{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:14Z","timestamp":1740134534244,"version":"3.37.3"},"reference-count":16,"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":["11201357","2012-Ia-024","201308420194"],"award-info":[{"award-number":["11201357","2012-Ia-024","201308420194"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Central Universities","award":["11201357","2012-Ia-024","201308420194"],"award-info":[{"award-number":["11201357","2012-Ia-024","201308420194"]}]},{"name":"State Scholarship","award":["11201357","2012-Ia-024","201308420194"],"award-info":[{"award-number":["11201357","2012-Ia-024","201308420194"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>An implementable nonlinear Lagrange algorithm for stochastic minimax problems is presented based on sample average approximation method in this paper, in which the second step minimizes a nonlinear Lagrange function with sample average approximation functions of original functions and the sample average approximation of the Lagrange multiplier is adopted. Under a set of mild assumptions, it is proven that the sequences of solution and multiplier obtained by the proposed algorithm converge to the Kuhn-Tucker pair of the original problem with probability one as the sample size increases. At last, the numerical experiments for five test examples are performed and the numerical results indicate that the algorithm is promising.<\/jats:p>","DOI":"10.1155\/2014\/497262","type":"journal-article","created":{"date-parts":[[2014,4,3]],"date-time":"2014-04-03T21:06:11Z","timestamp":1396559171000},"page":"1-8","source":"Crossref","is-referenced-by-count":0,"title":["A Nonlinear Lagrange Algorithm for Stochastic Minimax Problems Based on Sample Average Approximation Method"],"prefix":"10.1155","volume":"2014","author":[{"given":"Suxiang","family":"He","sequence":"first","affiliation":[{"name":"School of Science, Wuhan University of Technology, Wuhan 430070, China"}]},{"given":"Yunyun","family":"Nie","sequence":"additional","affiliation":[{"name":"School of Science, Wuhan University of Technology, Wuhan 430070, China"}]},{"given":"Xiaopeng","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Science, Wuhan University of Technology, Wuhan 430070, China"}]}],"member":"311","reference":[{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01300861"},{"key":"5","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1080\/17442508708833436","volume":"20","year":"1987","journal-title":"Stochastic"},{"issue":"5","key":"7","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1137\/0323044","volume":"23","year":"1985","journal-title":"SIAM Journal on Control and Optimization"},{"key":"17","first-page":"47","volume":"6","year":"1997","journal-title":"Archives Control Science"},{"key":"8","doi-asserted-by":"crossref","first-page":"75","DOI":"10.3934\/jimo.2013.9.75","volume":"9","year":"2013","journal-title":"Journal of Industrial and Management Optimization"},{"key":"1","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1137\/S1052623499363220","volume":"12","year":"2002","journal-title":"SIAM Journal of Optimization"},{"key":"4","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1137\/110825248","volume":"22","year":"2012","journal-title":"SIAM Journal on Optimization"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1137\/050638242"},{"year":"2009","series-title":"MPS-SIAM Series on Optimization","key":"11"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-009-9606-4"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1070.0260"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1142\/S0217595910002569"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2011.08.073"},{"year":"1953","key":"16"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01593788"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01580609"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/497262.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/497262.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/497262.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,17]],"date-time":"2020-08-17T06:03:21Z","timestamp":1597644201000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/497262\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":16,"alternative-id":["497262","497262"],"URL":"https:\/\/doi.org\/10.1155\/2014\/497262","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}