{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T03:14:14Z","timestamp":1775099654152,"version":"3.50.1"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2009,3,12]],"date-time":"2009-03-12T00:00:00Z","timestamp":1236816000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2009,8]]},"DOI":"10.1007\/s10957-009-9523-6","type":"journal-article","created":{"date-parts":[[2009,3,11]],"date-time":"2009-03-11T22:43:26Z","timestamp":1236811406000},"page":"399-416","source":"Crossref","is-referenced-by-count":436,"title":["Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications"],"prefix":"10.1007","volume":"142","author":[{"given":"B. K.","family":"Pagnoncelli","sequence":"first","affiliation":[]},{"given":"S.","family":"Ahmed","sequence":"additional","affiliation":[]},{"given":"A.","family":"Shapiro","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2009,3,12]]},"reference":[{"key":"9523_CR1","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1287\/mnsc.4.3.235","volume":"4","author":"A. Charnes","year":"1958","unstructured":"Charnes, A., Cooper, W.W., Symmonds, G.H.: Cost horizons and certainty equivalents: an approach to stochastic programming of heating oil. Manag. Sci. 4, 235\u2013263 (1958)","journal-title":"Manag. Sci."},{"key":"9523_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-017-3087-7","volume-title":"Stochastic Programming","author":"A. Pr\u00e9kopa","year":"1995","unstructured":"Pr\u00e9kopa, A.: Stochastic Programming. Kluwer Academic, Dordrecht (1995)"},{"key":"9523_CR3","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/0377-2217(91)90333-Q","volume":"52","author":"J. Dupa\u010dov\u00e1","year":"1991","unstructured":"Dupa\u010dov\u00e1, J., Gaivoronski, A., Kos, Z., Sz\u00e1ntai, T.: Stochastic programming in water management: a case study and a comparison of solution techniques. Eur. J. Oper. Res. 52, 28\u201344 (1991)","journal-title":"Eur. J. Oper. Res."},{"key":"9523_CR4","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/978-3-662-04331-8_24","volume-title":"Online Optimization of Large Scale Systems","author":"R. Henrion","year":"2001","unstructured":"Henrion, R., Li, P., M\u00f6ller, A., Steinbach, S.G., Wendt, M., Wozny, G.: Stochastic optimization for operating chemical processes under uncertainty. In: Gr\u00f6tschel, M., Krunke, S., Rambau, J. (eds.) Online Optimization of Large Scale Systems, pp. 457\u2013478. Springer, Berlin (2001)"},{"key":"9523_CR5","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/S0898-1221(03)80017-2","volume":"45","author":"R. Henrion","year":"2003","unstructured":"Henrion, R., M\u00f6ller, A.: Optimization of a continuous distillation process under random inflow rate. Comput. Math. Appl. 45, 247\u2013262 (2003)","journal-title":"Comput. Math. Appl."},{"key":"9523_CR6","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/PL00011393","volume":"89","author":"D. Dentcheva","year":"2000","unstructured":"Dentcheva, D., Pr\u00e9kopa, A., Ruszczy\u0144ski, A.: Concavity and efficient points of discrete distributions in probabilistic programming. Math. Program. 89, 55\u201377 (2000)","journal-title":"Math. Program."},{"key":"9523_CR7","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1137\/070702928","volume":"19","author":"J. Luedtke","year":"2008","unstructured":"Luedtke, J., Ahmed, S.: A sample approximation approach for optimization with probabilistic constraints. SIAM J. Optim. 19, 674\u2013699 (2008)","journal-title":"SIAM J. Optim."},{"issue":"4","key":"9523_CR8","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1137\/050622328","volume":"17","author":"A. Nemirovski","year":"2006","unstructured":"Nemirovski, A., Shapiro, A.: Convex approximations of chance constrained programs. SIAM J. Optim. 17(4), 969\u2013996 (2006)","journal-title":"SIAM J. Optim."},{"key":"9523_CR9","series-title":"Handbooks in OR & MS","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/S0927-0507(03)10006-0","volume-title":"Stochastic Programming","author":"A. Shapiro","year":"2003","unstructured":"Shapiro, A.: Monte Carlo sampling methods. In: Ruszczy\u0144ski, A., Shapiro, A. (eds.) Stochastic Programming. Handbooks in OR & MS, vol. 10, pp. 353\u2013425. North-Holland, Amsterdam (2003)"},{"key":"9523_CR10","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1287\/mnsc.1070.0774","volume":"54","author":"J. Atlason","year":"2008","unstructured":"Atlason, J., Epelman, M.A., Henderson, S.G.: Optimizing call center staffing using simulation and analytic center cutting plane methods. Manag. Sci. 54, 295\u2013309 (2008)","journal-title":"Manag. Sci."},{"key":"9523_CR11","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1137\/070702928","volume":"19","author":"J. Luedtke","year":"2008","unstructured":"Luedtke, J., Ahmed, S.: A sample approximation approach for optimization with probabilistic constraints. SIAM J. Optim. 19, 674\u2013699 (2008)","journal-title":"SIAM J. Optim."},{"key":"9523_CR12","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-02431-3","volume-title":"Variational Analysis","author":"R.T. Rockafellar","year":"1998","unstructured":"Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Springer, Berlin (1998)"},{"key":"9523_CR13","first-page":"1","volume":"2","author":"Z. Artstein","year":"1996","unstructured":"Artstein, Z., Wets, R.J.-B.: Consistency of minimizers and the SLLN for stochastic programs. J.\u00a0Convex Anal. 2, 1\u201317 (1996)","journal-title":"J.\u00a0Convex Anal."},{"key":"9523_CR14","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1214\/aoms\/1177729330","volume":"23","author":"H. Chernoff","year":"1952","unstructured":"Chernoff, H.: A measure of asymptotic efficiency for tests of a hypothesis based on the sum observations. Ann. Math. Stat. 23, 493\u2013507 (1952)","journal-title":"Ann. Math. Stat."},{"key":"9523_CR15","first-page":"77","volume":"7","author":"H. Markowitz","year":"1952","unstructured":"Markowitz, H.: Portfolio selection. J. Financ. 7, 77\u201397 (1952)","journal-title":"J. Financ."},{"issue":"4","key":"9523_CR16","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1142\/S0217595907001401","volume":"24","author":"Y. Wang","year":"2007","unstructured":"Wang, Y., Chen, Z., Zhang, K.: A chance-constrained portfolio selection problem under t-distribution. Asia Pac. J. Oper. Res. 24(4), 535\u2013556 (2007)","journal-title":"Asia Pac. J. Oper. Res."},{"key":"9523_CR17","doi-asserted-by":"crossref","unstructured":"Campi, M.C., Garatti, S.: The exact feasibility of randomized solutions of robust convex programs. Optimization online ( www.optimization-online.org ) (2007)","DOI":"10.1137\/07069821X"},{"key":"9523_CR18","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1109\/TAC.2006.875041","volume":"51","author":"G. Calafiore","year":"2006","unstructured":"Calafiore, G., Campi, M.C.: The scenario approach to robust control design. IEEE Trans. Autom. Control. 51, 742\u2013753 (2006)","journal-title":"IEEE Trans. Autom. Control."},{"key":"9523_CR19","unstructured":"Klein Haneveld, W.K., van der Vlerk, M.H.: Stochastic Programming (lecture notes) (2007)"},{"key":"9523_CR20","series-title":"Industrial Engineering and Management Science Series","volume-title":"Simulation Modeling and Analysis","author":"A. Law","year":"1999","unstructured":"Law, A., Kelton, W.D.: Simulation Modeling and Analysis. Industrial Engineering and Management Science Series. McGraw\u2013Hill Science\/Engineering\/Math, New York (1999)"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-009-9523-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-009-9523-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-009-9523-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,24]],"date-time":"2023-05-24T11:24:37Z","timestamp":1684927477000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-009-9523-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,3,12]]},"references-count":20,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2009,8]]}},"alternative-id":["9523"],"URL":"https:\/\/doi.org\/10.1007\/s10957-009-9523-6","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,3,12]]}}}