{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T10:39:18Z","timestamp":1649155158402},"reference-count":16,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"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":["11226238","11226230","2012LDGY01","2012427"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"Expected residual minimization (ERM) model which minimizes an expected residual function defined by an NCP function has been studied in the literature for solving stochastic complementarity problems. In this paper, we first give the definitions of stochasticP<\/mml:mi><\/mml:mrow><\/mml:math>-function, stochasticP<\/mml:mi><\/mml:mrow>0<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>-function, and stochastic uniformlyP<\/mml:mi><\/mml:mrow><\/mml:math>-function. Furthermore, the conditions such that the function is a stochasticP<\/mml:mi>P<\/mml:mi><\/mml:mrow>0<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:mfenced><\/mml:math>-function are considered. We then study the boundedness of solution set and global error bounds of the expected residual functions defined by the \u201cFischer-Burmeister\u201d (FB) function and \u201cmin\u201d function. The conclusion indicates that solutions of the ERM model are robust in the sense that they may have a minimum sensitivity with respect to random parameter variations in stochastic complementarity problems. On the other hand, we employ quasi-Monte Carlo methods and derivative-free methods to solve ERM model.<\/jats:p>","DOI":"10.1155\/2013\/497586","type":"journal-article","created":{"date-parts":[[2013,5,28]],"date-time":"2013-05-28T14:14:09Z","timestamp":1369750449000},"page":"1-7","source":"Crossref","is-referenced-by-count":4,"title":["Properties of Expected Residual Minimization Model for a Class of Stochastic Complementarity Problems"],"prefix":"10.1155","volume":"2013","author":[{"given":"Mei-Ju","family":"Luo","sequence":"first","affiliation":[{"name":"School of Mathematics, Liaoning University, Liaoning 110036, China"}]},{"given":"Yuan","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Sciences, Shenyang University, Liaoning 110044, China"}]}],"member":"98","reference":[{"key":"1","year":"2003"},{"key":"2","series-title":"Computer Science and Scientific Computing","first-page":"xxiv+762","year":"1992"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1080\/10556780600627610"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/s101070050024"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1050.0160"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-007-0163-z"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/BF02192639"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1137\/050630805"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1080\/02331930701617320"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2008.01.010"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-008-9358-6"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1137\/070702187"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-008-9406-2"},{"issue":"1","key":"13","first-page":"123","volume":"31","year":"2011","journal-title":"Journal of Systems Science and Mathematical Sciences"},{"key":"14","first-page":"xii+365","year":"1974"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623495280615"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/497586.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/497586.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/497586.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,30]],"date-time":"2016-07-30T09:31:14Z","timestamp":1469871074000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/497586\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":16,"alternative-id":["497586","497586"],"URL":"https:\/\/doi.org\/10.1155\/2013\/497586","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}