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...
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| Vydáno v: | Set-valued and variational analysis Ročník 19; číslo 2; s. 283 - 309 |
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01.06.2011
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| ISSN: | 1877-0533, 1877-0541 |
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| 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. |
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| 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 |
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| 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 |
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| Keywords | 90C31 SMPEC 90C30 90C46 Coderivative 90C33 C-stationary point M-stationary point 90C15 Graphical convergence Sample average approximation |
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| Snippet | We investigate sample average approximation of a general class of one-stage stochastic mathematical programs with equilibrium constraints. By using graphical... |
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| 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 |
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