Convex Parametric Programming in Abstract Spaces

This article studies stability and optimality for convex parametric programming models in abstract spaces. Necessary conditions for continuity of the feasible set mapping are given in complete metric spaces. This continuity is characterized for models in which the space of decision variables is refl...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Optimization Jg. 51; H. 6; S. 841 - 861
Hauptverfasser: Asgharian, M., Zlobec, S.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Taylor & Francis Group 01.12.2002
Schlagworte:
Infinite-dimensional Parametric Programming
Optimality
Stability
ISSN:0233-1934, 1029-4945
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Abstract This article studies stability and optimality for convex parametric programming models in abstract spaces. Necessary conditions for continuity of the feasible set mapping are given in complete metric spaces. This continuity is characterized for models in which the space of decision variables is reflexive Banach space. The main result on optimality characterizes locally optimal parameters relative to stable perturbations of the parameter. The result is stated in terms of the existence of a saddle-point for a Lagrangian that uses a finite Borel measure. It does not hold for unstable perturbations even if the model is finite dimensional. The results are applicable to various formulations of control and optimal control problems.
AbstractList This article studies stability and optimality for convex parametric programming models in abstract spaces. Necessary conditions for continuity of the feasible set mapping are given in complete metric spaces. This continuity is characterized for models in which the space of decision variables is reflexive Banach space. The main result on optimality characterizes locally optimal parameters relative to stable perturbations of the parameter. The result is stated in terms of the existence of a saddle-point for a Lagrangian that uses a finite Borel measure. It does not hold for unstable perturbations even if the model is finite dimensional. The results are applicable to various formulations of control and optimal control problems.
Author Zlobec, S.
Asgharian, M.
Author_xml – sequence: 1
  givenname: M.
  surname: Asgharian
  fullname: Asgharian, M.
  organization: Department of Mathematics and Statistics , McGill University
– sequence: 2
  givenname: S.
  surname: Zlobec
  fullname: Zlobec, S.
  organization: Department of Mathematics and Statistics , McGill University
BookMark eNqFj89KAzEQh4NUsK0-gZd9gdX82XQ3F6EUtULBgnpeJtmkRHaTkgRt394Ue5Ji5zIMfN_M_CZo5LzTCN0SfEdwg-8xZYwIhinBuQifcXGBxgRTUVai4iM0PhBlRqorNInxE2d0RqsxwgvvvvSuWEOAQadgVbEOfpOHwbpNYV0xlzEFUKl424LS8RpdGuijvjn2Kfp4enxfLMvV6_PLYr4qFeM0lVLyCjQYwrgwUnBDmk7KGVY1YaLDNQDtmhpEpg3BIGotKRbCaJGRJmtTJH73quBjDNq0yiZI1rv8je1bgttD9PZE9OyyP-422AHC_ox1vGid8WGAbx_6rk2w730wAZyy8ZTXpl3K7sNZl_13_AdhDYJs
CitedBy_id crossref_primary_10_1023_B_JOGO_0000035004_66019_3b
Cites_doi 10.1007/BF01279450
10.1080/02331939908844440
10.1080/02331939508844056
10.1007/BF01442543
10.1017/S0334270000006275
10.1080/02331939408843924
10.1137/1015073
10.1007/978-3-642-46564-2
10.1080/01621459.1996.10477003
10.1137/1036001
10.1080/02331889808802623
10.1007/978-1-4615-0011-7
10.1007/BF02591721
10.1007/978-1-4757-4286-2
10.1137/1035089
10.1070/RM1995v050n05ABEH002618
10.1007/BF00047497
10.1007/978-1-4613-0307-7_14
10.1007/978-3-0348-6328-5
ContentType Journal Article
Copyright Copyright Taylor & Francis Group, LLC 2002
Copyright_xml – notice: Copyright Taylor & Francis Group, LLC 2002
DBID AAYXX
CITATION
DOI 10.1080/0233193021000015659
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 1029-4945
EndPage 861
ExternalDocumentID 10_1080_0233193021000015659
10085864
GroupedDBID .7F
.DC
.QJ
0BK
0R~
123
29N
30N
4.4
5VS
AAENE
AAGDL
AAHIA
AAJMT
AALDU
AAMIU
AAPUL
AAQRR
ABCCY
ABFIM
ABHAV
ABJNI
ABLIJ
ABPAQ
ABPEM
ABTAI
ABXUL
ABXYU
ACAGQ
ACGEJ
ACGFS
ACIWK
ACTIO
ADCVX
ADGTB
ADXPE
AEISY
AENEX
AEOZL
AEPSL
AEYOC
AFKVX
AFRVT
AGDLA
AGMYJ
AGROQ
AHDZW
AHMOU
AIJEM
AIYEW
AJWEG
AKBVH
AKOOK
ALCKM
ALMA_UNASSIGNED_HOLDINGS
ALQZU
AMEWO
AQRUH
AQTUD
AVBZW
AWYRJ
BLEHA
CAG
CCCUG
CE4
COF
CRFIH
CS3
DKSSO
DMQIW
DU5
EBS
EJD
E~A
E~B
GTTXZ
H13
HZ~
H~P
IPNFZ
J.P
KYCEM
M4Z
NA5
O9-
P2P
PQQKQ
QCRFL
RIG
RNANH
ROSJB
RTWRZ
S-T
SNACF
TASJS
TBQAZ
TDBHL
TEJ
TFL
TFT
TFW
TOXWX
TTHFI
TUROJ
TWF
UT5
UU3
ZGOLN
~S~
07G
1TA
AAIKQ
AAKBW
AAYXX
ACGEE
ACTCW
AEUMN
AGCQS
AGLEN
AMVHM
AMXXU
BCCOT
BPLKW
C06
CITATION
DWIFK
HF~
IVXBP
LJTGL
NUSFT
TAQ
TFMCV
UB9
UU8
V3K
V4Q
ID FETCH-LOGICAL-c352t-bb54aeaf1359fb95f18dbb60c7139d07aa2d87a9c35f10a97eb2099fe90c78f13
IEDL.DBID TFW
ISICitedReferencesCount 1
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000179887500004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0233-1934
IngestDate Tue Nov 18 21:46:27 EST 2025
Sat Nov 29 06:01:34 EST 2025
Mon Oct 20 23:43:13 EDT 2025
Mon May 13 12:09:11 EDT 2019
IsPeerReviewed true
IsScholarly true
Issue 6
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c352t-bb54aeaf1359fb95f18dbb60c7139d07aa2d87a9c35f10a97eb2099fe90c78f13
PageCount 21
ParticipantIDs crossref_primary_10_1080_0233193021000015659
crossref_citationtrail_10_1080_0233193021000015659
informaworld_taylorfrancis_310_1080_0233193021000015659
PublicationCentury 2000
PublicationDate 2002-12-01
PublicationDateYYYYMMDD 2002-12-01
PublicationDate_xml – month: 12
  year: 2002
  text: 2002-12-01
  day: 01
PublicationDecade 2000
PublicationTitle Optimization
PublicationYear 2002
Publisher Taylor & Francis Group
Publisher_xml – name: Taylor & Francis Group
References Brosowski B. (CIT0009) 1982
CIT0030
Sethi S.P. (CIT0023) 1978; 6
Aubinand J.P. (CIT0004) 1984
CIT0010
Connorsand M.M. (CIT0011) 1967
CIT0032
Zlobec S. (CIT0031) 2001
Berger J.O. (CIT0007) 1985
Hilland E. (CIT0017) 1975
Kirnand H.O. (CIT0020) 1999; 4
Bensoussan A. (CIT0006) 1978; 9
CIT0014
Zlobec S. (CIT0033) 2001
CIT0035
CIT0016
CIT0015
CIT0018
Lignolaand M.B. (CIT0021) 1998
Kassand R.E. (CIT0019) 1996; 91
Andersonand E.J. (CIT0002) 1985; 259
Andersenand E.J. (CIT0001) 1987
CIT0003
Bank B. (CIT0005) 1982
Fiaccoand A.V. (CIT0013) 1983; 215
Lopez M.A. (CIT0022) 2000
CIT0024
Tikhonovand A.N. (CIT0025) 1977
CIT0027
Zlobec S. (CIT0034) 1982; 73
Deutsch F. (CIT0012) 1988; 40
CIT0026
CIT0029
Beyko T. (CIT0008) 2000
CIT0028
References_xml – volume: 6
  start-page: 33
  year: 1978
  ident: CIT0023
  publication-title: A Survey of Management Science Applications of the Deterministic Maximum Principle
– ident: CIT0029
  doi: 10.1007/BF01279450
– ident: CIT0030
  doi: 10.1080/02331939908844440
– volume-title: Optimal Control of Dynamic Operations Research Models
  year: 1967
  ident: CIT0011
– ident: CIT0015
  doi: 10.1080/02331939508844056
– volume: 73
  start-page: 69
  volume-title: Mathematical Programming with Data perturbations, Lecture Notes in Pure and Applied Mathematics
  year: 1982
  ident: CIT0034
– ident: CIT0035
  doi: 10.1007/BF01442543
– volume-title: Solutions of Ill-posed Problems
  year: 1977
  ident: CIT0025
– ident: CIT0026
  doi: 10.1017/S0334270000006275
– ident: CIT0014
  doi: 10.1080/02331939408843924
– volume: 40
  start-page: 213
  year: 1988
  ident: CIT0012
  publication-title: Duke Mathematical Journal
– start-page: 57
  volume-title: Encyclopaedia of Optimization
  year: 2001
  ident: CIT0031
– volume: 9
  volume-title: Applied Optimal Control, Studies in the Management Sciences
  year: 1978
  ident: CIT0006
– volume: 215
  volume-title: Semi-infinite programming and applications, proceedings of the international symposium held in Austin, 1981
  year: 1983
  ident: CIT0013
– volume-title: Functional Analysis and Semi-groups
  year: 1975
  ident: CIT0017
– ident: CIT0018
  doi: 10.1137/1015073
– volume-title: Stability and interior-point Methods
  year: 2000
  ident: CIT0008
– volume-title: Parametric Semi-infinite Optimization
  year: 1982
  ident: CIT0009
– volume: 259
  volume-title: Infinite programming, proceedings of the international symposium on infinite-dimensional linear programming held at Churchill College
  year: 1985
  ident: CIT0002
  doi: 10.1007/978-3-642-46564-2
– volume: 91
  start-page: 1343
  year: 1996
  ident: CIT0019
  publication-title: JASA
  doi: 10.1080/01621459.1996.10477003
– volume-title: Applied Nonlinear Analysis
  year: 1984
  ident: CIT0004
– ident: CIT0024
  doi: 10.1137/1036001
– volume: 4
  start-page: 222
  year: 1999
  ident: CIT0020
  publication-title: Applied and Computational Harmonic Analysis
– ident: CIT0003
  doi: 10.1080/02331889808802623
– volume-title: Stable parametric programming
  year: 2001
  ident: CIT0033
  doi: 10.1007/978-1-4615-0011-7
– ident: CIT0027
  doi: 10.1007/BF02591721
– year: 2000
  ident: CIT0022
  publication-title: Linear Algebra and Its Applications
– volume-title: Statistical Decision Theory and Bayesian Analysis
  year: 1985
  ident: CIT0007
  doi: 10.1007/978-1-4757-4286-2
– ident: CIT0016
  doi: 10.1137/1035089
– ident: CIT0010
  doi: 10.1070/RM1995v050n05ABEH002618
– volume-title: Linear Programming in Infinite-dimensional Spaces
  year: 1987
  ident: CIT0001
– ident: CIT0028
  doi: 10.1007/BF00047497
– ident: CIT0032
  doi: 10.1007/978-1-4615-0011-7
– start-page: 315
  volume-title: Multilevel Optimization: Algorithms and Applications
  year: 1998
  ident: CIT0021
  doi: 10.1007/978-1-4613-0307-7_14
– volume-title: Nonlinear Parametric Optimization
  year: 1982
  ident: CIT0005
  doi: 10.1007/978-3-0348-6328-5
SSID ssj0021624
Score 1.5688888
Snippet This article studies stability and optimality for convex parametric programming models in abstract spaces. Necessary conditions for continuity of the feasible...
SourceID crossref
informaworld
SourceType Enrichment Source
Index Database
Publisher
StartPage 841
SubjectTerms Infinite-dimensional Parametric Programming
Optimality
Stability
Title Convex Parametric Programming in Abstract Spaces
URI https://www.tandfonline.com/doi/abs/10.1080/0233193021000015659
Volume 51
WOSCitedRecordID wos000179887500004&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 Journals Complete
  customDbUrl:
  eissn: 1029-4945
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0021624
  issn: 0233-1934
  databaseCode: TFW
  dateStart: 19850101
  isFulltext: true
  titleUrlDefault: https://www.tandfonline.com
  providerName: Taylor & Francis
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3NS8MwFH-IeNCD3-L8IgePBpt2TZvjGA4PMgZO3a0kaQIDrWOLsj_fl36MDccOeu57bUle-z745fcDuOXCcqGikOpQpNigJDlVOdfUGmEVN5bl5cDt9Snp99PRSAxqndNZDav0PbStiCLKf7X_uKWaNYi4e0wzGDiR71aqo8CxP8CHid8rGAx7b4uGi_FS1NbbU3RoN6xD6--xkplWeEuXMk7v4N_vegj7dbFJOlV0HMGWKY5hb4mC8ASCroedz8lAepSWp-sngwqy9YHXybggHeWnIdqR54mHb53CS-9h2H2ktYoC1VhcOapU3JZGWhbFuPwitizNleKBxvZU5EEiZZiniRRobVkgRYK9NpaNuFlokqLbGWwXn4U5ByJkbLiOI57quG2lZ3rJlTWJCVNpsP5tQdisYKZrinGvdPGesYaJ9PdytOBu4TSpGDY2m4fLW5O5crBhKxWSdQ6Zm7sWJBucog2Pu_iz5yXsNsoxAbuCbTf9Mtewo7_deDa9KQP1B-cq4Y0
linkProvider Taylor & Francis
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1NS8NAEB20CurBb7F-5uDRYDbpbrLHUiyKtRSs2lvY3exCQWOpUfrznU2akmLpQc_Zl4SdSWbeMPsG4Ipxw7gMfFf5PEKCEiauTJhyjeZGMm1IkhfcXjphtxsNBrxXOcVv2yothzaFUET-r7Yfty1Gly1xNxhn0HMCS1eKs8CUr8IaxUhrfbzffp1RLsLysbYW4CKiUeoOLb7JXGyaUy6txJz2zv_fdhe2p_mm0ywcZA9WdLoPWxUVwgPwWrbzfOL0hG3Usor9Tq_o2nrH684wdZrSFkRU5jyNbAfXITy3b_utO3c6SMFVmF9lrpS0IbQwJKBoAU4NiRIpmaeQofLEC4XwkygUHFcb4gkeIt3GzBHthUsihB1BLf1I9TE4XFDNFA1YpGjDCCv2kkijQ-1HQmMKXAe_3MJYTVXG7bCLt5iUYqS_t6MO1zPQqBDZWL7cr9omzvLahikGkSwCxNkkq0O4BBQsedzJn5GXsHHXf-zEnfvuwylsloNkPHIGtWz8pc9hXX1nw8_xRe61P08p5bg
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8NAEB60iujBt1ifOXg0mEezyR5LNSiWErA-bmGfUNBY2ij9-c7mUVosPeg58yVhd5KZb5j9BuCKUE0o9z1beDRCghJKm0sibK2o5kRpVxYFt5du2OtFb280qeacjqu2SsOhdSkUUfyrzcc9lLruiLvBMIOO4xu2Uh4FDugqrGHiTAz76sevU8blkmKqrQHYiGjVskOLbzIXmuaES2dCTrzz75fdhe0q27TapXvswYrK9mFrRoPwAJyO6TufWAkzbVpGr99Kyp6tD7xuDTKrzU05ROTW09D0bx3Cc3zX79zb1RgFW2B2lducBy2mmHb9ANefBtqNJOfEEchPqXRCxjwZhYyitXYdRkMk25g34m6hSYSwI2hkn5k6BouyQBER-CQSQUszI_UiuVah8iKmMAFuglevYCoqjXEz6uI9dWsp0t_L0YTrKWhYSmwsN_dmtybNi8qGLseQLAKk-SRvQrgE5C953MmfkZewkdzGafeh93gKm_UUGcc9g0Y--lLnsC6-88F4dFH47A-eYeRp
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=Convex+Parametric+Programming+in+Abstract+Spaces&rft.jtitle=Optimization&rft.au=Asgharian%2C+M.&rft.au=Zlobec%2C+S.&rft.date=2002-12-01&rft.issn=0233-1934&rft.eissn=1029-4945&rft.volume=51&rft.issue=6&rft.spage=841&rft.epage=861&rft_id=info:doi/10.1080%2F0233193021000015659&rft.externalDBID=n%2Fa&rft.externalDocID=10_1080_0233193021000015659
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0233-1934&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0233-1934&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0233-1934&client=summon