{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T20:58:48Z","timestamp":1782939528945,"version":"3.54.5"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T00:00:00Z","timestamp":1664409600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T00:00:00Z","timestamp":1664409600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100002858","name":"Postdoctoral Science Foundation of China","doi-asserted-by":"crossref","award":["2020M673117"],"award-info":[{"award-number":["2020M673117"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871276"],"award-info":[{"award-number":["11871276"]}],"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":["12122108"],"award-info":[{"award-number":["12122108"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2023,2]]},"DOI":"10.1007\/s10957-022-02099-8","type":"journal-article","created":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T17:04:01Z","timestamp":1664471041000},"page":"433-460","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Monotonicity and Complexity of Multistage Stochastic Variational Inequalities"],"prefix":"10.1007","volume":"196","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3985-8701","authenticated-orcid":false,"given":"Jie","family":"Jiang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1036-6327","authenticated-orcid":false,"given":"Hailin","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,9,29]]},"reference":[{"key":"2099_CR1","volume-title":"Perturbation Analysis of Optimization Problems","author":"JF Bonnans","year":"2013","unstructured":"Bonnans, J.F., Shapiro, A.: Perturbation Analysis of Optimization Problems. Springer, New York (2013)"},{"issue":"4","key":"2099_CR2","doi-asserted-by":"crossref","first-page":"1022","DOI":"10.1287\/moor.1050.0160","volume":"30","author":"X Chen","year":"2005","unstructured":"Chen, X., Fukushima, M.: Expected residual minimization method for stochastic linear complementarity problems. Math. Oper. Res. 30(4), 1022\u20131038 (2005)","journal-title":"Math. Oper. Res."},{"issue":"1","key":"2099_CR3","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/s10107-017-1132-9","volume":"165","author":"X Chen","year":"2017","unstructured":"Chen, X., Pong, T.K., Wets, R.J.B.: Two-stage stochastic variational inequalities: an ERM-solution procedure. Math. Program. 165(1), 71\u2013111 (2017)","journal-title":"Math. Program."},{"issue":"1","key":"2099_CR4","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1137\/17M1162822","volume":"29","author":"X Chen","year":"2019","unstructured":"Chen, X., Shapiro, A., Sun, H.: Convergence analysis of sample average approximation of two-stage stochastic generalized equations. SIAM J. Optim. 29(1), 135\u2013161 (2019)","journal-title":"SIAM J. Optim."},{"issue":"1\u20132","key":"2099_CR5","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/s10107-018-1266-4","volume":"177","author":"X Chen","year":"2019","unstructured":"Chen, X., Sun, H., Xu, H.: Discrete approximation of two-stage stochastic and distributionally robust linear complementarity problems. Math. Program. 177(1\u20132), 255\u2013289 (2019)","journal-title":"Math. Program."},{"issue":"2","key":"2099_CR6","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1137\/110825248","volume":"22","author":"X Chen","year":"2012","unstructured":"Chen, X., Wets, R.J.B., Zhang, Y.: Stochastic variational inequalities: residual minimization smoothing sample average approximations. SIAM J. Optim. 22(2), 649\u2013673 (2012)","journal-title":"SIAM J. Optim."},{"key":"2099_CR7","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719000","volume-title":"The Linear Complementarity Problem","author":"RW Cottle","year":"2009","unstructured":"Cottle, R.W., Pang, J.S., Stone, R.E.: The Linear Complementarity Problem. SIAM, Philadelphia (2009)"},{"key":"2099_CR8","unstructured":"Cui, X., Sun, J., Zhang, L.: Solvability of multistage pseudomonotone stochastic variational inequalities. arXiv:2201.01454 (2022)"},{"key":"2099_CR9","volume-title":"Finite-dimensional Variational Inequalities and Complementarity Problems","author":"F Facchinei","year":"2007","unstructured":"Facchinei, F., Pang, J.S.: Finite-dimensional Variational Inequalities and Complementarity Problems. Springer, New York (2007)"},{"issue":"2","key":"2099_CR10","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1007\/s101070050024","volume":"84","author":"G G\u00fcrkan","year":"1999","unstructured":"G\u00fcrkan, G., Yonca \u00d6zge, A., Robinson, S.M.: Sample-path solution of stochastic variational inequalities. Math. Program. 84(2), 313\u2013333 (1999)","journal-title":"Math. Program."},{"issue":"2","key":"2099_CR11","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1007\/s10589-020-00185-z","volume":"76","author":"J Jiang","year":"2020","unstructured":"Jiang, J., Chen, X., Chen, Z.: Quantitative analysis for a class of two-stage stochastic linear variational inequality problems. Comput. Optim. Appl. 76(2), 431\u2013460 (2020)","journal-title":"Comput. Optim. Appl."},{"issue":"2","key":"2099_CR12","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/j.orl.2021.01.016","volume":"49","author":"J Jiang","year":"2021","unstructured":"Jiang, J., Li, S.: On complexity of multistage stochastic programs under heavy tailed distributions. Oper. Res. Lett. 49(2), 265\u2013269 (2021)","journal-title":"Oper. Res. Lett."},{"issue":"2","key":"2099_CR13","doi-asserted-by":"crossref","first-page":"650","DOI":"10.1007\/s10957-021-01905-z","volume":"190","author":"J Jiang","year":"2021","unstructured":"Jiang, J., Li, S.: Regularized sample average approximation approach for two-stage stochastic variational inequalities. J. Optim. Theory Appl. 190(2), 650\u2013671 (2021)","journal-title":"J. Optim. Theory Appl."},{"issue":"6","key":"2099_CR14","doi-asserted-by":"crossref","first-page":"813","DOI":"10.4208\/jcm.1906-m2019-0025","volume":"37","author":"J Jiang","year":"2019","unstructured":"Jiang, J., Shi, Y., Wang, X., Chen, X.: Regularized two-stage stochastic variational inequalities for Cournot-Nash equilibrium under uncertainty. J. Comput. Math. 37(6), 813\u2013842 (2019)","journal-title":"J. Comput. Math."},{"issue":"1","key":"2099_CR15","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/s11075-021-01110-z","volume":"89","author":"J Jiang","year":"2022","unstructured":"Jiang, J., Sun, H., Zhou, B.: Convergence analysis of sample average approximation for a class of stochastic nonlinear complementarity problems: from two-stage to multistage. Numer. Algorithms 89(1), 167\u2013194 (2022)","journal-title":"Numer. Algorithms"},{"issue":"1\u20133","key":"2099_CR16","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/BF01582260","volume":"48","author":"J Kyparisis","year":"1990","unstructured":"Kyparisis, J.: Solution differentiability for variational inequalities. Math. Program. 48(1\u20133), 285\u2013301 (1990)","journal-title":"Math. Program."},{"issue":"1","key":"2099_CR17","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1007\/s10957-020-01686-x","volume":"186","author":"M Li","year":"2020","unstructured":"Li, M., Zhang, C.: Two-stage stochastic variational inequality arising from stochastic programming. J. Optim. Theory Appl. 186(1), 324\u2013343 (2020)","journal-title":"J. Optim. Theory Appl."},{"key":"2099_CR18","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.apm.2021.09.033","volume":"102","author":"M Li","year":"2022","unstructured":"Li, M., Zhang, C., Ding, M., Lv, R.: A two-stage stochastic variational inequality model for storage and dynamic distribution of medical supplies in epidemic management. Appl. Math. Model. 102, 35\u201361 (2022)","journal-title":"Appl. Math. Model."},{"issue":"8","key":"2099_CR19","doi-asserted-by":"crossref","first-page":"3122","DOI":"10.1080\/00036811.2020.1836352","volume":"101","author":"J Liu","year":"2022","unstructured":"Liu, J., Li, S., Jiang, J.: Quantitative stability of two-stage stochastic linear variational inequality problems with fixed recourse. Appl. Anal. 101(8), 3122\u20133138 (2022)","journal-title":"Appl. Anal."},{"issue":"5","key":"2099_CR20","doi-asserted-by":"crossref","first-page":"971","DOI":"10.1007\/s11590-017-1185-y","volume":"12","author":"KD Pham","year":"2018","unstructured":"Pham, K.D., Bui, N.M.: Error bounds for strongly monotone and Lipshitz continuous variational inequalities. Optim. Lett. 12(5), 971\u2013984 (2018)","journal-title":"Optim. Lett."},{"issue":"1\u20132","key":"2099_CR21","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1007\/s10107-018-1251-y","volume":"174","author":"RT Rockafellar","year":"2019","unstructured":"Rockafellar, R.T., Sun, J.: Solving monotone stochastic variational inequalities and complementarity problems by progressive hedging. Math. Program. 174(1\u20132), 453\u2013471 (2019)","journal-title":"Math. Program."},{"key":"2099_CR22","volume-title":"Variational Analysis","author":"RT Rockafellar","year":"2009","unstructured":"Rockafellar, R.T., Wets, R.J.B.: Variational Analysis. Springer, New York (2009)"},{"issue":"1","key":"2099_CR23","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s10107-016-0995-5","volume":"165","author":"RT Rockafellar","year":"2017","unstructured":"Rockafellar, R.T., Wets, R.J.B.: Stochastic variational inequalities: single-stage to multistage. Math. Program. 165(1), 331\u2013360 (2017)","journal-title":"Math. Program."},{"key":"2099_CR24","doi-asserted-by":"crossref","unstructured":"Shanbhag, U.V.: Stochastic variational inequality problems: Applications, analysis, and algorithms. In: INFORMS TutORials in Operations Research, pp. 71\u2013107. INFORMS (2013)","DOI":"10.1287\/educ.2013.0120"},{"issue":"1","key":"2099_CR25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.orl.2005.02.003","volume":"34","author":"A Shapiro","year":"2006","unstructured":"Shapiro, A.: On complexity of multistage stochastic programs. Oper. Res. Lett. 34(1), 1\u20138 (2006)","journal-title":"Oper. Res. Lett."},{"key":"2099_CR26","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611973433","volume-title":"Lectures on Stochastic Programming: Modeling and Theory","author":"A Shapiro","year":"2014","unstructured":"Shapiro, A., Dentcheva, D., Ruszczy\u0144ski, A.: Lectures on Stochastic Programming: Modeling and Theory, 2nd edn. SIAM, Philadelphia (2014)","edition":"2"},{"issue":"1","key":"2099_CR27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s40305-019-00267-8","volume":"9","author":"H Sun","year":"2021","unstructured":"Sun, H., Chen, X.: Two-stage stochastic variational inequalities: theory, algorithms and applications. J. Oper. Res. Soc. China 9(1), 1\u201332 (2021)","journal-title":"J. Oper. Res. Soc. China"},{"key":"2099_CR28","doi-asserted-by":"crossref","unstructured":"Wang, X., Chen, X.: Solving two-stage stochastic variational inequalities by a projection semismooth Newton algorithm. Working paper (2022)","DOI":"10.1137\/22M1475302"},{"issue":"01","key":"2099_CR29","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1142\/S0217595910002569","volume":"27","author":"H Xu","year":"2010","unstructured":"Xu, H.: Sample average approximation methods for a class of stochastic variational inequality problems. Asia-Pacific J. Oper. Res. 27(01), 103\u2013119 (2010)","journal-title":"Asia-Pacific J. Oper. Res."},{"issue":"3","key":"2099_CR30","doi-asserted-by":"crossref","first-page":"1799","DOI":"10.1137\/17M1151067","volume":"29","author":"M Zhang","year":"2019","unstructured":"Zhang, M., Sun, J., Xu, H.: Two-stage quadratic games under uncertainty and their solution by progressive hedging algorithms. SIAM J. Optim. 29(3), 1799\u20131818 (2019)","journal-title":"SIAM J. Optim."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-022-02099-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-022-02099-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-022-02099-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,28]],"date-time":"2023-11-28T03:38:42Z","timestamp":1701142722000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-022-02099-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,29]]},"references-count":30,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["2099"],"URL":"https:\/\/doi.org\/10.1007\/s10957-022-02099-8","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,29]]},"assertion":[{"value":"25 March 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 August 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 September 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}