{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T01:46:02Z","timestamp":1774057562449,"version":"3.50.1"},"reference-count":26,"publisher":"Pleiades Publishing Ltd","issue":"6","license":[{"start":{"date-parts":[[2013,6,1]],"date-time":"2013-06-01T00:00:00Z","timestamp":1370044800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2013,6,1]],"date-time":"2013-06-01T00:00:00Z","timestamp":1370044800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Autom Remote Control"],"published-print":{"date-parts":[[2013,6]]},"DOI":"10.1134\/s0005117913060064","type":"journal-article","created":{"date-parts":[[2013,6,13]],"date-time":"2013-06-13T20:47:08Z","timestamp":1371156428000},"page":"951-967","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":39,"title":["On reducing a quantile optimization problem with discrete distribution to a mixed integer programming problem"],"prefix":"10.1134","volume":"74","author":[{"given":"A. I.","family":"Kibzun","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. V.","family":"Naumov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V. I.","family":"Norkin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"137","published-online":{"date-parts":[[2013,6,15]]},"reference":[{"key":"9885_CR1","volume-title":"Metody stokhasticheskogo programmirovaniya","author":"YuM Ermol\u2019ev","year":"1976","unstructured":"Ermol\u2019ev, Yu.M., Metody stokhasticheskogo programmirovaniya (Methods of Stochastic Programming), Moscow: Nauka, 1976."},{"key":"9885_CR2","volume-title":"Zadachi i metody stokhasticheskogo programmirovaniya","author":"DB Yudin","year":"1979","unstructured":"Yudin, D.B., Zadachi i metody stokhasticheskogo programmirovaniya (Problems and Methods of Stochastic Programming), Moscow: Sovetskoe Radio, 1979."},{"key":"9885_CR3","volume-title":"Analiz i sintez vysokotochnogo upravleniya letatel\u2019nymi apparatami","author":"VV Malyshev","year":"1987","unstructured":"Malyshev, V.V. and Kibzun, A.I., Analiz i sintez vysokotochnogo upravleniya letatel\u2019nymi apparatami (Analysis and Synthesis of High Precision Control for Flying Vehicles), Moscow: Mashinostroenie, 1987."},{"key":"9885_CR4","volume-title":"Stochastic Programming Problems with Probability and Quantile Functions","author":"AI Kibzun","year":"1996","unstructured":"Kibzun, A.I. and Kan, Y.S., Stochastic Programming Problems with Probability and Quantile Functions, New York: Wiley, 1996."},{"key":"9885_CR5","volume-title":"Zadachi stokhasticheskogo programmirovaniya s veroyatnostnymi kriteriyami","author":"AI Kibzun","year":"2009","unstructured":"Kibzun, A.I. and Kan, Yu.S., Zadachi stokhasticheskogo programmirovaniya s veroyatnostnymi kriteriyami (Stochastic Programming Problems with Probabilistic Criteria), Moscow: Fizmatlit, 2009."},{"issue":"2","key":"9885_CR6","first-page":"160","volume":"33","author":"AI Kibzun","year":"1995","unstructured":"Kibzun, A.I. and Naumov, A.V., A Guaranteeing Algorithm for the Quantile Optimization Problem, Kosm. Issled., 1995, vol. 33, no. 2, pp. 160\u2013165.","journal-title":"Kosm. Issled."},{"key":"9885_CR7","first-page":"129","volume-title":"Financial Engineering, e-Commerce, and Supply Chain","author":"N Larsen","year":"2002","unstructured":"Larsen, N., Mausser, H., and Uryasev, S., Algorithms for Optimization of Value-at-Risk, in Financial Engineering, e-Commerce, and Supply Chain, Pardalos, S. and Tsitsiringos, V.K., Eds., New York: Kluwer, 2002, pp. 129\u2013157."},{"issue":"3","key":"9885_CR8","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1080\/02331931003700731","volume":"59","author":"D Wozabal","year":"2010","unstructured":"Wozabal, D., Hochreiter, R., and Pflug, G.Ch., A D.C. Formulation of Value-at-Risk Constrained Optimization, Optimization, 2010, vol. 59, no. 3, pp. 377\u2013400.","journal-title":"Optimization"},{"key":"9885_CR9","volume-title":"On Mixed Integer Reformulations of Monotonic Probabilistic Programming Problems with Discrete Distributions","author":"V Norkin","year":"2010","unstructured":"Norkin, V., On Mixed Integer Reformulations of Monotonic Probabilistic Programming Problems with Discrete Distributions, http:\/\/www.optimization-online.org\/DB HTML\/2010\/05\/2619.html, 2010."},{"issue":"1","key":"9885_CR10","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1134\/S0005117912010080","volume":"73","author":"SV Ivanov","year":"2012","unstructured":"Ivanov, S.V. and Naumov, A.V., Algorithm to Optimize the Quantile Criterion for the Polyhedral Loss Function and Discrete Distribution of Random Parameters, Autom. Remote Control, 2012, vol. 73, no. 1, pp. 105\u2013117.","journal-title":"Autom. Remote Control"},{"key":"9885_CR11","first-page":"81","volume-title":"Operations Res. Lett.","author":"S Sen","year":"1992","unstructured":"Sen, S., Relaxation for Probabilistically Constrained Programs with Discrete Random Variables, Operations Res. Lett., 1992, no. 11, pp. 81\u201386."},{"key":"9885_CR12","first-page":"195","volume-title":"Math. Program.","author":"A Ruszczy\u2019nski","year":"2002","unstructured":"Ruszczy\u2019nski, A., Probabilistic Programming with Discrete Distributions and Precedence Constrained Knapsack Polyhedra, Math. Program., 2002, no. 93, pp. 195\u2013215."},{"key":"9885_CR13","first-page":"423","volume-title":"Eur. J. Operational Res.","author":"S Benati","year":"2007","unstructured":"Benati, S. and Rizzi, R., A Mixed Integer Linear Programming Formulation of the Optimal Mean\/Valueat-Risk Portfolio Problem, Eur. J. Operational Res., 2007, no. 176, pp. 423\u2013434."},{"key":"9885_CR14","first-page":"247","volume-title":"Math. Program.","author":"J Luedtke","year":"2010","unstructured":"Luedtke, J., Ahmed, S., and Nemhauser, G., An Integer Programming Approach for Linear Programs with Probabilistic Constraints, Math. Program., 2010, no. 122(2), pp. 247\u2013272."},{"key":"9885_CR15","volume-title":"Diskretnoe programmirovanie","author":"AA Korbut","year":"1969","unstructured":"Korbut, A.A. and Finkel\u2019shtein, Yu.Yu., Diskretnoe programmirovanie (Discrete Programming), Moscow: Nauka, 1969."},{"key":"9885_CR16","first-page":"29","volume-title":"Kibern. Sist. Anal.","author":"VI Norkin","year":"2012","unstructured":"Norkin, V.I. and Boiko, S.V., Optimizing a Financial Portfolio Based on the Safety First Principle, Kibern. Sist. Anal., 2012, no. 2, pp. 29\u201341 (electronic version: Norkin, V.I. and Boyko, S.V., On the Safety First Portfolio Selection, http:\/\/www.optimization-online.org\/DBHTML\/2010\/07\/2686.html, 2010)."},{"issue":"2","key":"9885_CR17","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1134\/S0005117912020051","volume":"73","author":"AV Naumov","year":"2012","unstructured":"Naumov, A.V. and Bobylev, I.M., On the Two-stage Problem of Linear Stochastic Programming with Quantile Criterion and Discrete Distribution of the Random Parameters, Autom. Remote Control, 2012, vol. 73, no. 2, pp. 265\u2013275.","journal-title":"Autom. Remote Control"},{"key":"9885_CR18","unstructured":"IBM ILOG CPLEX V12.1. User\u2019s Manual for CPLEX, Armonk: IBM, 2009."},{"issue":"1","key":"9885_CR19","first-page":"8","volume":"20","author":"E Raik","year":"1971","unstructured":"Raik, E., Qualitative Studies in Stochastic Nonlinear Programming Problems, Izv. Akad. Nauk Eston. SSR, Fiz. Mat., 1971, vol. 20, no. 1, pp. 8\u201314.","journal-title":"Izv. Akad. Nauk Eston. SSR, Fiz. Mat."},{"key":"9885_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-3087-7","volume-title":"Stochastic Programming","author":"A Prekopa","year":"1995","unstructured":"Prekopa, A. Stochastic Programming, New York: Kluwer, 1995."},{"issue":"2","key":"9885_CR21","first-page":"229","volume":"20","author":"E Raik","year":"1971","unstructured":"Raik, E., On the Quantile Function in Stochastic Nonlinear Programming, Izv. Akad. Nauk Eston. SSR, Fiz. Mat., 1971, vol. 20, no. 2, pp. 229\u2013231.","journal-title":"Izv. Akad. Nauk Eston. SSR, Fiz. Mat."},{"key":"9885_CR22","first-page":"258","volume":"21","author":"E Raik","year":"1972","unstructured":"Raik, E., On Stochastic Programming Problems with Decision Functions, Izv. Akad. Nauk Eston. SSR, 1972, vol. 21, pp. 258\u2013263.","journal-title":"Izv. Akad. Nauk Eston. SSR"},{"key":"9885_CR23","volume-title":"Applied Nonlinear Analysis","author":"JP Aubin","year":"1984","unstructured":"Aubin, J.P. and Ekeland, I., Applied Nonlinear Analysis, New York: Wiley, 1984. Translated under the title Prikladnoi nelineinyi analiz, Moscow: Mir, 1988."},{"key":"9885_CR24","doi-asserted-by":"publisher","first-page":"181","DOI":"10.2307\/1910956","volume":"31","author":"S Kataoka","year":"1963","unstructured":"Kataoka, S., A Stochastic Programming Model, Econometrica, 1963, vol. 31, pp. 181\u2013196.","journal-title":"Econometrica"},{"key":"9885_CR25","volume-title":"Metody nevypukloi optimizatsii","author":"VS Mikhalevich","year":"1987","unstructured":"Mikhalevich, V.S., Gupal, A.M., and Norkin, V.I., Metody nevypukloi optimizatsii (Methods of Nonconvex Optimization), Moscow: Nauka, 1987."},{"key":"9885_CR26","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1007\/s10957-009-9523-6","volume":"142","author":"BK Pagnoncelli","year":"2009","unstructured":"Pagnoncelli, B.K., Ahmed, S., and Shapiro, A., Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications, J. Optim. Theory Appl., 2009, vol. 142, pp. 399\u2013416.","journal-title":"J. Optim. Theory Appl."}],"container-title":["Automation and Remote Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0005117913060064.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1134\/S0005117913060064","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1134\/S0005117913060064","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0005117913060064.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T22:24:21Z","timestamp":1773613461000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1134\/S0005117913060064"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6]]},"references-count":26,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2013,6]]}},"alternative-id":["9885"],"URL":"https:\/\/doi.org\/10.1134\/s0005117913060064","relation":{},"ISSN":["0005-1179","1608-3032"],"issn-type":[{"value":"0005-1179","type":"print"},{"value":"1608-3032","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,6]]},"assertion":[{"value":"2 May 2012","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 June 2013","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}