{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,7]],"date-time":"2025-08-07T20:35:03Z","timestamp":1754598903581,"version":"3.37.3"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,3,25]],"date-time":"2021-03-25T00:00:00Z","timestamp":1616630400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,3,25]],"date-time":"2021-03-25T00:00:00Z","timestamp":1616630400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["401371\/2014-0"],"award-info":[{"award-number":["401371\/2014-0"]}],"id":[{"id":"10.13039\/501100003593","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":[[2021,5]]},"DOI":"10.1007\/s10957-021-01842-x","type":"journal-article","created":{"date-parts":[[2021,3,25]],"date-time":"2021-03-25T22:40:18Z","timestamp":1616712018000},"page":"513-559","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Stochastic Dynamic Cutting Plane for Multistage Stochastic Convex Programs"],"prefix":"10.1007","volume":"189","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8862-3696","authenticated-orcid":false,"given":"Vincent","family":"Guigues","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Renato D. C.","family":"Monteiro","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,3,25]]},"reference":[{"key":"1842_CR1","unstructured":"Andersen, E.D., Andersen, K.D.: The MOSEK optimization toolbox for MATLAB manual. Version 9.2, 2019. https:\/\/www.mosek.com\/documentation\/"},{"key":"1842_CR2","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1007\/BF01386316","volume":"4","author":"JF Benders","year":"1962","unstructured":"Benders, J.F.: Partitioning procedures for solving mixed-variables programming problems. Numer. Math. 4, 238\u2013252 (1962)","journal-title":"Numer. Math."},{"key":"1842_CR3","doi-asserted-by":"publisher","first-page":"989","DOI":"10.1287\/opre.33.5.989","volume":"33","author":"JR Birge","year":"1985","unstructured":"Birge, J.R.: Decomposition and partitioning methods for multistage stochastic linear programs. Oper. Res. 33, 989\u20131007 (1985)","journal-title":"Oper. Res."},{"key":"1842_CR4","unstructured":"Ding, L., Ahmed, S., Shapiro, A.: A python package for multi-stage stochastic programming. Optimization Online (2019)"},{"key":"1842_CR5","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1287\/moor.2014.0664","volume":"40","author":"P Girardeau","year":"2015","unstructured":"Girardeau, P., Leclere, V., Philpott, A.B.: On the convergence of decomposition methods for multistage stochastic convex programs. Math. Oper. Res. 40, 130\u2013145 (2015)","journal-title":"Math. Oper. Res."},{"key":"1842_CR6","doi-asserted-by":"publisher","first-page":"2468","DOI":"10.1137\/140983136","volume":"26","author":"V Guigues","year":"2016","unstructured":"Guigues, V.: Convergence analysis of sampling-based decomposition methods for risk-averse multistage stochastic convex programs. SIAM J. Optim. 26, 2468\u20132494 (2016)","journal-title":"SIAM J. Optim."},{"key":"1842_CR7","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.ejor.2016.10.047","volume":"258","author":"V Guigues","year":"2017","unstructured":"Guigues, V.: Dual dynamic programing with cut selection: convergence proof and numerical experiments. Eur. J. Oper. Res. 258, 47\u201357 (2017)","journal-title":"Eur. J. Oper. Res."},{"key":"1842_CR8","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1137\/18M1211799","volume":"30","author":"V Guigues","year":"2020","unstructured":"Guigues, V.: Inexact cuts in stochastic dual dynamic programming. SIAM J. Optim. 30, 407\u2013438 (2020)","journal-title":"SIAM J. Optim."},{"key":"1842_CR9","unstructured":"Guigues, V.: Inexact stochastic mirror descent for two-stage nonlinear stochastic programs. Accepted for publication in Mathematical Programming (2020). https:\/\/arxiv.org\/pdf\/1805.11732.pdf"},{"key":"1842_CR10","unstructured":"Guigues, V., Bandarra, M.: Single cut and multicut SDDP with cut selection for multistage stochastic linear programs: convergence proof and numerical experiments. Computational Management Science. https:\/\/arxiv.org\/abs\/1902.06757"},{"key":"1842_CR11","unstructured":"Guigues, V., Monteiro, R., Svaiter, B.: Inexact cuts in SDDP applied to multistage stochastic nondifferentiable problems. arXiv (2020). https:\/\/arxiv.org\/abs\/2004.02701"},{"key":"1842_CR12","doi-asserted-by":"publisher","first-page":"286","DOI":"10.1137\/100811696","volume":"22","author":"V Guigues","year":"2012","unstructured":"Guigues, V., R\u00f6misch, W.: Sampling-based decomposition methods for multistage stochastic programs based on extended polyhedral risk measures. SIAM J. Optim. 22, 286\u2013312 (2012)","journal-title":"SIAM J. Optim."},{"key":"1842_CR13","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1016\/j.orl.2012.04.006","volume":"40","author":"V Guigues","year":"2012","unstructured":"Guigues, V., R\u00f6misch, W.: SDDP for multistage stochastic linear programs based on spectral risk measures. Oper. Res. Lett. 40, 313\u2013318 (2012)","journal-title":"Oper. Res. Lett."},{"key":"1842_CR14","unstructured":"Guigues, V., Shapiro, A., Cheng, Y.: Duality and sensitivity analysis of multistage linear stochastic programs. Optimization OnLine (2019)"},{"key":"1842_CR15","doi-asserted-by":"publisher","first-page":"1133","DOI":"10.1007\/s11081-020-09511-0","volume":"21","author":"V Guigues","year":"2020","unstructured":"Guigues, V., Tekaya, W., Lejeune, M.: Regularized decomposition methods for deterministic and stochastic convex optimization and application to portfolio selection with direct transaction and market impact costs. Optim. Eng. 21, 1133\u20131165 (2020)","journal-title":"Optim. Eng."},{"key":"1842_CR16","first-page":"703","volume":"8","author":"JE Kelley","year":"1960","unstructured":"Kelley, J.E.: The cutting plane method for solving convex programs. J. SIAM 8, 703\u2013712 (1960)","journal-title":"J. SIAM"},{"key":"1842_CR17","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1007\/BF02591907","volume":"27","author":"KC Kiwiel","year":"1983","unstructured":"Kiwiel, K.C.: An aggregate subgradient method for nonsmooth convex minimization. Math. Program. 27, 320\u2013341 (1983)","journal-title":"Math. Program."},{"key":"1842_CR18","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/BF01585731","volume":"46","author":"KC Kiwiel","year":"1990","unstructured":"Kiwiel, K.C.: Proximity control in bundle methods for convex nondifferentiable minimization. Math. Program. 46, 105\u2013122 (1990)","journal-title":"Math. Program."},{"key":"1842_CR19","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1007\/s10107-014-0787-8","volume":"152","author":"V Kozm\u00edk","year":"2015","unstructured":"Kozm\u00edk, V., Morton, D.P.: Evaluating policies in risk-averse multi-stage stochastic programming. Math. Program. 152, 275\u2013300 (2015)","journal-title":"Math. Program."},{"key":"1842_CR20","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/BFb0120700","volume":"3","author":"C Lemar\u00e9chal","year":"1975","unstructured":"Lemar\u00e9chal, C.: An extension of Davidon methods to non-differentiable problems. Math. Program. Study 3, 95\u2013109 (1975)","journal-title":"Math. Program. Study"},{"key":"1842_CR21","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/BF01585555","volume":"69","author":"C Lemar\u00e9chal","year":"1995","unstructured":"Lemar\u00e9chal, C., Nemirovski, A., Nesterov, Y.: New variants of bundle methods. Math. Program. 69, 111\u2013147 (1995)","journal-title":"Math. Program."},{"key":"1842_CR22","unstructured":"Liu, R.P., Shapiro, A.: Risk neutral reformulation approach to risk averse stochastc programming. arXiv (2018). arXiv:1901.01302"},{"key":"1842_CR23","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/BF01582895","volume":"52","author":"MVF Pereira","year":"1991","unstructured":"Pereira, M.V.F., Pinto, L.M.V.G.: Multi-stage stochastic optimization applied to energy planning. Math. Program. 52, 359\u2013375 (1991)","journal-title":"Math. Program."},{"key":"1842_CR24","doi-asserted-by":"publisher","first-page":"470","DOI":"10.1016\/j.ejor.2011.10.056","volume":"218","author":"A Philpott","year":"2012","unstructured":"Philpott, A., de Matos, V.: Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion. Eur. J. Oper. Res. 218, 470\u2013483 (2012)","journal-title":"Eur. J. Oper. Res."},{"key":"1842_CR25","first-page":"196","volume":"290","author":"A Philpott","year":"2012","unstructured":"Philpott, A., de Matos, V., Finardi, E.: Improving the performance of stochastic dual dynamic programming. J. Comput. Appl. Math. 290, 196\u2013208 (2012)","journal-title":"J. Comput. Appl. Math."},{"key":"1842_CR26","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1016\/j.orl.2008.01.013","volume":"36","author":"AB Philpott","year":"2008","unstructured":"Philpott, A.B., Guan, Z.: On the convergence of stochastic dual dynamic programming and related methods. Oper. Res. Lett. 36, 450\u2013455 (2008)","journal-title":"Oper. Res. Lett."},{"key":"1842_CR27","doi-asserted-by":"crossref","unstructured":"Powell, W.P.: Approximate Dynamic Programming, 2nd edn. Wiley (2011)","DOI":"10.1002\/9780470400531.eorms0043"},{"key":"1842_CR28","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)"},{"key":"1842_CR29","doi-asserted-by":"crossref","unstructured":"Rockafellar, T.: Conjugate Duality and Optimization. No 16 in Conference Board of Math. Sciences Series, pp. 1\u201379. SIAM Publications (1974)","DOI":"10.1137\/1.9781611970524.ch1"},{"key":"1842_CR30","doi-asserted-by":"publisher","first-page":"544","DOI":"10.1287\/moor.1060.0204","volume":"31","author":"A Ruszczy\u0144ski","year":"2006","unstructured":"Ruszczy\u0144ski, A., Shapiro, A.: Conditional risk mappings. Math. Oper. Res. 31, 544\u2013561 (2006)","journal-title":"Math. Oper. Res."},{"key":"1842_CR31","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1287\/moor.1050.0186","volume":"31","author":"A Ruszczy\u0144ski","year":"2006","unstructured":"Ruszczy\u0144ski, A., Shapiro, A.: Optimization of convex risk functions. Math. Oper. Res. 31, 433\u2013452 (2006)","journal-title":"Math. Oper. Res."},{"key":"1842_CR32","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/j.ejor.2010.08.007","volume":"209","author":"A Shapiro","year":"2011","unstructured":"Shapiro, A.: Analysis of stochastic dual dynamic programming method. Eur. J. Oper. Res. 209, 63\u201372 (2011)","journal-title":"Eur. J. Oper. Res."},{"key":"1842_CR33","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718751","volume-title":"Lectures on Stochastic Programming: Modeling and Theory","author":"A Shapiro","year":"2009","unstructured":"Shapiro, A., Dentcheva, D., Ruszczy\u0144ski, A.: Lectures on Stochastic Programming: Modeling and Theory. SIAM, Philadelphia (2009)"},{"key":"1842_CR34","doi-asserted-by":"publisher","first-page":"2083","DOI":"10.1137\/19M129406X","volume":"30","author":"A Shapiro","year":"2020","unstructured":"Shapiro, A., Ding, L.: Periodical multistage stochastic programs. SIAM J. Optim. 30, 2083\u20132102 (2020)","journal-title":"SIAM J. Optim."},{"key":"1842_CR35","doi-asserted-by":"publisher","first-page":"638","DOI":"10.1137\/0117061","volume":"17","author":"RM Van Slyke","year":"1969","unstructured":"Van Slyke, R.M., Wets, R.J.-B.: L-shaped linear programs with applications to optimal control and stochastic programming. SIAM J. Appl. Math. 17, 638\u2013663 (1969)","journal-title":"SIAM J. Appl. Math."},{"key":"1842_CR36","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-4381-7","volume-title":"Handbook of Semidefinite Programming","author":"H Wolkowicz","year":"2000","unstructured":"Wolkowicz, H., Saigal, R., Vandenberghe, L.: Handbook of Semidefinite Programming. Springer, Berlin (2000)"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-021-01842-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-021-01842-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-021-01842-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,8]],"date-time":"2021-05-08T13:13:55Z","timestamp":1620479635000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-021-01842-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,25]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,5]]}},"alternative-id":["1842"],"URL":"https:\/\/doi.org\/10.1007\/s10957-021-01842-x","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"type":"print","value":"0022-3239"},{"type":"electronic","value":"1573-2878"}],"subject":[],"published":{"date-parts":[[2021,3,25]]},"assertion":[{"value":"17 July 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 February 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 April 2021","order":4,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Update","order":5,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Under the section \u20184 Inexact Cuts in StoDCuP\u2019, part b), the missing term \u2018denote the\u2019 has been reinserted so it reads \u2018...denote the corresponding linearizations\u2019.","order":6,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}}]}}