Approximating Stationary Points of Stochastic Mathematical Programs with Equilibrium Constraints via Sample Averaging
We investigate sample average approximation of a general class of one-stage stochastic mathematical programs with equilibrium constraints. By using graphical convergence of unbounded set-valued mappings, we demonstrate almost sure convergence of a sequence of stationary points of sample average appr...
Gespeichert in:
| Veröffentlicht in: | Set-valued and variational analysis Jg. 19; H. 2; S. 283 - 309 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
01.06.2011
|
| Schlagworte: | |
| ISSN: | 1877-0533, 1877-0541 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | We investigate sample average approximation of a general class of one-stage stochastic mathematical programs with equilibrium constraints. By using graphical convergence of unbounded set-valued mappings, we demonstrate almost sure convergence of a sequence of stationary points of sample average approximation problems to their true counterparts as the sample size increases. In particular we show the convergence of M(Mordukhovich)-stationary point and C(Clarke)-stationary point of the sample average approximation problem to those of the true problem. The research complements the existing work in the literature by considering a general constraint to be represented by a stochastic generalized equation and exploiting graphical convergence of coderivative mappings. |
|---|---|
| AbstractList | We investigate sample average approximation of a general class of one-stage stochastic mathematical programs with equilibrium constraints. By using graphical convergence of unbounded set-valued mappings, we demonstrate almost sure convergence of a sequence of stationary points of sample average approximation problems to their true counterparts as the sample size increases. In particular we show the convergence of M(Mordukhovich)-stationary point and C(Clarke)-stationary point of the sample average approximation problem to those of the true problem. The research complements the existing work in the literature by considering a general constraint to be represented by a stochastic generalized equation and exploiting graphical convergence of coderivative mappings. |
| Author | Xu, Huifu Ye, Jane J. |
| Author_xml | – sequence: 1 givenname: Huifu surname: Xu fullname: Xu, Huifu email: h.xu@soton.ac.uk organization: School of Mathematics, University of Southampton – sequence: 2 givenname: Jane J. surname: Ye fullname: Ye, Jane J. organization: Department of Mathematics and Statistics, University of Victoria |
| BookMark | eNp9kMtOwzAQRS0EEm3hA9j5BwJ2nOeyqspDKqJSYW05rp26SuxgO6X9exyCWLDoYjQjy2dG90zBpTZaAHCH0T1GKH9wGMdxESGMQmUoOl6ACS7yPEJpgi__ZkKuwdS5fUAQKvEE9POus-aoWuaVruHGh240sye4Nkp7B40Mj4bvmPOKw1fmd2L4y1kD19bUlrUOfim_g8vPXjWqsqpv4cJo5y37WXBQDG5Y2zUCzg_CsjrcuQFXkjVO3P72Gfh4XL4vnqPV29PLYr6KeFwUPuJJTIiQSVGVmJSIpTGpBNqWmchyIUqexYIUPJEIySorJCFFSuS2JAxVohJpRmYAj3u5Nc5ZIWlnQ1R7ohjRwRsdvdHgjQ7e6DEw-T-Gq9HKkKg5S8Yj6cIVXQtL96a3OgQ8A30Ddw2H8Q |
| CitedBy_id | crossref_primary_10_1007_s10107_020_01582_2 crossref_primary_10_1016_j_cam_2014_11_057 crossref_primary_10_1007_s10107_021_01720_4 crossref_primary_10_1016_j_jmaa_2012_11_048 crossref_primary_10_1016_j_jmaa_2012_04_022 crossref_primary_10_1155_2018_8680540 crossref_primary_10_1007_s11228_011_0181_0 crossref_primary_10_1007_s10107_022_01893_6 crossref_primary_10_1007_s10107_017_1116_9 |
| Cites_doi | 10.1007/s11228-008-0095-7 10.1016/0022-247X(65)90049-1 10.1111/1467-937X.00075 10.1214/aop/1176996275 10.1007/s10107-002-0365-3 10.1007/s10492-007-0028-z 10.1287/moor.22.4.977 10.1007/978-3-642-02431-3 10.1137/S0363012999361718 10.1007/s10957-005-4724-0 10.1137/S1052623497321882 10.1007/s10107-007-0119-3 10.1080/02331930701778874 10.1016/0021-8928(76)90136-2 10.1016/S0167-6377(99)00052-8 10.1007/s00186-007-0201-x 10.1137/090748974 10.1016/j.jmaa.2004.10.032 10.1007/s10107-006-0005-4 10.1137/S105262349834847X 10.1007/BF01581199 10.1080/02331930801954177 10.1016/j.na.2008.11.089 10.1016/B978-044450263-6/50015-4 10.1137/S036301290139926X 10.1007/s10957-005-7566-x 10.1287/moor.1060.0215 10.1016/j.jmaa.2010.03.021 10.1287/moor.1070.0260 10.1007/BFb0120989 10.1515/9781400873173 10.1016/j.jmaa.2004.10.045 10.1137/1.9781611970081 10.1007/3-540-31246-3 10.1007/978-1-4757-2825-5 |
| ContentType | Journal Article |
| Copyright | Springer Science+Business Media B.V. 2010 |
| Copyright_xml | – notice: Springer Science+Business Media B.V. 2010 |
| DBID | AAYXX CITATION |
| DOI | 10.1007/s11228-010-0160-x |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1877-0541 |
| EndPage | 309 |
| ExternalDocumentID | 10_1007_s11228_010_0160_x |
| GroupedDBID | -5D -5G -BR -EM -Y2 -~C .VR 06D 0R~ 0VY 199 1N0 203 2J2 2JN 2JY 2KG 2LR 2~H 30V 4.4 406 408 409 40D 40E 5VS 6NX 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AOCGG ARMRJ AXYYD AYJHY AZFZN B-. BAPOH BDATZ BGNMA BSONS CSCUP DDRTE DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 H13 HF~ HG6 HLICF HMJXF HQYDN HRMNR HVGLF HZ~ IJ- IKXTQ ITM IWAJR IZIGR I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KOV LAK LLZTM M4Y MA- N9A NB0 NPVJJ NQJWS NU0 O9- O93 O9G O9J P9R PF0 PT4 QOS R89 R9I ROL RSV S16 S3B SAP SCLPG SDH SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN TSG TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 ZMTXR ZWQNP ~A9 AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION |
| ID | FETCH-LOGICAL-c288t-c4233ef48b91390a523be0d96e67ee9c62e38c4f00fb68f33853fd93a0bebe563 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 11 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000290031100006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1877-0533 |
| IngestDate | Tue Nov 18 21:55:06 EST 2025 Sat Nov 29 01:59:31 EST 2025 Fri Feb 21 02:32:59 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | 90C31 SMPEC 90C30 90C46 Coderivative 90C33 C-stationary point M-stationary point 90C15 Graphical convergence Sample average approximation |
| Language | English |
| License | http://www.springer.com/tdm |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c288t-c4233ef48b91390a523be0d96e67ee9c62e38c4f00fb68f33853fd93a0bebe563 |
| PageCount | 27 |
| ParticipantIDs | crossref_primary_10_1007_s11228_010_0160_x crossref_citationtrail_10_1007_s11228_010_0160_x springer_journals_10_1007_s11228_010_0160_x |
| PublicationCentury | 2000 |
| PublicationDate | 20110600 2011-6-00 |
| PublicationDateYYYYMMDD | 2011-06-01 |
| PublicationDate_xml | – month: 6 year: 2011 text: 20110600 |
| PublicationDecade | 2010 |
| PublicationPlace | Dordrecht |
| PublicationPlace_xml | – name: Dordrecht |
| PublicationSubtitle | Theory and Applications |
| PublicationTitle | Set-valued and variational analysis |
| PublicationTitleAbbrev | Set-Valued Anal |
| PublicationYear | 2011 |
| Publisher | Springer Netherlands |
| Publisher_xml | – name: Springer Netherlands |
| References | Henrion, Römisch (CR9) 2007; 52 Henrion, Outrata (CR7) 2008; 57 Rubinstein, Shapiro (CR34) 1993 King, Rockafellar (CR11) 1992; 55 Von Stackelberg (CR38) 1934 CR39 CR16 Mordukhovich (CR24) 1980; 22 CR37 Robinson (CR31) 1982; 19 Rockafellar (CR32) 1970 CR12 Patriksson, Wynter (CR30) 1999; 25 Ye (CR45) 2000; 10 Mordukhovich (CR23) 1976; 40 Henrion, Outrata, Surowiec (CR8) 2009; 71 Lucet, Ye (CR18) 2002; 41 Xu, Ye (CR43) 2010; 20 Anitescu, Tseng, Wright (CR1) 2007; 110 Hess (CR10) 2002 Shapiro, Xu (CR36) 2008; 57 Birbil, Gurkan, Listes (CR4) 2006; 31 Ye (CR46) 2005; 307 Aumann (CR3) 1965; 12 Lucet, Ye (CR17) 2001; 40 Outrata, Römisch (CR29) 2005; 126 Meng, Xu (CR20) 2006; 24 CR5 Lin, Chen, Fukushima (CR13) 2009; 116 CR28 CR26 Xu (CR41) 2010; 368 Ye, Ye (CR47) 1997; 22 CR25 Lin, Xu, Fukushima (CR14) 2008; 67 Liu, Ye, Zhou (CR15) 2008; 16 CR22 Xu, Meng (CR42) 2007; 32 Rockafellar, Wets (CR33) 1998 CR40 Luo, Pang, Ralph (CR19) 1996 Artstein, Vitale (CR2) 1975; 3 Mirrlees (CR21) 1999; 66 Ye, Zhu (CR48) 2003; 96 Ye (CR44) 1999; 9 Niederreiter (CR27) 1992 Clarke (CR6) 1983 Shapiro (CR35) 2006; 128 Y Lucet (160_CR18) 2002; 41 160_CR39 160_CR16 H Xu (160_CR41) 2010; 368 R Henrion (160_CR7) 2008; 57 GH Lin (160_CR14) 2008; 67 BS Mordukhovich (160_CR23) 1976; 40 JJ Ye (160_CR44) 1999; 9 160_CR12 160_CR37 C Hess (160_CR10) 2002 AJ King (160_CR11) 1992; 55 SM Robinson (160_CR31) 1982; 19 GS Liu (160_CR15) 2008; 16 A Shapiro (160_CR36) 2008; 57 Y Lucet (160_CR17) 2001; 40 160_CR40 H Xu (160_CR43) 2010; 20 160_CR5 R Henrion (160_CR8) 2009; 71 GH Lin (160_CR13) 2009; 116 H Xu (160_CR42) 2007; 32 SI Birbil (160_CR4) 2006; 31 JJ Ye (160_CR47) 1997; 22 F Meng (160_CR20) 2006; 24 H Niederreiter (160_CR27) 1992 A Shapiro (160_CR35) 2006; 128 RJ Aumann (160_CR3) 1965; 12 R Henrion (160_CR9) 2007; 52 JJ Ye (160_CR46) 2005; 307 H Stackelberg Von (160_CR38) 1934 160_CR28 J Mirrlees (160_CR21) 1999; 66 BS Mordukhovich (160_CR24) 1980; 22 M Anitescu (160_CR1) 2007; 110 160_CR26 ZQ Luo (160_CR19) 1996 160_CR25 JJ Ye (160_CR48) 2003; 96 J Outrata (160_CR29) 2005; 126 160_CR22 RT Rockafellar (160_CR32) 1970 RT Rockafellar (160_CR33) 1998 RY Rubinstein (160_CR34) 1993 FH Clarke (160_CR6) 1983 M Patriksson (160_CR30) 1999; 25 JJ Ye (160_CR45) 2000; 10 Z Artstein (160_CR2) 1975; 3 |
| References_xml | – volume: 16 start-page: 785 year: 2008 end-page: 804 ident: CR15 article-title: Partial exact penalty for mathematical programs with equilibrium constraints publication-title: Set-valued Anal. doi: 10.1007/s11228-008-0095-7 – ident: CR22 – volume: 12 start-page: 1 year: 1965 end-page: 12 ident: CR3 article-title: Integrals of set-valued functions publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(65)90049-1 – volume: 66 start-page: 3 year: 1999 end-page: 21 ident: CR21 article-title: The theory of moral hazard and unobservable behaviour: part I publication-title: Rev. Econ. Stud. doi: 10.1111/1467-937X.00075 – volume: 3 start-page: 879 year: 1975 end-page: 882 ident: CR2 article-title: A strong law of large numbers for random compact sets publication-title: Ann. Probab. doi: 10.1214/aop/1176996275 – year: 1934 ident: CR38 publication-title: Marktform and Gleichgewicht – volume: 96 start-page: 139 year: 2003 end-page: 160 ident: CR48 article-title: Multiobjective optimization problem with variational inequality constraints publication-title: Math. Program., Ser. A doi: 10.1007/s10107-002-0365-3 – ident: CR39 – ident: CR16 – ident: CR37 – year: 1983 ident: CR6 publication-title: Optimization and Nonsmooth Analysis – volume: 52 start-page: 473 year: 2007 end-page: 494 ident: CR9 article-title: On M-stationary point for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling publication-title: Appl. Math. doi: 10.1007/s10492-007-0028-z – volume: 22 start-page: 977 year: 1997 end-page: 997 ident: CR47 article-title: Necessary optimality conditions for optimization problems with variational inequality constraints publication-title: Math. Oper. Res. doi: 10.1287/moor.22.4.977 – ident: CR12 – year: 1998 ident: CR33 publication-title: Variational Analysis doi: 10.1007/978-3-642-02431-3 – year: 1996 ident: CR19 publication-title: Mathematical Programs with Equilibrium Constraints – year: 1993 ident: CR34 publication-title: Discrete Events Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Methods – volume: 40 start-page: 699 year: 2001 end-page: 723 ident: CR17 article-title: Sensitivity analysis of the value function for optimization problems with variational inequality constraints publication-title: SIAM J. Control Optim. doi: 10.1137/S0363012999361718 – volume: 126 start-page: 411 year: 2005 end-page: 438 ident: CR29 article-title: On optimization conditions for some nonsmooth optimization problems over spaces publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-005-4724-0 – year: 1992 ident: CR27 publication-title: Random Number Generation and Quasi-Monte-Carlo Methods – volume: 9 start-page: 374 year: 1999 end-page: 387 ident: CR44 article-title: Optimality conditions for optimization problems with complementarity constraints publication-title: SIAM J. Optim. doi: 10.1137/S1052623497321882 – volume: 116 start-page: 343 year: 2009 end-page: 368 ident: CR13 article-title: Solving stochastic mathematical programs with equilibrium constraints via approximation and smoothing implicit programming with penalization publication-title: Math. Program. Ser. B doi: 10.1007/s10107-007-0119-3 – ident: CR40 – volume: 57 start-page: 57 year: 2008 end-page: 78 ident: CR7 article-title: On calculating the normal to a finite union of convex polyhedra publication-title: Optimization doi: 10.1080/02331930701778874 – ident: CR25 – volume: 40 start-page: 960 year: 1976 end-page: 969 ident: CR23 article-title: Maximum principle in problems of time optimal control with nonsmooth constraints publication-title: J. Appl. Math. Mech. doi: 10.1016/0021-8928(76)90136-2 – volume: 25 start-page: 159 year: 1999 end-page: 167 ident: CR30 article-title: Stochastic mathematical programs with equilibrium constraints publication-title: Oper. Res. lett. doi: 10.1016/S0167-6377(99)00052-8 – volume: 67 start-page: 423 year: 2008 end-page: 441 ident: CR14 article-title: Monte Carlo and quasi-Monte Carlo sampling methods for a class of stochastic mathematical programs with equilibrium constraints publication-title: Math. Methods Oper. Res. doi: 10.1007/s00186-007-0201-x – volume: 22 start-page: 526 year: 1980 end-page: 530 ident: CR24 article-title: Metric approximation and necessary optimality conditions for general classes of nonsmooth extremal problems publication-title: Sov. Math., Dokl. – volume: 20 start-page: 1685 year: 2010 end-page: 1715 ident: CR43 article-title: Necessary optimality conditions for two-stage stochastic programs with equilibrium constraints publication-title: SIAM J. Optim. doi: 10.1137/090748974 – volume: 19 start-page: 200 year: 1982 end-page: 221 ident: CR31 article-title: Generalized equations and their solutions, part II: applications to nonlinear programming publication-title: Math. Program. Study – volume: 307 start-page: 305 year: 2005 end-page: 369 ident: CR46 article-title: Necessary and sufficient optimality conditions for mathemtical programs with equilibrium constraints publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2004.10.032 – volume: 110 start-page: 337 year: 2007 end-page: 371 ident: CR1 article-title: Elastic-mode algorithms for mathematical programs with equilibrium constraints: global convergence and stationarity properties publication-title: Math. Program. doi: 10.1007/s10107-006-0005-4 – volume: 10 start-page: 943 year: 2000 end-page: 962 ident: CR45 article-title: Constraint qualifications and necessary optimality conditions for optimization problems with variational inequality constraints publication-title: SIAM J. Optim. doi: 10.1137/S105262349834847X – volume: 55 start-page: 193 year: 1992 end-page: 212 ident: CR11 article-title: Sensitivity analysis for nonsmooth generalized equations publication-title: Math. Program. doi: 10.1007/BF01581199 – volume: 24 start-page: 733 year: 2006 end-page: 748 ident: CR20 article-title: Exponential convergence of sample average approximation methods for a class of stochastic mathematical programs with complementarity constraints publication-title: J. Comput. Math. – volume: 57 start-page: 395 year: 2008 end-page: 418 ident: CR36 article-title: Stochastic mathematical programs with equilibrium constraints, modeling and sample average approximation publication-title: Optimization doi: 10.1080/02331930801954177 – ident: CR5 – volume: 71 start-page: 1213 year: 2009 end-page: 1226 ident: CR8 article-title: On the co-derivative of normal cone mappings to inequality systems publication-title: Nonlinear Anal. doi: 10.1016/j.na.2008.11.089 – start-page: 617 year: 2002 end-page: 673 ident: CR10 article-title: Set-valued integration and set-valued probability theory: an overview publication-title: Handbook of Measure Theory, vols. I and II doi: 10.1016/B978-044450263-6/50015-4 – ident: CR28 – volume: 41 start-page: 1315 year: 2002 end-page: 1319 ident: CR18 article-title: Erratum: sensitivity analysis of the value function for optimization problems with variational inequality constraints publication-title: SIAM J. Control Optim. doi: 10.1137/S036301290139926X – ident: CR26 – volume: 128 start-page: 223 year: 2006 end-page: 243 ident: CR35 article-title: Stochastic mathematical programs with equilibrium constraints publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-005-7566-x – year: 1970 ident: CR32 publication-title: Convex Analysis – volume: 31 start-page: 739 year: 2006 end-page: 760 ident: CR4 article-title: Solving stochastic mathematical programs with complementarity constraints using simulation publication-title: Math. Oper. Res. doi: 10.1287/moor.1060.0215 – volume: 368 start-page: 692 year: 2010 end-page: 710 ident: CR41 article-title: Uniform exponential convergence of sample average random functions under general sampling with applications in stochastic programming publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2010.03.021 – volume: 32 start-page: 648 year: 2007 end-page: 668 ident: CR42 article-title: Convergence analysis of sample average approximation methods for a class of stochastic mathematical programs with equality constraints publication-title: Math. Oper. Res. doi: 10.1287/moor.1070.0260 – volume-title: Discrete Events Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Methods year: 1993 ident: 160_CR34 – volume: 19 start-page: 200 year: 1982 ident: 160_CR31 publication-title: Math. Program. Study doi: 10.1007/BFb0120989 – volume: 9 start-page: 374 year: 1999 ident: 160_CR44 publication-title: SIAM J. Optim. doi: 10.1137/S1052623497321882 – volume: 67 start-page: 423 year: 2008 ident: 160_CR14 publication-title: Math. Methods Oper. Res. doi: 10.1007/s00186-007-0201-x – volume-title: Mathematical Programs with Equilibrium Constraints year: 1996 ident: 160_CR19 – volume: 71 start-page: 1213 year: 2009 ident: 160_CR8 publication-title: Nonlinear Anal. doi: 10.1016/j.na.2008.11.089 – volume-title: Convex Analysis year: 1970 ident: 160_CR32 doi: 10.1515/9781400873173 – volume: 40 start-page: 960 year: 1976 ident: 160_CR23 publication-title: J. Appl. Math. Mech. doi: 10.1016/0021-8928(76)90136-2 – volume: 52 start-page: 473 year: 2007 ident: 160_CR9 publication-title: Appl. Math. doi: 10.1007/s10492-007-0028-z – volume: 16 start-page: 785 year: 2008 ident: 160_CR15 publication-title: Set-valued Anal. doi: 10.1007/s11228-008-0095-7 – volume: 66 start-page: 3 year: 1999 ident: 160_CR21 publication-title: Rev. Econ. Stud. doi: 10.1111/1467-937X.00075 – volume: 22 start-page: 526 year: 1980 ident: 160_CR24 publication-title: Sov. Math., Dokl. – volume: 10 start-page: 943 year: 2000 ident: 160_CR45 publication-title: SIAM J. Optim. doi: 10.1137/S105262349834847X – volume: 31 start-page: 739 year: 2006 ident: 160_CR4 publication-title: Math. Oper. Res. doi: 10.1287/moor.1060.0215 – volume-title: Optimization and Nonsmooth Analysis year: 1983 ident: 160_CR6 – volume: 20 start-page: 1685 year: 2010 ident: 160_CR43 publication-title: SIAM J. Optim. doi: 10.1137/090748974 – start-page: 617 volume-title: Handbook of Measure Theory, vols. I and II year: 2002 ident: 160_CR10 doi: 10.1016/B978-044450263-6/50015-4 – volume: 25 start-page: 159 year: 1999 ident: 160_CR30 publication-title: Oper. Res. lett. doi: 10.1016/S0167-6377(99)00052-8 – volume: 55 start-page: 193 year: 1992 ident: 160_CR11 publication-title: Math. Program. doi: 10.1007/BF01581199 – ident: 160_CR40 – ident: 160_CR25 – volume: 126 start-page: 411 year: 2005 ident: 160_CR29 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-005-4724-0 – volume: 57 start-page: 57 year: 2008 ident: 160_CR7 publication-title: Optimization doi: 10.1080/02331930701778874 – volume-title: Marktform and Gleichgewicht year: 1934 ident: 160_CR38 – ident: 160_CR5 – volume: 368 start-page: 692 year: 2010 ident: 160_CR41 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2010.03.021 – volume: 22 start-page: 977 year: 1997 ident: 160_CR47 publication-title: Math. Oper. Res. doi: 10.1287/moor.22.4.977 – volume: 110 start-page: 337 year: 2007 ident: 160_CR1 publication-title: Math. Program. doi: 10.1007/s10107-006-0005-4 – ident: 160_CR12 – volume: 3 start-page: 879 year: 1975 ident: 160_CR2 publication-title: Ann. Probab. doi: 10.1214/aop/1176996275 – volume: 12 start-page: 1 year: 1965 ident: 160_CR3 publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(65)90049-1 – ident: 160_CR16 – volume: 128 start-page: 223 year: 2006 ident: 160_CR35 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-005-7566-x – volume: 32 start-page: 648 year: 2007 ident: 160_CR42 publication-title: Math. Oper. Res. doi: 10.1287/moor.1070.0260 – volume: 307 start-page: 305 year: 2005 ident: 160_CR46 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2004.10.045 – volume-title: Variational Analysis year: 1998 ident: 160_CR33 doi: 10.1007/978-3-642-02431-3 – ident: 160_CR37 – ident: 160_CR39 – volume: 40 start-page: 699 year: 2001 ident: 160_CR17 publication-title: SIAM J. Control Optim. doi: 10.1137/S0363012999361718 – volume: 24 start-page: 733 year: 2006 ident: 160_CR20 publication-title: J. Comput. Math. – volume: 116 start-page: 343 year: 2009 ident: 160_CR13 publication-title: Math. Program. Ser. B doi: 10.1007/s10107-007-0119-3 – volume: 41 start-page: 1315 year: 2002 ident: 160_CR18 publication-title: SIAM J. Control Optim. doi: 10.1137/S036301290139926X – ident: 160_CR22 – volume-title: Random Number Generation and Quasi-Monte-Carlo Methods year: 1992 ident: 160_CR27 doi: 10.1137/1.9781611970081 – ident: 160_CR26 doi: 10.1007/3-540-31246-3 – volume: 96 start-page: 139 year: 2003 ident: 160_CR48 publication-title: Math. Program., Ser. A doi: 10.1007/s10107-002-0365-3 – ident: 160_CR28 doi: 10.1007/978-1-4757-2825-5 – volume: 57 start-page: 395 year: 2008 ident: 160_CR36 publication-title: Optimization doi: 10.1080/02331930801954177 |
| SSID | ssj0070091 |
| Score | 1.9142448 |
| Snippet | We investigate sample average approximation of a general class of one-stage stochastic mathematical programs with equilibrium constraints. By using graphical... |
| SourceID | crossref springer |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 283 |
| SubjectTerms | Analysis Mathematics Mathematics and Statistics Optimization |
| Title | Approximating Stationary Points of Stochastic Mathematical Programs with Equilibrium Constraints via Sample Averaging |
| URI | https://link.springer.com/article/10.1007/s11228-010-0160-x |
| Volume | 19 |
| WOSCitedRecordID | wos000290031100006&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: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1877-0541 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0070091 issn: 1877-0533 databaseCode: RSV dateStart: 20090601 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/eLvHCXMwnV1LT8MwDI7Q4AAH3ojxUg6cQJHS9ZUeJ7SJA0wTg2m3Kk0TqAQtrO00_j1x2m6aBEhwbOVYkfOwHdufEbq0BIBCWR5RjDPixJEgAXU5iQPPiqLYCrhJohnf-YMBm0yCYV3HnTfZ7k1I0tzUy2I3qwNoyiaRyqNEG47rWtsx6NfwMBo316-vjQbjZTHfJ1Bo2oQyv2OxqoxWI6FGwfR3_jW1XbRd25O4W22APbQm0320db8AY80PUNkF3PB5At_pMx5VwXc-_cTDLEmLHGdK_8zECwfMZrwcq_kOq_StHMN7Le59lImpESjfMHT6NP0lNINZwvGIA84w7uqjYRofHaKnfu_x5pbU3RaI6DBWEKENK1sqh0WAFEq59lAjSfWaSc-XMhBeR9pMOIpSFXlMadfWtVUc2JxGeiO4nn2EWmmWymOEuXSl9nSkVn1KGygKhrmMMukoizEetRFtxB6KGoocZvwaLkGUQaKhlmgIEg3nbXS1GPJe4XD8RnzdrFNYH8n8Z-qTP1Gfos3qWRkeYs5Qq5iW8hxtiFmR5NMLsxW_AEa229E |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3dS8MwEA8yBfXBb3F-5sEnJZCuX-njkI2J2xhujr2VNE20oK2u7Zj_vUnabgxU0MeWyxEuH3eXu_sdANcGU6BQhoMEoQRZYcCQh22KQs8xgiA0PKqTaMZdt98nk4k3KOu40yrbvQpJ6pt6WexmNBSask6kcjCShuO6JRWWAsx_HI6r69eVRoP2sojrIlVoWoUyv2OxqoxWI6FawbR3_zW1PbBT2pOwWWyAfbDG4wOw3VuAsaaHIG8q3PB5pL7jZzgsgu90-gkHSRRnKUyE_JmwF6owm-FyrOQ7KNK3Uqjea2HrI490jUD-BlWnT91fQjKYRRQOqcIZhk15NHTjoyPw1G6N7jqo7LaAWIOQDDFpWJlcWCRQSKGYSg814FiuGXdczj3mNLhJmCUwFoFDhHRtbVOEnklxIDeC7ZjHoBYnMT8BkHKbS0-HS9UnpIEi1DCbYMItYRBCgzrAldh9VkKRqxm_-ksQZSVRX0rUVxL153VwsxjyXuBw_EZ8W62TXx7J9Gfq0z9RX4HNzqjX9bv3_YczsFU8MatHmXNQy6Y5vwAbbJZF6fRSb8svncfetQ |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LSwMxEA5SRfTgW6zPHDwpodnuK3ss2qJYS6Faeluy2UQXdFu721L_vZl9tBRUEI-7zAwhr5nJzHyD0KUhABTKcIhinBErDATxqM1J6DlGEISGx7Mkmn7b7XTYYOB1iz6nSZntXoYk85oGQGmK09ooVLVF4ZtRB2TlLKnKoUQbkasW5NGDu97rl1exqw2IzONirkug6LQMa34nYlkxLUdFM2XT2v73MHfQVmFn4ka-MXbRioz30ObjHKQ12UeTBuCJzyL4jl9wLw_K8_En7g6jOE3wUOmfQ_HKAcsZL3i13G6e1pVgeMfFzY9JlNUOTN4xdADN-k5oAdOI4x4H_GHc0Ecma4h0gJ5bzaebO1J0YSCizlhKhDa4TKksFgCCKOXacw0k1WspHVdKTzh1aTJhKUpV4DClXV7bVKFnchroDWI75iGqxMNYHiHMpS21ByS1SlTacFHAZjPKpKUMxnhQRbRcAl8UEOUw4jd_Aa4MM-rrGfVhRv1ZFV3NWUY5PsdvxNflmvnFUU1-pj7-E_UFWu_etvz2fefhBG3kL8_wVnOKKul4Is_QmpimUTI-z3boF30h55k |
| 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=Approximating+Stationary+Points+of+Stochastic+Mathematical+Programs+with+Equilibrium+Constraints+via+Sample+Averaging&rft.jtitle=Set-valued+and+variational+analysis&rft.au=Xu%2C+Huifu&rft.au=Ye%2C+Jane+J.&rft.date=2011-06-01&rft.issn=1877-0533&rft.eissn=1877-0541&rft.volume=19&rft.issue=2&rft.spage=283&rft.epage=309&rft_id=info:doi/10.1007%2Fs11228-010-0160-x&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s11228_010_0160_x |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1877-0533&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1877-0533&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1877-0533&client=summon |