Optimization and equilibrium problems with equilibrium constraints in infinite-dimensional spaces
The article is devoted to applications of modern variational analysis to the study of constrained optimization and equilibrium problems in infinite-dimensional spaces. We pay a particular attention to the remarkable classes of optimization and equilibrium problems identified as mathematical programs...
Uložené v:
| Vydané v: | Optimization Ročník 57; číslo 5; s. 715 - 741 |
|---|---|
| Hlavný autor: | |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Philadelphia
Taylor & Francis Group
01.01.2008
Taylor & Francis LLC |
| Predmet: | |
| ISSN: | 0233-1934, 1029-4945 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | The article is devoted to applications of modern variational analysis to the study of constrained optimization and equilibrium problems in infinite-dimensional spaces. We pay a particular attention to the remarkable classes of optimization and equilibrium problems identified as mathematical programs with equilibrium constraints (MPECs) and equilibrium problems with equilibrium constraints (EPECs) treated from the viewpoint of multiobjective optimization. Their underlying feature is that the major constraints are governed by parametric generalized equations/variational conditions in the sense of Robinson. Such problems are intrinsically non-smooth and can be handled by using an appropriate machinery of generalized differentiation exhibiting a rich/full calculus. The case of infinite-dimensional spaces is significantly more involved in comparison with finite dimensions, requiring in addition a certain sufficient amount of compactness and an efficient calculus of the corresponding 'sequential normal compactness' (SNC) properties. |
|---|---|
| AbstractList | The article is devoted to applications of modern variational analysis to the study of constrained optimization and equilibrium problems in infinite-dimensional spaces. We pay a particular attention to the remarkable classes of optimization and equilibrium problems identified as mathematical programs with equilibrium constraints (MPECs) and equilibrium problems with equilibrium constraints (EPECs) treated from the viewpoint of multiobjective optimization. Their underlying feature is that the major constraints are governed by parametric generalized equations/variational conditions in the sense of Robinson. Such problems are intrinsically non-smooth and can be handled by using an appropriate machinery of generalized differentiation exhibiting a rich/full calculus. The case of infinite-dimensional spaces is significantly more involved in comparison with finite dimensions, requiring in addition a certain sufficient amount of compactness and an efficient calculus of the corresponding 'sequential normal compactness' (SNC) properties. The article is devoted to applications of modern variational analysis to the study of constrained optimization and equilibrium problems in infinite-dimensional spaces. We pay a particular attention to the remarkable classes of optimization and equilibrium problems identified as mathematical programs with equilibrium constraints (MPECs) and equilibrium problems with equilibrium constraints (EPECs) treated from the viewpoint of multiobjective optimization. Their underlying feature is that the major constraints are governed by parametric generalized equations/variational conditions in the sense of Robinson. Such problems are intrinsically non-smooth and can be handled by using an appropriate machinery of generalized differentiation exhibiting a rich/full calculus. The case of infinite-dimensional spaces is significantly more involved in comparison with finite dimensions, requiring in addition a certain sufficient amount of compactness and an efficient calculus of the corresponding 'sequential normal compactness' (SNC) properties. [PUBLICATION ABSTRACT] |
| Author | Mordukhovich, Boris S. |
| Author_xml | – sequence: 1 givenname: Boris S. surname: Mordukhovich fullname: Mordukhovich, Boris S. email: boris@math.wayne.edu organization: Department of Mathematics , Wayne State University |
| BookMark | eNqNkE1LAzEQhoMo2FZ_gLfF-2qS2a-AFyl-QaGX3kM2m8WU3WSbZKn115taL1pEITCBeZ93Zt4pOjXWKISuCL4huMK3mAIQBvFLIc-B4RM0IZiyNGNZfoom-34aBdk5mnq_xpiSgmYTJJZD0L1-F0FbkwjTJGoz6k7XTo99Mjhbd6r3yVaH128daY0PTmgTfKJNfK02Oqi00b0yPnqJLvGDkMpfoLNWdF5dftUZWj0-rObP6WL59DK_X6QSSghpU-ImaxVAARWjhaohq_K2xg1WBBekIowoCVhIRhVgqMu8bgBLwoqc1ZTCDF0fbOPOm1H5wNd2dHENzylh0SveHkXkIJLOeu9Uywene-F2nGC-z5Ef5RiZ8gcjdfiMa39_9x8ypmNdL7bWdQ0PYtdZ1zphpPbHFA9vIZJ3f5Lw--AP8UOenw |
| CODEN | OPTZDQ |
| CitedBy_id | crossref_primary_10_1007_s40995_019_00683_8 crossref_primary_10_1007_s11117_023_01001_8 crossref_primary_10_15807_jorsj_58_1 crossref_primary_10_1007_s10957_018_1373_7 crossref_primary_10_1016_j_na_2010_04_066 crossref_primary_10_1007_s11117_023_00998_2 |
| Cites_doi | 10.1080/02331930701778759 10.1137/S1052623495284029 10.1023/B:SVAN.0000023398.73288.82 10.1080/1055678042000218966 10.1137/S0363012999352911 10.1007/BFb0120850 10.1287/moor.5.1.43 10.1080/02331930701421079 10.1137/S1052623402414701 10.1287/moor.22.4.977 10.2307/2154809 10.1007/978-1-4757-2825-5 10.1137/S0363012999350821 10.1137/0317019 10.1137/S1052623400377153 10.1016/S0362-546X(03)00126-3 10.1007/s10107-002-0365-3 10.1016/0362-546X(85)90095-1 10.1007/s10107-005-0623-2 10.1007/BFb0120929 10.1287/moor.9.1.87 10.1007/s10107-003-0443-1 10.1080/0233193031000149894 10.1137/0804029 |
| ContentType | Journal Article |
| Copyright | Copyright Taylor & Francis Group, LLC 2008 Copyright Taylor & Francis Group Jan 2008 |
| Copyright_xml | – notice: Copyright Taylor & Francis Group, LLC 2008 – notice: Copyright Taylor & Francis Group Jan 2008 |
| DBID | AAYXX CITATION 7SC 7TB 8FD FR3 H8D JQ2 L7M L~C L~D |
| DOI | 10.1080/02331930802355390 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database Aerospace Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Aerospace Database 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 | Aerospace Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1029-4945 |
| EndPage | 741 |
| ExternalDocumentID | 1597881391 10_1080_02331930802355390 335706 |
| Genre | Feature |
| 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 ACGEJ ACGFS ACIWK ACTCW ACTIO ADCVX ADGTB ADXPE AEISY AENEX AEOZL AEPSL AEYOC AFKVX AFRVT AGCQS AGDLA AGMYJ AHDZW AIJEM AIYEW AJWEG AKBVH AKOOK ALMA_UNASSIGNED_HOLDINGS ALQZU AMVHM AQRUH AQTUD AVBZW AWYRJ BLEHA CAG CCCUG CE4 COF CS3 DKSSO DU5 EBS EJD E~A E~B GTTXZ H13 HZ~ H~P IPNFZ J.P KYCEM M4Z NA5 O9- P2P PQQKQ RIG RNANH ROSJB RTWRZ S-T SNACF TASJS TBQAZ TDBHL TEJ TFL TFT TFW TTHFI TUROJ TWF UT5 UU3 ZGOLN ~S~ 07G 1TA AAIKQ AAKBW AAYXX ACAGQ ACGEE AEUMN AGLEN AGROQ AHMOU ALCKM AMEWO AMXXU BCCOT BPLKW C06 CITATION CRFIH DMQIW DWIFK HF~ IVXBP LJTGL NUSFT QCRFL TAQ TFMCV TOXWX UB9 UU8 V3K V4Q 7SC 7TB 8FD FR3 H8D JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c373t-d70d4fe33638926eb3485fb0d0e10618191ec30ac92e303b75bd30c19659b223 |
| IEDL.DBID | TFW |
| ISICitedReferencesCount | 8 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000260770800010&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 | Wed Aug 13 07:10:23 EDT 2025 Sat Nov 29 06:01:38 EST 2025 Tue Nov 18 22:34:16 EST 2025 Mon May 13 12:09:12 EDT 2019 Mon Oct 20 23:36:37 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c373t-d70d4fe33638926eb3485fb0d0e10618191ec30ac92e303b75bd30c19659b223 |
| Notes | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 |
| PQID | 219485934 |
| PQPubID | 27961 |
| PageCount | 27 |
| ParticipantIDs | crossref_primary_10_1080_02331930802355390 informaworld_taylorfrancis_310_1080_02331930802355390 crossref_citationtrail_10_1080_02331930802355390 proquest_journals_219485934 |
| PublicationCentury | 2000 |
| PublicationDate | 2008-01-01 |
| PublicationDateYYYYMMDD | 2008-01-01 |
| PublicationDate_xml | – month: 01 year: 2008 text: 2008-01-01 day: 01 |
| PublicationDecade | 2000 |
| PublicationPlace | Philadelphia |
| PublicationPlace_xml | – name: Philadelphia |
| PublicationTitle | Optimization |
| PublicationYear | 2008 |
| Publisher | Taylor & Francis Group Taylor & Francis LLC |
| Publisher_xml | – name: Taylor & Francis Group – name: Taylor & Francis LLC |
| References | Mordukhovich BS (CIT0015) 2006; 331 CIT0030 CIT0010 CIT0032 CIT0031 CIT0012 Robinson SM (CIT0024) 1979; 10 Rockafellar RT (CIT0028) 1998; 317 Luo ZQ (CIT0011) 1996 Chen G-Y (CIT0003) 2005; 541 Robinson SM (CIT0026) 1981; 14 CIT0013 CIT0016 Robinson SM (CIT0027) 2003; 97 CIT0018 CIT0017 CIT0019 Phelps RR (CIT0023) 1993; 1364 CIT0020 CIT0001 Outrata JV (CIT0022) 1998 Jahn J (CIT0009) 2004 Mordukhovich BS (CIT0014) 2006; 330 CIT0025 CIT0002 CIT0005 CIT0004 Outrata JV (CIT0021) 2004; 40 CIT0007 CIT0029 CIT0006 CIT0008 |
| References_xml | – ident: CIT0019 doi: 10.1080/02331930701778759 – ident: CIT0005 doi: 10.1137/S1052623495284029 – ident: CIT0012 doi: 10.1023/B:SVAN.0000023398.73288.82 – ident: CIT0013 doi: 10.1080/1055678042000218966 – volume: 1364 volume-title: Lecture Notes in Mathematics year: 1993 ident: CIT0023 – volume: 330 volume-title: Grundlehren Series (Fundamental Principles of Mathematical Sciences) year: 2006 ident: CIT0014 – ident: CIT0020 doi: 10.1137/S0363012999352911 – volume: 10 start-page: 128 year: 1979 ident: CIT0024 publication-title: Math. Prog. Study doi: 10.1007/BFb0120850 – ident: CIT0025 doi: 10.1287/moor.5.1.43 – ident: CIT0017 doi: 10.1080/02331930701421079 – ident: CIT0018 doi: 10.1137/S1052623402414701 – ident: CIT0029 doi: 10.1287/moor.22.4.977 – ident: CIT0010 doi: 10.2307/2154809 – volume: 40 start-page: 585 year: 2004 ident: CIT0021 publication-title: Kybernetika – volume-title: Nonsmooth Approach to Optimization Problems with Equilibrium Constraints year: 1998 ident: CIT0022 doi: 10.1007/978-1-4757-2825-5 – ident: CIT0032 doi: 10.1137/S0363012999350821 – ident: CIT0008 doi: 10.1137/0317019 – volume-title: Mathematical Programs with Equilibrium Constraints year: 1996 ident: CIT0011 – ident: CIT0016 doi: 10.1137/S1052623400377153 – ident: CIT0006 doi: 10.1016/S0362-546X(03)00126-3 – ident: CIT0030 doi: 10.1007/s10107-002-0365-3 – ident: CIT0002 doi: 10.1016/0362-546X(85)90095-1 – volume: 331 volume-title: Grundlehren Series (Fundamental Principles of Mathematical Sciences) year: 2006 ident: CIT0015 – ident: CIT0007 doi: 10.1007/s10107-005-0623-2 – volume: 14 start-page: 206 year: 1981 ident: CIT0026 publication-title: Math. Prog. Study doi: 10.1007/BFb0120929 – ident: CIT0001 doi: 10.1287/moor.9.1.87 – volume: 97 start-page: 245 year: 2003 ident: CIT0027 publication-title: Math. Prog. doi: 10.1007/s10107-003-0443-1 – ident: CIT0004 doi: 10.1080/0233193031000149894 – volume-title: Springer Series in Operations Research year: 2004 ident: CIT0009 – ident: CIT0031 doi: 10.1137/0804029 – volume: 541 volume-title: Vector Optimization. Set-Valued and Variational Analysis. Lecture Notes in Economics and Mathematical Systems year: 2005 ident: CIT0003 – volume: 317 volume-title: Grundlehren Series (Fundamental Principles of Mathematical Sciences) year: 1998 ident: CIT0028 |
| SSID | ssj0021624 |
| Score | 1.7777243 |
| Snippet | The article is devoted to applications of modern variational analysis to the study of constrained optimization and equilibrium problems in infinite-dimensional... |
| SourceID | proquest crossref informaworld |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 715 |
| SubjectTerms | Calculus of variations Comparative analysis Equilibrium equilibrium constraints generalized differentiation infinite-dimensional spaces Mathematical programming necessary optimality conditions non-smooth and multiobjective optimization Optimization Primary: 49J52 Secondary: 90C29 Studies variational analysis |
| Title | Optimization and equilibrium problems with equilibrium constraints in infinite-dimensional spaces |
| URI | https://www.tandfonline.com/doi/abs/10.1080/02331930802355390 https://www.proquest.com/docview/219485934 |
| Volume | 57 |
| WOSCitedRecordID | wos000260770800010&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 and Francis Online Journals 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/eLvHCXMwpV07T8MwELZQxQADb0QpIA9MSBZu7LxGhKgYUGGoRLcosR0pEg3QpBU_nzvHqVqKOoCULX7JOd_d59x9R8i1F2sllM-ZpwLNpO-lcKR4xIwMslj7EehHW7XkKRwOo_E4fnGxOZULq0QMnTdEEVZX4-FOs6qNiLsFMwOCIzBLFKwlgHbQwODVo3yPBq8LuNUPbElbbM2guWz_af42wopVWuEsXdPR1vAM9v-55AOy5zxOeteIyCHZMuUR2V3iITwm6TMojonLyKQwCTWfs8JmA8wm1NWcqSje2a68UehcYo2JuqJFCU9eoAvLNJYMaOg-KGgsUEUnZDR4GN0_Mld7gSkRiprpkGuZGyHQo_ECgNwy8vOMa24QRCLMM0rwVMWeASuYhX6mBVeWnzADl-OUdMr30pwRCv4k5rfmOboDKoNdUIhxAFjqNJKx1yW83fpEOV5yXPpb0m_pS39uXpfcLLp8NKQcmxrz5e-Z1PYmJG_Klqw3T-qvukv8DV3Ehql6rawkThVUCZgEiaRy8vyPo_bIThOkgvc-F6RTT2fmkmyreV1U0ysr89_mgfwp |
| linkProvider | Taylor & Francis |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8NAEB60CurBt1jrIwdPwuI2m-dRxFKxVg8BewvJ7gYKNmqTij_fmTxKa6UHhdyyLza7M_NNZr4BuDR9JYW0OTOlo5hlmxFeKe4xbTmxr2wP5WNRtaTn9vveYOA_Vw63rAqrJAydlEQRhaymy03O6Dok7hr1DJ4cQWmiqC4Rta_Cmo16lkL6gs7LFHC1naKoLTVn2N6q_2r-NsScXppjLV2Q0oXq6ez8d9G7sF0ZncZNeUr2YEWn-7A1Q0V4ANETyo5RlZRp4CyG_pgMi4SAycioys5kBrlt595Isi-pzESeGcMUn2RIVixTVDWgZPwwUGihNDqEoHMX3HZZVX6BSeGKnCmXKyvRQpBRYzqIui3PTmKuuCYcSUhPS8Ej6ZsaFWHs2rESXBYUhTFaHUfQSN9SfQwGmpSU4pokZBHIGHdBEsxBbKkiz_LNJvB670NZUZPT0l_Dds1g-nPzmnA17fJe8nIsa8xnP2iYF86QpKxcstg8zL_yJthLuoglU7XqwxJW0iALUStYxCtnnfxx1AvY6AaPvbB3339owWYZs0JuoFNo5OOJPoN1-ZkPs_F5cQG-AceIAFk |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8NAEB60iujBt1jrIwdPQnCbzfMoalEstYeCvYVkdwMBG2uTij_fmU1SrJUeFHLLvtjMzsy3mfkG4NIKpODCYaYlXGnajhXhkWK-qWw3DqTjo37UVUu6Xq_nD4dBv4rNyauwSsLQSUkUoXU1He6xTOqIuGs0Myg4nLJE0VoiaF-FNU2MheI86LzM8Fbb1TVtqbmJ7e36p-ZvQ8yZpTnS0gUlrS1PZ-efa96F7crlNG5KGdmDFZXtw9Y3IsIDiJ5Rc4yqlEwDJzHU-zTV6QDTkVEVnckNurSdeyPIu6QiE0VupBk-SUo-rCmpZkDJ92GgykJddAiDzv3g9sGsii-Ygnu8MKXHpJ0ozsmlsVzE3LbvJDGTTBGKJJynBGeRCCyFZjD2nFhyJjRBYYw-xxE0srdMHYOBDiUluCYJ-QMixl0QBHIQWcrItwOrCaze-lBUxOS09NewXfOX_ty8JlzNuoxLVo5ljdn37xkW-iokKeuWLDYPi8-iCc6SLnzJVK1aVsJKF-Qh2gSbWOXskz-OegEb_btO2H3sPbVgswxYoTugU2gUk6k6g3XxUaT55FyL_xeR-f7u |
| 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=Optimization+and+equilibrium+problems+with+equilibrium+constraints+in+infinite-dimensional+spaces&rft.jtitle=Optimization&rft.au=Mordukhovich%2C+Boris+S.&rft.date=2008-01-01&rft.pub=Taylor+%26+Francis+Group&rft.issn=0233-1934&rft.eissn=1029-4945&rft.volume=57&rft.issue=5&rft.spage=715&rft.epage=741&rft_id=info:doi/10.1080%2F02331930802355390&rft.externalDocID=335706 |
| 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 |