An extended Kuhn–Tucker approach for linear bilevel programming
Kuhn–Tucker approach has been applied with remarkable success in linear bilevel programming (BLP). However, it still has some extent unsatisfactory and incomplete. One principle challenges is that it could not well handle a linear BLP problem when the constraint functions at the upper-level are of a...
Uložené v:
| Vydané v: | Applied mathematics and computation Ročník 162; číslo 1; s. 51 - 63 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
New York, NY
Elsevier Inc
04.03.2005
Elsevier |
| Predmet: | |
| ISSN: | 0096-3003, 1873-5649 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | Kuhn–Tucker approach has been applied with remarkable success in linear bilevel programming (BLP). However, it still has some extent unsatisfactory and incomplete. One principle challenges is that it could not well handle a linear BLP problem when the constraint functions at the upper-level are of arbitrary linear form. This paper describes theoretical foundation of Kuhn–Tucker approach and proposes an extended Kuhn–Tucker approach to deal with the problem. The results have demonstrated that the extended Kuhn–Tucker approach can solve a wider class of linear BLP problems can than current capabilities permit. |
|---|---|
| AbstractList | Kuhn–Tucker approach has been applied with remarkable success in linear bilevel programming (BLP). However, it still has some extent unsatisfactory and incomplete. One principle challenges is that it could not well handle a linear BLP problem when the constraint functions at the upper-level are of arbitrary linear form. This paper describes theoretical foundation of Kuhn–Tucker approach and proposes an extended Kuhn–Tucker approach to deal with the problem. The results have demonstrated that the extended Kuhn–Tucker approach can solve a wider class of linear BLP problems can than current capabilities permit. |
| Author | Shi, Chenggen Lu, Jie Zhang, Guangquan |
| Author_xml | – sequence: 1 givenname: Chenggen surname: Shi fullname: Shi, Chenggen email: cshi@it.uts.edu.au – sequence: 2 givenname: Jie surname: Lu fullname: Lu, Jie email: jielu@it.uts.edu.au – sequence: 3 givenname: Guangquan surname: Zhang fullname: Zhang, Guangquan email: zhangg@it.uts.edu.au |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=16530287$$DView record in Pascal Francis |
| BookMark | eNp9kL1OwzAUhS0EEm3hAdiyMCb4J40dMVUVf6ISS5kt5-amdUmcyE4r2HgH3pAnIVWRkBg63eGc70rnG5NT1zok5IrRhFGW3WwS00DCKRUJ4wlV-QkZMSVFPM3S_JSMKM2zWAzxORmHsKGUyoylIzKbuQjfe3QlltHzdu2-P7-WW3hDH5mu862BdVS1PqqtQ-Ojwta4wzoakpU3TWPd6oKcVaYOePl7J-T1_m45f4wXLw9P89kiBsFlH0teVShEiQI4gASWFSrjILnguUi5EEWpCgAlU8UrUTBApLLgBZsqJQ1HMSHXh7-dCWDqyhsHNujO28b4D82yqaB8WDwh7NAD34bgsfqrUL13pTd6cKX3rjTjenA1MPIfA7Y3vW1d742tj5K3BxKH6TuLXgew6ABL6xF6Xbb2CP0DoCqGhA |
| CODEN | AMHCBQ |
| CitedBy_id | crossref_primary_10_1089_omi_2010_0070 crossref_primary_10_1007_s11044_024_09969_1 crossref_primary_10_1016_j_swevo_2018_06_004 crossref_primary_10_1007_s00170_023_11102_z crossref_primary_10_1109_TCAD_2024_3467220 crossref_primary_10_1007_s12046_020_01486_z crossref_primary_10_1016_j_eswa_2007_09_011 crossref_primary_10_1109_TEVC_2017_2712906 crossref_primary_10_1016_j_amc_2004_06_047 crossref_primary_10_1049_ein2_12004 crossref_primary_10_1108_17410390710725760 crossref_primary_10_1109_TSTE_2021_3084211 crossref_primary_10_1016_j_amc_2005_12_039 crossref_primary_10_1016_j_jclepro_2018_12_236 crossref_primary_10_1016_j_amc_2015_06_025 crossref_primary_10_1007_s10994_023_06329_6 crossref_primary_10_1109_TII_2018_2867878 crossref_primary_10_1111_coin_12008 crossref_primary_10_1051_e3sconf_202125303005 crossref_primary_10_2166_ws_2018_165 crossref_primary_10_1016_j_knosys_2018_05_022 crossref_primary_10_1016_j_amc_2005_11_134 crossref_primary_10_1016_j_eswa_2012_01_185 crossref_primary_10_1016_j_tre_2018_04_014 crossref_primary_10_1142_S021759591750035X crossref_primary_10_4018_ijsds_2013100104 crossref_primary_10_1142_S021759591250011X crossref_primary_10_3390_su9020251 crossref_primary_10_1080_0305215X_2021_1895991 crossref_primary_10_1016_j_amc_2006_01_043 crossref_primary_10_1016_j_knosys_2007_01_003 crossref_primary_10_1007_s12665_016_5483_y crossref_primary_10_1016_j_amc_2011_01_066 crossref_primary_10_1016_j_ins_2016_08_022 crossref_primary_10_1177_02783649251353181 crossref_primary_10_1080_01605682_2019_1590132 crossref_primary_10_1007_s10489_020_02003_9 crossref_primary_10_1016_j_ecolind_2023_110334 crossref_primary_10_3233_JIFS_169213 crossref_primary_10_1137_23M1566753 crossref_primary_10_1007_s10898_004_7739_4 crossref_primary_10_1109_TRO_2024_3386390 crossref_primary_10_1109_TPWRS_2008_922573 crossref_primary_10_1007_s12597_009_0011_4 crossref_primary_10_1016_j_jenvman_2015_06_036 crossref_primary_10_1287_opre_2017_1589 crossref_primary_10_1016_j_amc_2007_05_004 crossref_primary_10_1109_TCYB_2024_3492075 crossref_primary_10_1016_j_omega_2016_09_008 crossref_primary_10_1016_j_endm_2010_05_075 crossref_primary_10_1007_s11276_016_1360_6 crossref_primary_10_1007_s13042_012_0145_1 crossref_primary_10_1049_iet_gtd_2015_1344 crossref_primary_10_1016_j_cie_2016_11_004 crossref_primary_10_1016_j_amc_2006_11_176 |
| Cites_doi | 10.1137/0913069 10.1016/j.amc.2003.10.031 10.1109/TSMC.1981.4308712 10.1016/0305-0548(82)90006-5 10.1016/0305-0548(82)90007-7 10.1287/mnsc.30.8.1004 10.1007/BF01096412 |
| ContentType | Journal Article |
| Copyright | 2004 Elsevier Inc. 2005 INIST-CNRS |
| Copyright_xml | – notice: 2004 Elsevier Inc. – notice: 2005 INIST-CNRS |
| DBID | AAYXX CITATION IQODW |
| DOI | 10.1016/j.amc.2003.12.089 |
| DatabaseName | CrossRef Pascal-Francis |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1873-5649 |
| EndPage | 63 |
| ExternalDocumentID | 16530287 10_1016_j_amc_2003_12_089 S0096300304000554 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 1B1 1RT 1~. 1~5 23M 4.4 457 4G. 5GY 5VS 6J9 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABEFU ABFNM ABFRF ABJNI ABMAC ABXDB ABYKQ ACAZW ACDAQ ACGFO ACGFS ACRLP ADBBV ADEZE ADGUI ADIYS ADMUD AEBSH AEFWE AEKER AENEX AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AI. AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CS3 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HLZ HMJ HVGLF HZ~ IHE J1W KOM LG9 M26 M41 MHUIS MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ RXW SBC SDF SDG SES SEW SME SPC SPCBC SSW SSZ T5K TAE TN5 VH1 VOH WH7 WUQ X6Y XPP ZMT ~02 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH |
| ID | FETCH-LOGICAL-c327t-72ffe33de3c2cc7c16b862c7232934233bd8bcc87482f3b1cee07b2b15887a2e3 |
| ISICitedReferencesCount | 126 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000226859900006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0096-3003 |
| IngestDate | Mon Jul 21 09:13:35 EDT 2025 Sat Nov 29 02:46:04 EST 2025 Tue Nov 18 21:22:31 EST 2025 Fri Feb 23 02:29:03 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | Kuhn–Tucker conditions Decision-making Linear bilevel programming Optimization Von Stackelberg game Numerical analysis Applied mathematics Decision making Optimization method Linear programming Kuhn-Tucker conditions Constrained optimization Mathematical programming |
| Language | English |
| License | https://www.elsevier.com/tdm/userlicense/1.0 CC BY 4.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c327t-72ffe33de3c2cc7c16b862c7232934233bd8bcc87482f3b1cee07b2b15887a2e3 |
| PageCount | 13 |
| ParticipantIDs | pascalfrancis_primary_16530287 crossref_primary_10_1016_j_amc_2003_12_089 crossref_citationtrail_10_1016_j_amc_2003_12_089 elsevier_sciencedirect_doi_10_1016_j_amc_2003_12_089 |
| PublicationCentury | 2000 |
| PublicationDate | 2005-03-04 |
| PublicationDateYYYYMMDD | 2005-03-04 |
| PublicationDate_xml | – month: 03 year: 2005 text: 2005-03-04 day: 04 |
| PublicationDecade | 2000 |
| PublicationPlace | New York, NY |
| PublicationPlace_xml | – name: New York, NY |
| PublicationTitle | Applied mathematics and computation |
| PublicationYear | 2005 |
| Publisher | Elsevier Inc Elsevier |
| Publisher_xml | – name: Elsevier Inc – name: Elsevier |
| References | Hansen, Jaumard, Savard (BIB7) 1992; 13 W. Bialas, M. Karwan, J. Shaw, A parametric complementary pivot approach for two-level linear programming, Technical Report 80-2, Operations Research Program, State University of New York at Buffalo, 1978 C. Shi, G. Zhang, J. Lu, On the definition of linear bilevel programming solution, Applied Mathematics and Computation, in press Bard (BIB1) 1998 W. Bialas, M. Karwan, Multilevel linear programming, Technical Report 78-1, Operations Research Program, State University of New York at Buffalo, 1978 University of Cambridge, 2001. Available from Bard, Falk (BIB5) 1982; 9 Aiyoshi, Shimizu (BIB9) 1981; 11 White, Anandalingam (BIB10) 1993; 3 Von Stackelberg (BIB2) 1952 Candler, Townsley (BIB3) 1982; 9 Bialas, Karwan (BIB4) 1984; 30 > 10.1016/j.amc.2003.12.089_BIB12 Aiyoshi (10.1016/j.amc.2003.12.089_BIB9) 1981; 11 10.1016/j.amc.2003.12.089_BIB11 Bard (10.1016/j.amc.2003.12.089_BIB5) 1982; 9 Candler (10.1016/j.amc.2003.12.089_BIB3) 1982; 9 Von Stackelberg (10.1016/j.amc.2003.12.089_BIB2) 1952 White (10.1016/j.amc.2003.12.089_BIB10) 1993; 3 10.1016/j.amc.2003.12.089_BIB6 Bialas (10.1016/j.amc.2003.12.089_BIB4) 1984; 30 Hansen (10.1016/j.amc.2003.12.089_BIB7) 1992; 13 Bard (10.1016/j.amc.2003.12.089_BIB1) 1998 10.1016/j.amc.2003.12.089_BIB8 |
| References_xml | – volume: 9 start-page: 59 year: 1982 end-page: 76 ident: BIB3 article-title: A linear two-level programming problem publication-title: Computers and Operations Research – year: 1952 ident: BIB2 article-title: The Theory of the Market Economy – volume: 3 start-page: 397 year: 1993 end-page: 419 ident: BIB10 article-title: A penalty function approach for solving bi-level linear programs publication-title: Journal of Global Optimization – reference: W. Bialas, M. Karwan, J. Shaw, A parametric complementary pivot approach for two-level linear programming, Technical Report 80-2, Operations Research Program, State University of New York at Buffalo, 1978 – reference: C. Shi, G. Zhang, J. Lu, On the definition of linear bilevel programming solution, Applied Mathematics and Computation, in press – volume: 13 start-page: 1194 year: 1992 end-page: 1217 ident: BIB7 article-title: An extended branch-and-bound rules for linear bilevel programming publication-title: SIAM Journal on Scientific and Statistical Computing – reference: W. Bialas, M. Karwan, Multilevel linear programming, Technical Report 78-1, Operations Research Program, State University of New York at Buffalo, 1978 – reference: > – volume: 9 start-page: 77 year: 1982 end-page: 100 ident: BIB5 article-title: An explicit solution to the multi-level programming problem publication-title: Computers and Operations Research – volume: 11 start-page: 444 year: 1981 end-page: 449 ident: BIB9 article-title: Hierarchical decentralized systems and its new solution by a barrier method publication-title: IEEE Transactions on Systems, Man, and Cybernetics – year: 1998 ident: BIB1 article-title: Practical Bilevel Optimization: Algorithms and Applications – volume: 30 start-page: 1004 year: 1984 end-page: 1020 ident: BIB4 article-title: Two-level linear programming publication-title: Management Science – reference: University of Cambridge, 2001. Available from < – volume: 13 start-page: 1194 year: 1992 ident: 10.1016/j.amc.2003.12.089_BIB7 article-title: An extended branch-and-bound rules for linear bilevel programming publication-title: SIAM Journal on Scientific and Statistical Computing doi: 10.1137/0913069 – ident: 10.1016/j.amc.2003.12.089_BIB11 – ident: 10.1016/j.amc.2003.12.089_BIB12 doi: 10.1016/j.amc.2003.10.031 – year: 1998 ident: 10.1016/j.amc.2003.12.089_BIB1 – volume: 11 start-page: 444 year: 1981 ident: 10.1016/j.amc.2003.12.089_BIB9 article-title: Hierarchical decentralized systems and its new solution by a barrier method publication-title: IEEE Transactions on Systems, Man, and Cybernetics doi: 10.1109/TSMC.1981.4308712 – ident: 10.1016/j.amc.2003.12.089_BIB6 – ident: 10.1016/j.amc.2003.12.089_BIB8 – year: 1952 ident: 10.1016/j.amc.2003.12.089_BIB2 – volume: 9 start-page: 59 year: 1982 ident: 10.1016/j.amc.2003.12.089_BIB3 article-title: A linear two-level programming problem publication-title: Computers and Operations Research doi: 10.1016/0305-0548(82)90006-5 – volume: 9 start-page: 77 year: 1982 ident: 10.1016/j.amc.2003.12.089_BIB5 article-title: An explicit solution to the multi-level programming problem publication-title: Computers and Operations Research doi: 10.1016/0305-0548(82)90007-7 – volume: 30 start-page: 1004 year: 1984 ident: 10.1016/j.amc.2003.12.089_BIB4 article-title: Two-level linear programming publication-title: Management Science doi: 10.1287/mnsc.30.8.1004 – volume: 3 start-page: 397 year: 1993 ident: 10.1016/j.amc.2003.12.089_BIB10 article-title: A penalty function approach for solving bi-level linear programs publication-title: Journal of Global Optimization doi: 10.1007/BF01096412 |
| SSID | ssj0007614 |
| Score | 2.0947268 |
| Snippet | Kuhn–Tucker approach has been applied with remarkable success in linear bilevel programming (BLP). However, it still has some extent unsatisfactory and... |
| SourceID | pascalfrancis crossref elsevier |
| SourceType | Index Database Enrichment Source Publisher |
| StartPage | 51 |
| SubjectTerms | Calculus of variations and optimal control Decision-making Exact sciences and technology Global analysis, analysis on manifolds Kuhn–Tucker conditions Linear bilevel programming Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming, optimization and calculus of variations Optimization Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Von Stackelberg game |
| Title | An extended Kuhn–Tucker approach for linear bilevel programming |
| URI | https://dx.doi.org/10.1016/j.amc.2003.12.089 |
| Volume | 162 |
| WOSCitedRecordID | wos000226859900006&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: 1873-5649 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0007614 issn: 0096-3003 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwELZgywGEKl4VhVLlwIlVUGIncXKMqqKWR4VEkfYW2Y69bdU1y-6m6pH_wD_klzB-ZXdbtaIHLlEUbZxs5svMePL5G4TeJm0G8zXZxqJSKs7ShMUskSJuZc45azOFObfNJujRUTkaVV99KXtu2wlQrcvLy2r6X00Nx8DYZunsHczdDwoHYB-MDlswO2z_yfC1ke13le3hp-5EBzoDcRSKXkXcEgxNkslmQw6-4UKeB7bWJMSzIE_rU9VJr_E6D-vhpt36t_xvtknwcO9E6vF4uczsc2fhctrDqC9UA0b1-GfnQRrqD7klYGWrPrUy7LmErPnUAl8Dj_OQXl7WxVrn2655cVdQOHvPJlZkktiCres0tK6YfSWS9fzCQF07a2AI02mTNCluYIj7aAPTvCoHaKM-3B997IM2LZwMfPgz4QO4pQJeuY-bUpjHUzaHF0u5jigracrxE7Tp5xdR7XDxFN2T-hl69GVpuOeornUUEBIZhPz59dthIwrYiAAbkcNG5LERrWDjBfr-Yf947yD2nTRiQTBdxBQrJQlpJRFYCCrSgsNMVlBIpysjAUl4W3IhSpqVWBGeQuaUUI55mkMMYliSLTTQP7R8iSKVtyoxEkxMqIwpWlaCwPC8kIxmsk22URIeTiO8zLzpdnLe3GiUbfSuP2XqNFZu-3EWnnjjk0SX_DWAnttO212zzvJChembVdJXd7mJ1-jh8lXYQYPFrJNv0ANxsTidz3Y9tv4CojeUZw |
| 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=An+extended+Kuhn%E2%80%93Tucker+approach+for+linear+bilevel+programming&rft.jtitle=Applied+mathematics+and+computation&rft.au=Shi%2C+Chenggen&rft.au=Lu%2C+Jie&rft.au=Zhang%2C+Guangquan&rft.date=2005-03-04&rft.issn=0096-3003&rft.volume=162&rft.issue=1&rft.spage=51&rft.epage=63&rft_id=info:doi/10.1016%2Fj.amc.2003.12.089&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_amc_2003_12_089 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0096-3003&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0096-3003&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0096-3003&client=summon |