{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:10Z","timestamp":1740134530307,"version":"3.37.3"},"reference-count":20,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11201210","11171138","L2012385"],"award-info":[{"award-number":["11201210","11171138","L2012385"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11201210","11171138","L2012385"],"award-info":[{"award-number":["11201210","11171138","L2012385"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013099","name":"Scientific Research Fund of Liaoning Provincial Education Department","doi-asserted-by":"crossref","award":["11201210","11171138","L2012385"],"award-info":[{"award-number":["11201210","11171138","L2012385"]}],"id":[{"id":"10.13039\/501100013099","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>To reflect uncertain data in practical problems, stochastic versions of the mathematical program with complementarity constraints (MPCC) have drawn much attention in the recent literature. Our concern is the detailed analysis of convergence properties of a regularization sample average approximation (SAA) method for solving a stochastic mathematical program with complementarity constraints (SMPCC). The analysis of this regularization method is carried out in three steps: First, the almost sure convergence of optimal solutions of the regularized SAA problem to that of the true problem is established by the notion of epiconvergence in variational analysis. Second, under MPCC-MFCQ, which is weaker than MPCC-LICQ, we show that any accumulation point of Karash-Kuhn-Tucker points of the regularized SAA problem is almost surely a kind of stationary point of SMPCC as the sample size tends to infinity. Finally, some numerical results are reported to show the efficiency of the method proposed.<\/jats:p>","DOI":"10.1155\/2014\/321010","type":"journal-article","created":{"date-parts":[[2014,2,10]],"date-time":"2014-02-10T21:01:42Z","timestamp":1392066102000},"page":"1-12","source":"Crossref","is-referenced-by-count":0,"title":["A Regularization SAA Scheme for a Stochastic Mathematical Program with Complementarity Constraints"],"prefix":"10.1155","volume":"2014","author":[{"given":"Yu-xin","family":"Li","sequence":"first","affiliation":[{"name":"Institute of ORCT, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Liaoning Normal University, Dalian 116029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zun-quan","family":"Xia","sequence":"additional","affiliation":[{"name":"Institute of ORCT, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511983658"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-211-48243-8_5"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1060.0215"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.trb.2008.05.001"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1137\/040608544"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1080\/02331930801954177"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6377(99)00052-8"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1287\/moor.21.3.513"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2008.925853"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718751"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/S0025-5610(96)00010-X"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623498349541"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-006-6169-8"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/s11228-011-0181-0"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2011.08.073"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1287\/moor.25.1.1.15213"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623499361233"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-02431-3"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022662120550"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1287\/moor.5.1.43"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/321010.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/321010.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/321010.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,11]],"date-time":"2020-05-11T19:40:02Z","timestamp":1589226002000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/321010\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":20,"alternative-id":["321010","321010"],"URL":"https:\/\/doi.org\/10.1155\/2014\/321010","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}