5PQ
CODEN JOTABN
CitedBy_id crossref_primary_10_3390_math7050464
crossref_primary_10_1016_j_ins_2016_01_084
crossref_primary_10_1007_s11831_017_9216_5
crossref_primary_10_1016_j_ins_2016_08_022
crossref_primary_10_1007_s10287_007_0062_z
crossref_primary_10_1007_s10898_006_9100_6
Cites_doi 10.1109/TSMC.1984.6313291
10.1007/BF01096458
10.1007/BF00932907
10.1137/S0363012993249717
10.1007/BF00940342
10.1007/978-1-4613-0307-7_2
10.1016/0305-0548(82)90006-5
10.1007/BF02192648
10.1016/0305-0548(86)90023-7
10.1007/BF02192141
10.1007/BF00121269
10.1137/1015073
10.1287/moor.8.2.260
10.1137/0913069
10.1023/A:1008735010803
10.1023/A:1022610103712
10.1007/BF01580720
10.1515/9781400873173
10.1007/BF01099649
10.1137/0911017
10.1287/mnsc.30.8.1004
10.1002/nav.3800310104
10.1016/0377-2217(85)90133-X
10.1016/S0377-2217(98)00336-1
ContentType Journal Article
Copyright 2005 INIST-CNRS
Springer Science+Business Media, Inc. 2004
Copyright Kluwer Academic Publishers Nov 2004
Copyright_xml – notice: 2005 INIST-CNRS
– notice: Springer Science+Business Media, Inc. 2004
– notice: Copyright Kluwer Academic Publishers Nov 2004
DBID AAYXX
CITATION
IQODW
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.-
L.0
L6V
L7M
L~C
L~D
M0C
M2O
M2P
M7S
MBDVC
P5Z
P62
PHGZM
PHGZT
PKEHL
PQBIZ
PQBZA
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
Q9U
DOI 10.1007/s10957-004-5156-y
DatabaseName CrossRef
Pascal-Francis
ProQuest Central (Corporate)
Computer and Information Systems Abstracts
Mechanical & Transportation Engineering Abstracts
ABI/INFORM Collection
ABI/INFORM Global (PDF only)
ProQuest Central (purchase pre-March 2016)
ABI/INFORM Global (Alumni Edition)
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 Edition)
Research Library (Alumni Edition)
Materials Science & Engineering Collection
ProQuest Central (Alumni Edition)
ProQuest Central UK/Ireland
Advanced Technologies & Computer Science Collection
ProQuest Central Essentials
ProQuest Central
Business Premium Collection
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
ABI/INFORM Professional Standard
ProQuest Engineering Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
ProQuest ABI/INFORM Global
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
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
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
ABI/INFORM Professional Standard
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 Technology Research Database
Computer and Information Systems Abstracts
Civil Engineering Abstracts
ProQuest Business Collection (Alumni Edition)
Database_xml – sequence: 1
  dbid: BENPR
  name: ProQuest Central (subscription)
  url: https://www.proquest.com/central
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
Mathematics
Applied Sciences
EISSN 1573-2878
EndPage 429
ExternalDocumentID 778792451
945086261
16310575
10_1007_s10957_004_5156_y
Genre Feature
GroupedDBID -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
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
AAPKM
AARHV
AARTL
AASML
AATNV
AATVU
AAUYE
AAWCG
AAYIU
AAYQN
AAYTO
AAYXX
ABAKF
ABBBX
ABBRH
ABBXA
ABDBE
ABDPE
ABDZT
ABECU
ABFSG
ABFTV
ABHLI
ABHQN
ABJCF
ABJNI
ABJOX
ABKCH
ABKTR
ABMNI
ABMQK
ABNWP
ABQBU
ABQSL
ABRTQ
ABSXP
ABTEG
ABTHY
ABTKH
ABTMW
ABULA
ABUWG
ABWNU
ABXPI
ACAOD
ACBXY
ACDTI
ACGFS
ACGOD
ACHSB
ACHXU
ACIWK
ACKNC
ACMDZ
ACMLO
ACOKC
ACOMO
ACPIV
ACSTC
ACZOJ
ADHHG
ADHIR
ADHKG
ADKNI
ADKPE
ADRFC
ADTPH
ADURQ
ADXHL
ADYFF
ADZKW
AEBTG
AEFIE
AEFQL
AEGAL
AEGNC
AEJHL
AEJRE
AEKMD
AEMSY
AENEX
AEOHA
AEPYU
AETLH
AEVLU
AEXYK
AEZWR
AFBBN
AFDZB
AFEXP
AFFHD
AFGCZ
AFHIU
AFKRA
AFLOW
AFOHR
AFQWF
AFWTZ
AFZKB
AGAYW
AGDGC
AGGDS
AGJBK
AGMZJ
AGQEE
AGQMX
AGQPQ
AGRTI
AGWIL
AGWZB
AGYKE
AHAVH
AHBYD
AHKAY
AHPBZ
AHSBF
AHWEU
AHYZX
AI.
AIAKS
AIGIU
AIIXL
AILAN
AITGF
AIXLP
AJBLW
AJRNO
AJZVZ
ALMA_UNASSIGNED_HOLDINGS
ALWAN
AMKLP
AMVHM
AMXSW
AMYLF
AMYQR
AOCGG
ARAPS
ARCSS
ARMRJ
ASPBG
ATHPR
AVWKF
AXYYD
AYFIA
AYJHY
AZFZN
AZQEC
B-.
BA0
BAPOH
BBWZM
BDATZ
BENPR
BEZIV
BGLVJ
BGNMA
BPHCQ
BSONS
CAG
CCPQU
CITATION
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
GQ7
GQ8
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
PHGZM
PHGZT
PQBIZ
PQBZA
PQGLB
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
ZCG
ZMTXR
ZWQNP
ZY4
~EX
AAYZH
AESKC
IQODW
3V.
7SC
7TB
7XB
8FD
8FK
FR3
JQ2
KR7
L.-
L.0
L7M
L~C
L~D
MBDVC
PKEHL
PQEST
PQUKI
PRINS
Q9U
PUEGO
ID FETCH-LOGICAL-c389t-59690083fc6bd4913acfe3df8cd958cb99092a73dba7b91e2b430d6b3f9b8c0a3
IEDL.DBID 7WY
ISICitedReferencesCount 8
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000224912500010&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 Thu Oct 02 08:43:55 EDT 2025
Sun Nov 09 09:55:08 EST 2025
Tue Nov 04 16:34:56 EST 2025
Tue Nov 04 16:34:36 EST 2025
Mon Jul 21 09:12:36 EDT 2025
Tue Nov 18 21:10:51 EST 2025
Sat Nov 29 02:36:45 EST 2025
IsPeerReviewed true
IsScholarly true
Issue 2
Keywords multilevel programming
Decision support system
Decision making
Optimality condition
Bilevel programming
Linear programming
Optimality criterion
connectedness
Objective function
upper semicontinuity
Semi continuous function
Semicontinuous
Language English
License http://www.springer.com/tdm
CC BY 4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c389t-59690083fc6bd4913acfe3df8cd958cb99092a73dba7b91e2b430d6b3f9b8c0a3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ObjectType-Feature-1
ObjectType-Article-2
content type line 23
PQID 196587094
PQPubID 48247
PageCount 21
ParticipantIDs proquest_miscellaneous_29561073
proquest_miscellaneous_28843690
proquest_journals_196618955
proquest_journals_196587094
pascalfrancis_primary_16310575
crossref_primary_10_1007_s10957_004_5156_y
crossref_citationtrail_10_1007_s10957_004_5156_y
PublicationCentury 2000
PublicationDate 2004-11-01
PublicationDateYYYYMMDD 2004-11-01
PublicationDate_xml – month: 11
  year: 2004
  text: 2004-11-01
  day: 01
PublicationDecade 2000
PublicationPlace New York, NY
PublicationPlace_xml – name: New York, NY
– name: New York
PublicationTitle Journal of optimization theory and applications
PublicationYear 2004
Publisher Springer
Springer Nature B.V
Publisher_xml – name: Springer
– name: Springer Nature B.V
References J. F. Bard (CR21) 1998; 20
J. F. Bard (CR25) 1990; 11
P. Loridan (CR28) 1996; 8
P. Hansen (CR26) 1992; 13
W. Candler (CR3) 1982; 9
G. Z. Ruan (CR18) 1998; 18
G. Petriczek (CR19) 1991; 8
J. F. Bard (CR4) 1983; 8
A. Migdalas (CR20) 1995; 7
W. W. Hogan (CR32) 1973; 15
J. F. Bard (CR7) 1988; 40
CR10
L. N. Vicente (CR23) 1994; 5
J. E. Falk (CR8) 1995; 70
Q. Wang (CR29) 2000; 13
J. J. Ye (CR9) 1995; 33
X. J. Wang (CR24) 1995
Q. Wang (CR27) 1994; 13
D. J. White (CR14) 1997; 93
S. Y. Wang (CR11) 1996; 20
U. P. Wen (CR13) 1986; 13
CR2
J. F. Bard (CR12) 1984; 14
S. Dempe (CR30) 2000; 15
CR1
P. H. Naccache (CR33) 1978; 25
H. P. Benson (CR16) 1989; 60
M. A. Amouzegar (CR22) 1999; 119
D. J. White (CR17) 1995; 87
J. F. Bard (CR5) 1984; 31
W. F. Bialas (CR6) 1984; 30
R. T. Rockafellar (CR31) 1970
J. F. Bard (CR15) 1985; 19
References_xml – volume: 70
  start-page: 47
  year: 1995
  ident: CR8
  publication-title: Mathematical Programming
– volume: 14
  start-page: 711
  year: 1984
  ident: CR12
  publication-title: IEEE Transactions on Systems, Man, and Cybernetics
  doi: 10.1109/TSMC.1984.6313291
– volume: 5
  start-page: 291
  year: 1994
  ident: CR23
  publication-title: Journal of Global Optimization
  doi: 10.1007/BF01096458
– volume: 25
  start-page: 459
  year: 1978
  ident: CR33
  publication-title: Journal of Optimization Theory and Applications
  doi: 10.1007/BF00932907
– ident: CR2
– volume: 33
  start-page: 1208
  year: 1995
  ident: CR9
  publication-title: SIAM Journal on Control and Optimization
  doi: 10.1137/S0363012993249717
– volume: 60
  start-page: 353
  year: 1989
  ident: CR16
  publication-title: Journal of Optimization Theory and Applications
  doi: 10.1007/BF00940342
– volume: 20
  start-page: 23
  year: 1998
  ident: CR21
  publication-title: Nonconvex Optimization and Its Applications
  doi: 10.1007/978-1-4613-0307-7_2
– volume: 9
  start-page: 59
  year: 1982
  ident: CR3
  publication-title: Computers and Operations Research
  doi: 10.1016/0305-0548(82)90006-5
– ident: CR10
  doi: 10.1007/BF02192648
– volume: 13
  start-page: 367
  year: 1986
  ident: CR13
  publication-title: Computers and Operations Research
  doi: 10.1016/0305-0548(86)90023-7
– volume: 87
  start-page: 727
  year: 1995
  ident: CR17
  publication-title: Journal of Optimization Theory and Applications
  doi: 10.1007/BF02192141
– volume: 8
  start-page: 263
  year: 1996
  ident: CR28
  publication-title: Journal of Global Optimization
  doi: 10.1007/BF00121269
– volume: 15
  start-page: 591
  year: 1973
  ident: CR32
  publication-title: SIAM Review
  doi: 10.1137/1015073
– volume: 8
  start-page: 260
  year: 1983
  ident: CR4
  publication-title: Mathematics of Operations Research
  doi: 10.1287/moor.8.2.260
– volume: 13
  start-page: 1194
  year: 1992
  ident: CR26
  publication-title: SIAM Journal on Scientific and Statistical Computing
  doi: 10.1137/0913069
– volume: 20
  start-page: 215
  year: 1996
  ident: CR11
  publication-title: Q¨ uestii ´ o
– volume-title: Optimization Theory of Bilevel Systems
  year: 1995
  ident: CR24
– volume: 15
  start-page: 145
  year: 2000
  ident: CR30
  publication-title: Computational Optimization and Applications
  doi: 10.1023/A:1008735010803
– volume: 93
  start-page: 183
  year: 1997
  ident: CR14
  publication-title: Journal of Optimization Theory and Applications
  doi: 10.1023/A:1022610103712
– volume: 40
  start-page: 15
  year: 1988
  ident: CR7
  publication-title: Mathematical Programming
  doi: 10.1007/BF01580720
– volume-title: Convex Analysis
  year: 1970
  ident: CR31
  doi: 10.1515/9781400873173
– volume: 8
  start-page: 457
  year: 1991
  ident: CR19
  publication-title: Systems Analysis, Modeling, and Simulation
– volume: 7
  start-page: 381
  year: 1995
  ident: CR20
  publication-title: Journal of Global Optimization
  doi: 10.1007/BF01099649
– volume: 11
  start-page: 281
  year: 1990
  ident: CR25
  publication-title: SIAM Journal on Scientific and Statistical Computing
  doi: 10.1137/0911017
– ident: CR1
– volume: 18
  start-page: 159
  year: 1998
  ident: CR18
  publication-title: Journal of Systems Science and Mathematical Sciences
– volume: 13
  start-page: 265
  year: 2000
  ident: CR29
  publication-title: Systems Science and Mathematical Sciences
– volume: 30
  start-page: 1004
  year: 1984
  ident: CR6
  publication-title: Management Science
  doi: 10.1287/mnsc.30.8.1004
– volume: 31
  start-page: 13
  year: 1984
  ident: CR5
  publication-title: Naval Research Logistics Quarterly
  doi: 10.1002/nav.3800310104
– volume: 19
  start-page: 372
  year: 1985
  ident: CR15
  publication-title: European Journal of Operational Research
  doi: 10.1016/0377-2217(85)90133-X
– volume: 119
  start-page: 100
  year: 1999
  ident: CR22
  publication-title: European Journal of Operational Research
  doi: 10.1016/S0377-2217(98)00336-1
– volume: 13
  start-page: 269
  year: 1994
  ident: CR27
  publication-title: Journal of Systems Science and Systems Engineering
SSID ssj0009874
Score 1.7570912
Snippet In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the...
In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(/)) is proposed, where multiple reactions of the...
SourceID proquest
pascalfrancis
crossref
SourceType Aggregation Database
Index Database
Enrichment Source
StartPage 409
SubjectTerms Applied sciences
Decision making
Exact sciences and technology
Game theory
Investigations
Linear programming
Mathematical programming
Mathematics
Operational research and scientific management
Operational research. Management science
Optimization
Studies
Systems science
Variables
Title Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions
URI https://www.proquest.com/docview/196587094
https://www.proquest.com/docview/196618955
https://www.proquest.com/docview/28843690
https://www.proquest.com/docview/29561073
Volume 123
WOSCitedRecordID wos000224912500010&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: PRVPQU
  databaseName: ABI/INFORM Global
  customDbUrl:
  eissn: 1573-2878
  dateEnd: 20171231
  omitProxy: false
  ssIdentifier: ssj0009874
  issn: 0022-3239
  databaseCode: M0C
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/abiglobal
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Advanced Technologies & Aerospace Database
  customDbUrl:
  eissn: 1573-2878
  dateEnd: 20171231
  omitProxy: false
  ssIdentifier: ssj0009874
  issn: 0022-3239
  databaseCode: P5Z
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/hightechjournals
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Computer Science Database
  customDbUrl:
  eissn: 1573-2878
  dateEnd: 20171231
  omitProxy: false
  ssIdentifier: ssj0009874
  issn: 0022-3239
  databaseCode: K7-
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/compscijour
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Engineering Database
  customDbUrl:
  eissn: 1573-2878
  dateEnd: 20171231
  omitProxy: false
  ssIdentifier: ssj0009874
  issn: 0022-3239
  databaseCode: M7S
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: http://search.proquest.com
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest ABI/INFORM Collection
  customDbUrl:
  eissn: 1573-2878
  dateEnd: 20171231
  omitProxy: false
  ssIdentifier: ssj0009874
  issn: 0022-3239
  databaseCode: 7WY
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/abicomplete
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest Central (subscription)
  customDbUrl:
  eissn: 1573-2878
  dateEnd: 20171231
  omitProxy: false
  ssIdentifier: ssj0009874
  issn: 0022-3239
  databaseCode: BENPR
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/central
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Research Library
  customDbUrl:
  eissn: 1573-2878
  dateEnd: 20171231
  omitProxy: false
  ssIdentifier: ssj0009874
  issn: 0022-3239
  databaseCode: M2O
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/pqrl
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Science Database
  customDbUrl:
  eissn: 1573-2878
  dateEnd: 20171231
  omitProxy: false
  ssIdentifier: ssj0009874
  issn: 0022-3239
  databaseCode: M2P
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/sciencejournals
  providerName: ProQuest
– providerCode: PRVAVX
  databaseName: SpringerLINK Contemporary 1997-Present
  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/eLvHCXMwpV1Lb9QwELag5QCqeBZ1KSw-cEKySOw87BOiSxck1N2o5VG4RLZjS6Bust1sK1Xix3cmj10qxF64jGLFliOPPTOxx99HyKsw8uC004BxLRWLrAkZuBHNtAxs6BOlpfQN2UQ6mcjTU5V1uTl1l1bZ28TGUBeVxT3yN4h8B3NLRW_n5wxJo_BwtWPQuE22wU_HSGCQfvu-xtyVPQgzZ4IL1R9qtjfnVJwyzMIAh56wqxtuaWeuaxgh31Jb_GWlG9czfvCfH_2Q3O9iTvqunSSPyC1XPib3_kAihNLRCr61fkJ-T8GQzJoInY4qPNTGyUl1WdAPrpohCZelGW7jLxCPlVaeagp_tbBqaHOj9wxTkbAG5n7NoAd8RuIaivu-9H2FCTgQ69Kp-dVaXDoGB9t0s0u-jA8_jz6yjqaBWYh2lixW8IcNkZy3iSkiFQptvROFl7ZQsbQG_J3iOhWF0alRoeMmEkGRGOGVkTbQ4inZKqvS7REa2sQpKY3RRRx5brT2qUocd0nBtfPhgAS9lnLbYZgjlcZZvkZfRsXmoNgcFZtfDcjrVZN5C-CxqfLwhurXLRKBhMjxgOz3is67xV7nKy3_620SShVD25ert7CG8WBGl666qHMuZSRgEDfUwPvHYI2fbex_n9xtcShxh-g52VouLtwLcsdeLn_Wi2GzOIZk--Bwkh1D6VPKQB4FI5R82sgMZXoCMot_gDw--XoNLVQing
linkProvider ProQuest
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3Pb9MwFLbGQAKExm9RNjYf4IJkkdiJYx8QQhtlU7duhyHtFmzHljatSWk6UCX-Jf5H3kualgnR2w7cWsWuVefze89-z99HyOs4CeC0s4hxozRLnI0ZuBHDjIpcHKQ2SoVGbCIbDtXZmT5ZI7-6uzBYVtnZxMZQF5XDM_J3yHwH2NLJh_E3hqJRmFztFDRaVAz87Afs2Or3B3vwet9w3v90urvP5qICzIFvnrJUw34Q4o7gpC0SHQvjghdFUK7QqXIWrLPmJhOFNZnVsec2EVEhrQjaKhcZAb97i9xOhJK4oAYZW3L8qo70mTPBhe6SqO1NPZ1mDKs-IICQbHbNDT4YmxreSGilNP7yCo2r6z_8zybpEdmYx9T0Y7sIHpM1Xz4h9_9gWoRvRwt62vop-XkMhnLU7EDoboVJe1x81JQF_eyrEYqMOXqCaYoJ8s3SKlBDYdcOf402N5YvsdQKW2Bt2whGwM8ozEPxXJvuVVhgBLE8PbYXrUehfQggmmGekS83MhnPyXpZlf4FobGTXitlrSnSJHBrTMi09NzLghsf4h6JOlTkbs7RjlIhl_mSXRqBlAOQcgRSPuuRt4su45agZFXj7WtQW_aQAgWf0x7Z7ICVz41ZnS9Q9a-nMlY6hb47i6dgozDxZEpfXdU5VyoRMIkrWuD9avA2L1eOv0Pu7p8eHeaHB8PBJrnXcm7iadgWWZ9Orvwrcsd9n57Xk-1mYVLy9aZB_ht1tXiE
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1bb9MwFLZGhxAIcZ8og80P8IJkLbFzsR8QgnWFadBVCKS9ZbZjS0xrUpoOVIk_xr_jnFxaJkTf9sBbotix4nw-F5_j7xDyPIw8KO00YFxLxSJrQgZqRDMtAxv6RGkpfV1sIh2N5MmJGm-QX91ZGEyr7GRiLajz0uIe-R4y3wG2VLTn26yI8WD4evqNYQEpDLR21TQahBy5xQ_w3qpXhwP41S84Hx583n_P2gIDzIKenrNYgW8INoi3ickjFQptvRO5lzZXsbQGJLXiOhW50alRoeMmEkGeGOGVkTbQAt57jWymAnyeHtl8ezAaf1ox_sqOApozwYXqQqrNuT0VpwxzQMCcSNjiklK8PdUV_B_fFNb4S0fUim949z-esnvkTmtt0zfN8rhPNlzxgNz6g4MR7j4uiWurh-TnMYjQSe2b0P0Sw_m4LKkucvrOlRMsP2bpGAMYM2SipaWnmoI_D59G67PM55iEhS0w620CI-A1luyhuONNByWmHoGVT4_NWaNr6BBMi3qYR-TLlUzGFukVZeEeExraxCkpjdF5HHlutPapShx3Sc6182GfBB1CMtuyt2MRkfNsxTuNoMoAVBmCKlv0yctll2lDXbKu8c4l2K16JAJLQcd9st2BLGvFXJUtEfavp0koVQx9d5dPQXphSEoXrryoMi5lJGAS17TAk9egh56sHX-X3ABsZx8OR0fb5GZDxonbZE9Jbz67cM_Idft9_rWa7bSrlJLTq0b5b8iagtY
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=Optimality+conditions+and+geometric+properties+of+a+linear+multilevel+programming+problem+with+dominated+objective+functions&rft.jtitle=Journal+of+optimization+theory+and+applications&rft.au=RUAN%2C+G.+Z&rft.au=WANG%2C+S.+Y&rft.au=YAMAMOTO%2C+Y&rft.au=ZHU%2C+S.+S&rft.date=2004-11-01&rft.pub=Springer&rft.issn=0022-3239&rft.volume=123&rft.issue=2&rft.spage=409&rft.epage=429&rft_id=info:doi/10.1007%2Fs10957-004-5156-y&rft.externalDBID=n%2Fa&rft.externalDocID=16310575
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