Some vector optimization problems in Banach spaces with generalized convexity

In this paper, we consider a vector optimization problem where all functions involved are defined on Banach spaces. New classes of generalized type-I functions are introduced for functions between Banach spaces. Based upon these generalized type-I functions, we obtain a few sufficient optimality con...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Computers & mathematics with applications (1987) Jg. 54; H. 11; S. 1403 - 1410
Hauptverfasser: Yu, Guolin, Liu, Sanyang
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.12.2007
Schlagworte:
ISSN:0898-1221, 1873-7668
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Abstract In this paper, we consider a vector optimization problem where all functions involved are defined on Banach spaces. New classes of generalized type-I functions are introduced for functions between Banach spaces. Based upon these generalized type-I functions, we obtain a few sufficient optimality conditions and prove some results on duality.
AbstractList In this paper, we consider a vector optimization problem where all functions involved are defined on Banach spaces. New classes of generalized type-I functions are introduced for functions between Banach spaces. Based upon these generalized type-I functions, we obtain a few sufficient optimality conditions and prove some results on duality.
Author Liu, Sanyang
Yu, Guolin
Author_xml – sequence: 1
  givenname: Guolin
  surname: Yu
  fullname: Yu, Guolin
  email: guolin_yu@126.com
  organization: Department of Applied Mathematics, Xidian University, Xi’an, PR China
– sequence: 2
  givenname: Sanyang
  surname: Liu
  fullname: Liu, Sanyang
  email: liusanyang@263.net
  organization: Department of Applied Mathematics, Xidian University, Xi’an, PR China
BookMark eNqFkblOxDAQQC0EEsvxBTSuEE3C2Ekcp6AAxCWBKKC3vM4seJXYi22W4-vxslQUUE3z3mj0ZodsOu-QkAMGJQMmjuel0eObLjlAW0JTAvANMmGyrYpWCLlJJiA7WTDO2TbZiXEOAHXFYULuHvyIdIkm-UD9ItnRfupkvaOL4KcDjpFaR8-00-aZxoU2GOmbTc_0CR0GPdhP7KnxbonvNn3ska2ZHiLu_8xd8nh58Xh-XdzeX92cn94WphJtKsRMNMj7ruZVVaORhguUogfOp003RY7QwpTLDJie9a1kvewa2Yo6Q_VMVrvkcL023_jyijGp0UaDw6Ad-teoKga5RL0Cj_4EGUjOOt5JltFqjZrgYww4U4tgRx0-MqRWkdVcfUdWq8gKGpUjZ6v7ZRmbvvuloO3wj3uydjGXWloMKhqLzmBvQ_6H6r390_8CNYWbTA
CitedBy_id crossref_primary_10_1155_2012_458983
crossref_primary_10_1155_2012_540746
crossref_primary_10_1016_j_na_2011_12_009
crossref_primary_10_1007_s11424_014_1215_0
Cites_doi 10.1080/01630569608816697
10.1007/BF02207775
10.1016/j.camwa.2003.05.013
10.1006/jmaa.1999.6284
10.1016/j.jmaa.2005.02.064
10.1016/j.jmaa.2003.12.042
10.1023/A:1022628130448
10.1006/jmaa.1997.5238
10.1016/j.jmaa.2005.04.067
10.1023/A:1021769232224
10.1007/BF02591683
10.1016/0022-247X(88)90313-7
10.1007/BF00935364
10.1016/j.camwa.2006.08.006
10.1080/02331939208843857
ContentType Journal Article
Copyright 2007 Elsevier Ltd
Copyright_xml – notice: 2007 Elsevier Ltd
DBID 6I.
AAFTH
AAYXX
CITATION
7SC
7TB
8FD
FR3
JQ2
KR7
L7M
L~C
L~D
DOI 10.1016/j.camwa.2007.05.002
DatabaseName ScienceDirect Open Access Titles
Elsevier:ScienceDirect:Open Access
CrossRef
Computer and Information Systems Abstracts
Mechanical & Transportation Engineering Abstracts
Technology Research Database
Engineering Research Database
ProQuest Computer Science Collection
Civil Engineering Abstracts
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Civil Engineering Abstracts
Technology Research Database
Computer and Information Systems Abstracts – Academic
Mechanical & Transportation Engineering Abstracts
ProQuest Computer Science Collection
Computer and Information Systems Abstracts
Engineering Research Database
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts Professional
DatabaseTitleList Civil Engineering Abstracts
Civil Engineering Abstracts

DeliveryMethod fulltext_linktorsrc
Discipline Computer Science
EISSN 1873-7668
EndPage 1410
ExternalDocumentID 10_1016_j_camwa_2007_05_002
S0898122107004816
GroupedDBID --K
--M
-~X
.DC
.~1
0R~
1B1
1RT
1~.
1~5
29F
4.4
457
4G.
5GY
5VS
6I.
7-5
71M
8P~
9JN
AACTN
AAEDT
AAEDW
AAFTH
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AAXUO
AAYFN
ABAOU
ABBOA
ABFNM
ABMAC
ABTAH
ABVKL
ABXDB
ABYKQ
ACAZW
ACDAQ
ACGFS
ACIWK
ACNCT
ACNNM
ACRLP
ACZNC
ADBBV
ADEZE
ADMUD
ADTZH
AEBSH
AECPX
AEKER
AENEX
AEXQZ
AFFNX
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHJVU
AHZHX
AIALX
AIEXJ
AIGVJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
AOUOD
ARUGR
ASPBG
AVWKF
AXJTR
AZFZN
BJAXD
BKOJK
BLXMC
CS3
DU5
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
F5P
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
GBLVA
GBOLZ
HVGLF
HZ~
IHE
IXB
J1W
JJJVA
KOM
LG9
M26
M41
MHUIS
MO0
N9A
NCXOZ
O-L
O9-
OAUVE
OK1
OZT
P-8
P-9
P2P
PC.
PQQKQ
Q38
R2-
RIG
RNS
ROL
RPZ
SDF
SDG
SDP
SES
SEW
SPC
SPCBC
SST
SSV
SSW
SSZ
T5K
TAE
TN5
WUQ
XFK
XPP
ZMT
ZY4
~G-
9DU
AATTM
AAXKI
AAYWO
AAYXX
ABJNI
ABWVN
ACLOT
ACRPL
ACVFH
ADCNI
ADNMO
ADVLN
AEIPS
AEUPX
AFJKZ
AFPUW
AGQPQ
AIGII
AIIUN
AKBMS
AKRWK
AKYEP
ANKPU
APXCP
CITATION
EFKBS
~HD
7SC
7TB
8FD
FR3
JQ2
KR7
L7M
L~C
L~D
ID FETCH-LOGICAL-c367t-6f65e2d942334ec8c26e86d022b59be2e070b28d94cd1d781d895876486d4f83
ISICitedReferencesCount 6
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000251461000010&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0898-1221
IngestDate Sat Sep 27 22:22:02 EDT 2025
Wed Oct 01 14:15:24 EDT 2025
Tue Nov 18 21:51:12 EST 2025
Sat Nov 29 05:42:12 EST 2025
Fri Feb 23 02:16:56 EST 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 11
Keywords Optimality conditions
Duality
Type-I functions
Vector optimization
Generalized convexity
Language English
License http://www.elsevier.com/open-access/userlicense/1.0
https://www.elsevier.com/tdm/userlicense/1.0
https://www.elsevier.com/open-access/userlicense/1.0
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c367t-6f65e2d942334ec8c26e86d022b59be2e070b28d94cd1d781d895876486d4f83
Notes ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
OpenAccessLink https://dx.doi.org/10.1016/j.camwa.2007.05.002
PQID 1082192981
PQPubID 23500
PageCount 8
ParticipantIDs proquest_miscellaneous_31020048
proquest_miscellaneous_1082192981
crossref_primary_10_1016_j_camwa_2007_05_002
crossref_citationtrail_10_1016_j_camwa_2007_05_002
elsevier_sciencedirect_doi_10_1016_j_camwa_2007_05_002
PublicationCentury 2000
PublicationDate 2007-12-01
PublicationDateYYYYMMDD 2007-12-01
PublicationDate_xml – month: 12
  year: 2007
  text: 2007-12-01
  day: 01
PublicationDecade 2000
PublicationTitle Computers & mathematics with applications (1987)
PublicationYear 2007
Publisher Elsevier Ltd
Publisher_xml – name: Elsevier Ltd
References Kaul, Suneja, Srivastava (b3) 1994; 80
Mishra, Noor (b8) 2006; 316
Minami (b15) 1983; 41
Brandao, Rojas-Medar, Silva (b16) 1999; 103
Abdouni, Thibault (b13) 1992; 26
Osuna-Gómez, Rufián-Lizana, Ruíz-Canales (b10) 2000; 1
Suneja, Srivastava (b7) 1997; 206
Hanson, Mond (b1) 1987; 37
Osuna-Gómez, Beato-Moreno, Rufián-Lizana (b9) 1999; 233
Gulati, Agarwal (b6) 2006; 52
Osuna-Gómez, Rufián-Lizana, Ruíz-Canales (b11) 1998; 98
Rueda, Hanson (b2) 1998; 130
Hachimi, Aghezzaf (b4) 2004; 296
Craven (b17) 1995
Hachimi, Aghezzaf (b5) 2006; 319
Batista dos Santos, Osuna-Gómez, Rojas-Medar, Rufián-Lizana (b12) 2004; 48
Jeyakumar, Zaffaroni (b14) 1996; 17
Minami (10.1016/j.camwa.2007.05.002_b15) 1983; 41
Osuna-Gómez (10.1016/j.camwa.2007.05.002_b9) 1999; 233
Suneja (10.1016/j.camwa.2007.05.002_b7) 1997; 206
Osuna-Gómez (10.1016/j.camwa.2007.05.002_b10) 2000; 1
Brandao (10.1016/j.camwa.2007.05.002_b16) 1999; 103
Rueda (10.1016/j.camwa.2007.05.002_b2) 1998; 130
Mishra (10.1016/j.camwa.2007.05.002_b8) 2006; 316
Kaul (10.1016/j.camwa.2007.05.002_b3) 1994; 80
Abdouni (10.1016/j.camwa.2007.05.002_b13) 1992; 26
Osuna-Gómez (10.1016/j.camwa.2007.05.002_b11) 1998; 98
Jeyakumar (10.1016/j.camwa.2007.05.002_b14) 1996; 17
Gulati (10.1016/j.camwa.2007.05.002_b6) 2006; 52
Batista dos Santos (10.1016/j.camwa.2007.05.002_b12) 2004; 48
Craven (10.1016/j.camwa.2007.05.002_b17) 1995
Hachimi (10.1016/j.camwa.2007.05.002_b5) 2006; 319
Hachimi (10.1016/j.camwa.2007.05.002_b4) 2004; 296
Hanson (10.1016/j.camwa.2007.05.002_b1) 1987; 37
References_xml – volume: 80
  start-page: 465
  year: 1994
  end-page: 482
  ident: b3
  article-title: Optimality criteria and duality in multiple objective optimization involving generalized invexity
  publication-title: Journal of Optimization Theory and Applications
– volume: 17
  start-page: 323
  year: 1996
  end-page: 343
  ident: b14
  article-title: Asymptotic conditions for weak and proper optimality in infinite-dimensional convex vector optimization
  publication-title: Numerical Functional Analysis and Optimization
– volume: 41
  start-page: 451
  year: 1983
  end-page: 461
  ident: b15
  article-title: Weak Pareto-optimal necessary conditions in a nondifferential multiobjective program on a Banach space
  publication-title: Journal of Optimization Theory and Applications
– volume: 52
  start-page: 81
  year: 2006
  end-page: 94
  ident: b6
  article-title: Sufficiency and duality in nonsmooth multiobjective optimization involving generalized
  publication-title: Computers and Mathematics with Applications
– volume: 319
  start-page: 110
  year: 2006
  end-page: 123
  ident: b5
  article-title: Sufficiency and duality in nondifferentiable multiobjective programming involving generalized type I functions
  publication-title: Journal of Mathematical Analysis and Applications
– year: 1995
  ident: b17
  article-title: Control and Optimization
– volume: 37
  start-page: 51
  year: 1987
  end-page: 58
  ident: b1
  article-title: Necessary and sufficient conditions in constrained optimization
  publication-title: Mathemaical Programming
– volume: 206
  start-page: 465
  year: 1997
  end-page: 479
  ident: b7
  article-title: Optimality and duality in nondifferentiable multiobjective optimization involving
  publication-title: Journal of Mathematical Analysis and Applications
– volume: 316
  start-page: 472
  year: 2006
  end-page: 482
  ident: b8
  article-title: Some nondifferentiable multi-objective programming problems
  publication-title: Journal of Mathematical Analysis and Applications
– volume: 26
  start-page: 277
  year: 1992
  end-page: 285
  ident: b13
  article-title: Lagrange multipliers for Pareto nonsmooth programming problems in Banach spaces
  publication-title: Optimization
– volume: 98
  start-page: 651
  year: 1998
  end-page: 661
  ident: b11
  article-title: Invex functions and generalized convexity in multiobjective programming
  publication-title: Journal of Optimization Theory and Applications
– volume: 130
  start-page: 375
  year: 1998
  end-page: 385
  ident: b2
  article-title: Optimality criteria in mathematical programming involving generalized invexity
  publication-title: Journal of Mathematical Analysis and Applications
– volume: 296
  start-page: 382
  year: 2004
  end-page: 392
  ident: b4
  article-title: Sufficiency and duality in differentiable multiobjective programming involving generalized type I functions
  publication-title: Journal of Mathematical Analysis and Applications
– volume: 233
  start-page: 205
  year: 1999
  end-page: 220
  ident: b9
  article-title: Generalized convexity in multiobjective programming
  publication-title: Journal of Mathematical Analysis and Applications
– volume: 48
  start-page: 885
  year: 2004
  end-page: 895
  ident: b12
  article-title: Preinvex functions and weak efficient solutions for some vectorial optimization problem in Banach spaces
  publication-title: Computers and Mathematics with Applications
– volume: 103
  start-page: 65
  year: 1999
  end-page: 73
  ident: b16
  article-title: Optimality conditions for Pareto nonsmooth nonconvex programming in Banach spaces
  publication-title: Journal of Optimization Theory and Applications
– volume: 1
  start-page: 97
  year: 2000
  end-page: 110
  ident: b10
  article-title: Multiobjective fractional programming with generalized convexity
  publication-title: Sociedad de Estadística e Investigación Operativa Top 8
– volume: 17
  start-page: 323
  year: 1996
  ident: 10.1016/j.camwa.2007.05.002_b14
  article-title: Asymptotic conditions for weak and proper optimality in infinite-dimensional convex vector optimization
  publication-title: Numerical Functional Analysis and Optimization
  doi: 10.1080/01630569608816697
– volume: 80
  start-page: 465
  year: 1994
  ident: 10.1016/j.camwa.2007.05.002_b3
  article-title: Optimality criteria and duality in multiple objective optimization involving generalized invexity
  publication-title: Journal of Optimization Theory and Applications
  doi: 10.1007/BF02207775
– volume: 48
  start-page: 885
  year: 2004
  ident: 10.1016/j.camwa.2007.05.002_b12
  article-title: Preinvex functions and weak efficient solutions for some vectorial optimization problem in Banach spaces
  publication-title: Computers and Mathematics with Applications
  doi: 10.1016/j.camwa.2003.05.013
– volume: 1
  start-page: 97
  year: 2000
  ident: 10.1016/j.camwa.2007.05.002_b10
  article-title: Multiobjective fractional programming with generalized convexity
  publication-title: Sociedad de Estadística e Investigación Operativa Top 8
– volume: 233
  start-page: 205
  year: 1999
  ident: 10.1016/j.camwa.2007.05.002_b9
  article-title: Generalized convexity in multiobjective programming
  publication-title: Journal of Mathematical Analysis and Applications
  doi: 10.1006/jmaa.1999.6284
– volume: 319
  start-page: 110
  year: 2006
  ident: 10.1016/j.camwa.2007.05.002_b5
  article-title: Sufficiency and duality in nondifferentiable multiobjective programming involving generalized type I functions
  publication-title: Journal of Mathematical Analysis and Applications
  doi: 10.1016/j.jmaa.2005.02.064
– volume: 296
  start-page: 382
  year: 2004
  ident: 10.1016/j.camwa.2007.05.002_b4
  article-title: Sufficiency and duality in differentiable multiobjective programming involving generalized type I functions
  publication-title: Journal of Mathematical Analysis and Applications
  doi: 10.1016/j.jmaa.2003.12.042
– volume: 98
  start-page: 651
  year: 1998
  ident: 10.1016/j.camwa.2007.05.002_b11
  article-title: Invex functions and generalized convexity in multiobjective programming
  publication-title: Journal of Optimization Theory and Applications
  doi: 10.1023/A:1022628130448
– volume: 206
  start-page: 465
  year: 1997
  ident: 10.1016/j.camwa.2007.05.002_b7
  article-title: Optimality and duality in nondifferentiable multiobjective optimization involving d-type I and related functions
  publication-title: Journal of Mathematical Analysis and Applications
  doi: 10.1006/jmaa.1997.5238
– volume: 316
  start-page: 472
  year: 2006
  ident: 10.1016/j.camwa.2007.05.002_b8
  article-title: Some nondifferentiable multi-objective programming problems
  publication-title: Journal of Mathematical Analysis and Applications
  doi: 10.1016/j.jmaa.2005.04.067
– volume: 103
  start-page: 65
  year: 1999
  ident: 10.1016/j.camwa.2007.05.002_b16
  article-title: Optimality conditions for Pareto nonsmooth nonconvex programming in Banach spaces
  publication-title: Journal of Optimization Theory and Applications
  doi: 10.1023/A:1021769232224
– volume: 37
  start-page: 51
  year: 1987
  ident: 10.1016/j.camwa.2007.05.002_b1
  article-title: Necessary and sufficient conditions in constrained optimization
  publication-title: Mathemaical Programming
  doi: 10.1007/BF02591683
– volume: 130
  start-page: 375
  year: 1998
  ident: 10.1016/j.camwa.2007.05.002_b2
  article-title: Optimality criteria in mathematical programming involving generalized invexity
  publication-title: Journal of Mathematical Analysis and Applications
  doi: 10.1016/0022-247X(88)90313-7
– volume: 41
  start-page: 451
  year: 1983
  ident: 10.1016/j.camwa.2007.05.002_b15
  article-title: Weak Pareto-optimal necessary conditions in a nondifferential multiobjective program on a Banach space
  publication-title: Journal of Optimization Theory and Applications
  doi: 10.1007/BF00935364
– year: 1995
  ident: 10.1016/j.camwa.2007.05.002_b17
– volume: 52
  start-page: 81
  year: 2006
  ident: 10.1016/j.camwa.2007.05.002_b6
  article-title: Sufficiency and duality in nonsmooth multiobjective optimization involving generalized (F,α,ρ,d)-Type I functions
  publication-title: Computers and Mathematics with Applications
  doi: 10.1016/j.camwa.2006.08.006
– volume: 26
  start-page: 277
  year: 1992
  ident: 10.1016/j.camwa.2007.05.002_b13
  article-title: Lagrange multipliers for Pareto nonsmooth programming problems in Banach spaces
  publication-title: Optimization
  doi: 10.1080/02331939208843857
SSID ssj0004320
Score 1.8775922
Snippet In this paper, we consider a vector optimization problem where all functions involved are defined on Banach spaces. New classes of generalized type-I functions...
SourceID proquest
crossref
elsevier
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 1403
SubjectTerms Banach space
Convexity
Duality
Generalized convexity
Mathematical analysis
Mathematical models
Optimality conditions
Optimization
Type-I functions
Vector optimization
Vectors (mathematics)
Title Some vector optimization problems in Banach spaces with generalized convexity
URI https://dx.doi.org/10.1016/j.camwa.2007.05.002
https://www.proquest.com/docview/1082192981
https://www.proquest.com/docview/31020048
Volume 54
WOSCitedRecordID wos000251461000010&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: 1873-7668
  dateEnd: 20180131
  omitProxy: false
  ssIdentifier: ssj0004320
  issn: 0898-1221
  databaseCode: AIEXJ
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1bb9MwFLag44GXcRcdNyOxpxKpdS62H7fRClApSARUnqwkdlCmNe3WdlT8eo5vaQZsGg9IVVRFTqLm-3p8fHzOdxB6xRmn4HmrIJSsCLT6SJBHWRhkeclUPyGZMp3nvo7pZMKmU_7JpTUvTTsBWtdss-GL_wo1nAOwdensP8Dd3BROwHcAHY4AOxyvBfzn-Uz1zk0wvjcHgzBzlZY91zvGJMAeZrUupAJzojOyTDD2uxWgrn4qaXPRN9Xqwp6vbwCxNHSZNXqvvkCutRVu5J8uxhm-rU0IvkkAqtbbwKuPOtBWBoczThxWn8RWN3tLauWgPWMGgUuQtqZRCwO2plmdX_pXE26jCcewPJ_9yJzGpIl7bWcsv0s_-ShGX8ZjkQ6n6X44WpwGupuY3nXfD99YZG-iHUJjzjpo5-DdcPp-WzMbWslO_zu8IpXJ_fvj2Zd5Lb_N38YpSe-iXbeawAeWBffQDVXfR3c8UNgZ7gfogyYFtqTAbVJgTwpc1diSAltSYA0qbpECN6R4iNLRMD16G7hGGkERJnQVJGUSKyI5uM5hpApWkESxRIL7lsc8V0SB3c8JgwGFHEgKSxjGY5gmIxgUlSx8hDr1vFaPEc500JyWGY2JjLKyzHkhZS5VKHP49KMuIv49icKJzOteJyfCZxMeC_NydftTKvqxgJfbRa-bixZWY-Xq4YkHQDg30bp_Aih09YUvPVwCjKjeGctqNV8vtUouzNyEs0EXvbhkDKyDtJlhe9e4yxN0e_uneYo6q7O1eoZuFeerann23FHxF93Pn64
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=Some+vector+optimization+problems+in+Banach+spaces+with+generalized+convexity&rft.jtitle=Computers+%26+mathematics+with+applications+%281987%29&rft.au=Yu%2C+G&rft.au=Liu%2C+S&rft.date=2007-12-01&rft.issn=0898-1221&rft.volume=54&rft.issue=11-12&rft.spage=1403&rft.epage=1410&rft_id=info:doi/10.1016%2Fj.camwa.2007.05.002&rft.externalDBID=NO_FULL_TEXT
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0898-1221&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0898-1221&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0898-1221&client=summon