{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T08:07:09Z","timestamp":1759133229548,"version":"3.37.3"},"reference-count":26,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,10,8]],"date-time":"2020-10-08T00:00:00Z","timestamp":1602115200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation Guiding Project of Liaoning Provincial Department of Science and Technology","award":["2019-ZD-0194","LJC201902"],"award-info":[{"award-number":["2019-ZD-0194","LJC201902"]}]},{"DOI":"10.13039\/501100007620","name":"Department of Education of Liaoning Province","doi-asserted-by":"publisher","award":["2019-ZD-0194","LJC201902"],"award-info":[{"award-number":["2019-ZD-0194","LJC201902"]}],"id":[{"id":"10.13039\/501100007620","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,10,8]]},"abstract":"<jats:p>In this paper, we consider stochastic vector variational inequality problems (SVVIPs). Because of the existence of stochastic variable, the SVVIP may have no solutions generally. For solving this problem, we employ the regularized gap function of SVVIP to the loss function and then give a low-risk conditional value-at-risk (CVaR) model. However, this low-risk CVaR model is difficult to solve by the general constraint optimization algorithm. This is because the objective function is nonsmoothing function, and the objective function contains expectation, which is not easy to be computed. By using the sample average approximation technique and smoothing function, we present the corresponding approximation problems of the low-risk CVaR model to deal with these two difficulties related to the low-risk CVaR model. In addition, for the given approximation problems, we prove the convergence results of global optimal solutions and the convergence results of stationary points, respectively. Finally, a numerical experiment is given.<\/jats:p>","DOI":"10.1155\/2020\/1203627","type":"journal-article","created":{"date-parts":[[2020,10,8]],"date-time":"2020-10-08T18:37:31Z","timestamp":1602182251000},"page":"1-8","source":"Crossref","is-referenced-by-count":2,"title":["Convergence Analysis of the Approximation Problems for Solving Stochastic Vector Variational Inequality Problems"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1651-8413","authenticated-orcid":true,"given":"Meiju","family":"Luo","sequence":"first","affiliation":[{"name":"School of Mathematics, Liaoning University, Shenyang, Liaoning 110036, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0075-1432","authenticated-orcid":true,"given":"Kun","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Liaoning University, Shenyang, Liaoning 110036, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.omega.2007.02.001"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2012.11.098"},{"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":"10.1137\/110825248"},{"key":"6","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s10957-008-9439-6","volume":"140","year":"2009","journal-title":"Journal of Optimization Theory and Application"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.3934\/naco.2011.1.35"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/bf00940320"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/bf01415945"},{"volume-title":"Theorems of alternative, quadratic programs and complementarity problems","year":"1980","key":"10"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/s0893-9659(03)90087-5"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.11121\/ijocta.01.2014.00160"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1023\/a:1020844423345"},{"year":"1983","key":"14"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-016-0939-5"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1007\/bf01585696"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.21314\/jor.2000.038"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/s0378-4266(02)00271-6"},{"key":"19","first-page":"1081","volume":"35","year":"2015","journal-title":"Journal of Systems Science and Mathematical Sciences"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1186\/s13660-018-1814-8"},{"issue":"2","key":"21","first-page":"321","volume":"34","year":"2007","journal-title":"Japan Journal of Industrial and Applied Mathematics"},{"key":"22","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1007\/s10589-013-9625-9","volume":"58","year":"2014","journal-title":"Computational Optimization and Applications"},{"key":"23","first-page":"1467","volume":"34","year":"1991","journal-title":"Science in China (A)"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1287\/moor.21.3.513"},{"year":"2011","key":"25"},{"volume-title":"Stochastic programming","year":"2003","key":"26"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/1203627.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/1203627.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/1203627.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,11]],"date-time":"2020-10-11T12:53:29Z","timestamp":1602420809000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/1203627\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,8]]},"references-count":26,"alternative-id":["1203627","1203627"],"URL":"https:\/\/doi.org\/10.1155\/2020\/1203627","relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2020,10,8]]}}}