{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T04:37:34Z","timestamp":1773117454823,"version":"3.50.1"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T00:00:00Z","timestamp":1742860800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T00:00:00Z","timestamp":1742860800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"State of Minnesota"},{"DOI":"10.13039\/100007249","name":"University of Minnesota","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100007249","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Instituto Sistemas Complejos de Ingenieria","award":["ANID PIA\/PUENTE AFB230002"],"award-info":[{"award-number":["ANID PIA\/PUENTE AFB230002"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2026,1]]},"DOI":"10.1007\/s10898-025-01480-x","type":"journal-article","created":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T03:49:22Z","timestamp":1743047362000},"page":"95-126","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Column generation for multistage stochastic mixed-integer nonlinear programs with discrete state variables"],"prefix":"10.1007","volume":"94","author":[{"given":"Tushar","family":"Rathi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Benjamin P.","family":"Riley","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Angela","family":"Flores-Quiroz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8862-4675","authenticated-orcid":false,"given":"Qi","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,3,25]]},"reference":[{"key":"1480_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-0237-4","volume-title":"Introduction to Stochastic Programming","author":"JR Birge","year":"2011","unstructured":"Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming. Springer, New York (2011)"},{"issue":"2","key":"1480_CR2","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1137\/S1052623499363220","volume":"12","author":"AJ Kleywegt","year":"2002","unstructured":"Kleywegt, A.J., Shapiro, A., Homem-de-Mello, T.: The sample average approximation method for stochastic discrete optimization. SIAM J. Optim. 12(2), 479\u2013502 (2002)","journal-title":"SIAM J. Optim."},{"key":"1480_CR3","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1016\/j.cor.2017.04.007","volume":"85","author":"LF Escudero","year":"2017","unstructured":"Escudero, L.F., Gar\u00edn, M.A., Unzueta, A.: Scenario cluster Lagrangean decomposition for risk averse in multistage stochastic optimization. Comput. Oper. Res. 85, 154\u2013171 (2017)","journal-title":"Comput. Oper. Res."},{"key":"1480_CR4","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1007\/s10107-018-1249-5","volume":"175","author":"J Zou","year":"2019","unstructured":"Zou, J., Ahmed, S., Sun, X.A.: Stochastic dual dynamic integer programming. Math. Program. 175, 461\u2013502 (2019)","journal-title":"Math. Program."},{"key":"1480_CR5","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/BF01582895","volume":"52","author":"MV Pereira","year":"1991","unstructured":"Pereira, M.V., Pinto, L.M.: Multi-stage stochastic optimization applied to energy planning. Math. Program. 52, 359\u2013375 (1991)","journal-title":"Math. Program."},{"issue":"1","key":"1480_CR6","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(1), 63\u201372 (2011)","journal-title":"Eur. J. Oper. Res."},{"key":"1480_CR7","doi-asserted-by":"publisher","first-page":"1243","DOI":"10.1007\/s11081-019-09471-0","volume":"21","author":"CL Lara","year":"2020","unstructured":"Lara, C.L., Siirola, J.D., Grossmann, I.E.: Electric power infrastructure planning under uncertainty: stochastic dual dynamic integer programming (SDDiP) and parallelization scheme. Optim. Eng. 21, 1243\u20131281 (2020)","journal-title":"Optim. Eng."},{"issue":"2","key":"1480_CR8","doi-asserted-by":"publisher","first-page":"755","DOI":"10.1007\/s10107-020-01569-z","volume":"191","author":"S Ahmed","year":"2022","unstructured":"Ahmed, S., Cabral, F.G., Costa, B.: Stochastic lipschitz dynamic programming. Math. Program. 191(2), 755\u2013793 (2022)","journal-title":"Math. Program."},{"issue":"1","key":"1480_CR9","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1287\/moor.16.1.119","volume":"16","author":"RT Rockafellar","year":"1991","unstructured":"Rockafellar, R.T., Wets, R.J.-B.: Scenarios and policy aggregation in optimization under uncertainty. Math. Oper. Res. 16(1), 119\u2013147 (1991)","journal-title":"Math. Oper. Res."},{"key":"1480_CR10","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/BF00247208","volume":"2","author":"A L\u00f8kketangen","year":"1996","unstructured":"L\u00f8kketangen, A., Woodruff, D.L.: Progressive hedging and tabu search applied to mixed integer (0, 1) multistage stochastic programming. J. Heuristics 2, 111\u2013128 (1996)","journal-title":"J. Heuristics"},{"key":"1480_CR11","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1007\/s10287-010-0125-4","volume":"8","author":"J-P Watson","year":"2011","unstructured":"Watson, J.-P., Woodruff, D.L.: Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems. CMS 8, 355\u2013370 (2011)","journal-title":"CMS"},{"issue":"1","key":"1480_CR12","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1016\/j.orl.2016.11.006","volume":"45","author":"J Barnett","year":"2017","unstructured":"Barnett, J., Watson, J.-P., Woodruff, D.L.: BBPH: using progressive hedging within branch and bound to solve multi-stage stochastic mixed integer programs. Oper. Res. Lett. 45(1), 34\u201339 (2017)","journal-title":"Oper. Res. Lett."},{"issue":"3","key":"1480_CR13","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1007\/s10287-018-0311-3","volume":"15","author":"S Atakan","year":"2018","unstructured":"Atakan, S., Sen, S.: A progressive hedging based branch-and-bound algorithm for mixed-integer stochastic programs. CMS 15(3), 501\u2013540 (2018)","journal-title":"CMS"},{"issue":"5","key":"1480_CR14","doi-asserted-by":"publisher","first-page":"1271","DOI":"10.1287\/opre.1080.0678","volume":"57","author":"KJ Singh","year":"2009","unstructured":"Singh, K.J., Philpott, A.B., Wood, R.K.: Dantzig\u2013Wolfe decomposition for solving multistage stochastic capacity-planning problems. Oper. Res. 57(5), 1271\u20131286 (2009)","journal-title":"Oper. Res."},{"issue":"1","key":"1480_CR15","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1287\/opre.1050.0264","volume":"54","author":"S Sen","year":"2006","unstructured":"Sen, S., Yu, L., Genc, T.: A stochastic programming approach to power portfolio optimization. Oper. Res. 54(1), 55\u201372 (2006)","journal-title":"Oper. Res."},{"key":"1480_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.apenergy.2021.116736","volume":"291","author":"A Flores-Quiroz","year":"2021","unstructured":"Flores-Quiroz, A., Strunz, K.: A distributed computing framework for multi-stage stochastic planning of renewable power systems with energy storage as flexibility option. Appl. Energy 291, 116736 (2021)","journal-title":"Appl. Energy"},{"key":"1480_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.compchemeng.2022.107868","volume":"164","author":"T Rathi","year":"2022","unstructured":"Rathi, T., Zhang, Q.: Capacity planning with uncertain endogenous technology learning. Comput. Chem. Eng. 164, 107868 (2022)","journal-title":"Comput. Chem. Eng."},{"key":"1480_CR18","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1007\/s10957-011-9888-1","volume":"151","author":"X Li","year":"2011","unstructured":"Li, X., Tomasgard, A., Barton, P.I.: Nonconvex generalized benders decomposition for stochastic separable mixed-integer nonlinear programs. J. Optim. Theory Appl. 151, 425\u2013454 (2011)","journal-title":"J. Optim. Theory Appl."},{"key":"1480_CR19","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1007\/s10898-019-00769-y","volume":"75","author":"Y Cao","year":"2019","unstructured":"Cao, Y., Zavala, V.M.: A scalable global optimization algorithm for stochastic nonlinear programs. J. Glob. Optim. 75, 393\u2013416 (2019)","journal-title":"J. Glob. Optim."},{"key":"1480_CR20","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/j.compchemeng.2018.01.017","volume":"112","author":"C Li","year":"2018","unstructured":"Li, C., Grossmann, I.E.: An improved L-shaped method for two-stage convex 0\u20131 mixed integer nonlinear stochastic programs. Comput. Chem. Eng. 112, 165\u2013179 (2018)","journal-title":"Comput. Chem. Eng."},{"issue":"4","key":"1480_CR21","doi-asserted-by":"publisher","first-page":"921","DOI":"10.1007\/s10898-019-00820-y","volume":"75","author":"C Li","year":"2019","unstructured":"Li, C., Grossmann, I.E.: A finite $$\\epsilon $$-convergence algorithm for two-stage stochastic convex nonlinear programs with mixed-binary first and second-stage variables. J. Glob. Optim. 75(4), 921\u2013947 (2019)","journal-title":"J. Glob. Optim."},{"key":"1480_CR22","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/s10898-019-00816-8","volume":"75","author":"C Li","year":"2019","unstructured":"Li, C., Grossmann, I.E.: A generalized benders decomposition-based branch and cut algorithm for two-stage stochastic programs with nonconvex constraints and mixed-binary first and second stage variables. J. Glob. Optim. 75, 247\u2013272 (2019)","journal-title":"J. Glob. Optim."},{"key":"1480_CR23","doi-asserted-by":"publisher","first-page":"861","DOI":"10.1007\/s10898-021-01027-w","volume":"81","author":"A Allman","year":"2021","unstructured":"Allman, A., Zhang, Q.: Branch-and-price for a class of nonconvex mixed-integer nonlinear programs. J. Glob. Optim. 81, 861\u2013880 (2021)","journal-title":"J. Glob. Optim."},{"issue":"1\u20132","key":"1480_CR24","doi-asserted-by":"publisher","first-page":"935","DOI":"10.1007\/s10107-022-01875-8","volume":"196","author":"S Zhang","year":"2022","unstructured":"Zhang, S., Sun, X.A.: Stochastic dual dynamic programming for multistage stochastic mixed-integer nonlinear optimization. Math. Program. 196(1\u20132), 935\u2013985 (2022)","journal-title":"Math. Program."},{"issue":"1","key":"1480_CR25","doi-asserted-by":"publisher","first-page":"987","DOI":"10.1007\/s10107-021-01740-0","volume":"196","author":"C F\u00fcllner","year":"2022","unstructured":"F\u00fcllner, C., Rebennack, S.: Non-convex nested benders decomposition. Math. Program. 196(1), 987\u20131024 (2022)","journal-title":"Math. Program."},{"key":"1480_CR26","doi-asserted-by":"crossref","unstructured":"Vanderbeck, F.: Implementing mixed integer column generation. In: Column Generation, pp. 331\u2013358. Springer, New York, NY, USA (2005)","DOI":"10.1007\/0-387-25486-2_12"},{"issue":"3","key":"1480_CR27","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1287\/opre.46.3.316","volume":"46","author":"C Barnhart","year":"1998","unstructured":"Barnhart, C., Johnson, E.L., Nemhauser, G.L., Savelsbergh, M.W., Vance, P.H.: Branch-and-price: column generation for solving huge integer programs. Oper. Res. 46(3), 316\u2013329 (1998)","journal-title":"Oper. Res."},{"issue":"6","key":"1480_CR28","doi-asserted-by":"publisher","first-page":"1007","DOI":"10.1287\/opre.1050.0234","volume":"53","author":"ME L\u00fcbbecke","year":"2005","unstructured":"L\u00fcbbecke, M.E., Desrosiers, J.: Selected topics in column generation. Oper. Res. 53(6), 1007\u20131023 (2005)","journal-title":"Oper. Res."},{"key":"1480_CR29","volume-title":"Integer Programming","author":"LA Wolsey","year":"1998","unstructured":"Wolsey, L.A.: Integer Programming. John Wiley & Sons, New Jersey (1998)"},{"key":"1480_CR30","doi-asserted-by":"crossref","unstructured":"Desrosiers, J., L\u00fcbbecke, M.E.: A primer in column generation. In: Column Generation, pp. 1\u201332. Springer, New York, NY, USA (2005)","DOI":"10.1007\/0-387-25486-2_1"},{"issue":"1","key":"1480_CR31","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1287\/opre.48.1.111.12453","volume":"48","author":"F Vanderbeck","year":"2000","unstructured":"Vanderbeck, F.: On Dantzig\u2013Wolfe decomposition in integer programming and ways to perform branching in a branch-and-price algorithm. Oper. Res. 48(1), 111\u2013128 (2000)","journal-title":"Oper. Res."},{"issue":"1","key":"1480_CR32","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1137\/141000671","volume":"59","author":"J Bezanson","year":"2017","unstructured":"Bezanson, J., Edelman, A., Karpinski, S., Shah, V.B.: Julia: a fresh approach to numerical computing. SIAM Rev. 59(1), 65\u201398 (2017). https:\/\/doi.org\/10.1137\/141000671","journal-title":"SIAM Rev."},{"key":"1480_CR33","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1007\/s12532-023-00239-3","volume":"15","author":"M Lubin","year":"2023","unstructured":"Lubin, M., Dowson, O., Dias Garcia, J., Huchette, J., Legat, B., Vielma, J.P.: JuMP 1.0: recent improvements to a modeling language for mathematical optimization. Math. Program. Comput. 15, 581\u2013589 (2023). https:\/\/doi.org\/10.1007\/s12532-023-00239-3","journal-title":"Math. Program. Comput."},{"key":"1480_CR34","unstructured":"Gurobi Optimization, LLC: Gurobi Optimizer Reference Manual (2023). https:\/\/www.gurobi.com"},{"issue":"1","key":"1480_CR35","first-page":"3","volume":"8","author":"R Misener","year":"2009","unstructured":"Misener, R., Floudas, C.A.: Advances for the pooling problem: modeling, global optimization, and computational studies. Appl. Comput. Math. 8(1), 3\u201322 (2009)","journal-title":"Appl. Comput. Math."},{"issue":"3","key":"1480_CR36","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/s12667-012-0056-y","volume":"3","author":"S Frank","year":"2012","unstructured":"Frank, S., Steponavice, I., Rebennack, S.: Optimal power flow: a bibliographic survey I. Energy Syst. 3(3), 221\u2013258 (2012)","journal-title":"Energy Syst."},{"key":"1480_CR37","doi-asserted-by":"crossref","unstructured":"Riley, B.P., Daoutidis, P., Zhang, Q.: Multi-scenario design of ammonia-based energy storage systems for use as non-wires alternatives. J. Energy Storage 73(PA), 108795 (2023)","DOI":"10.1016\/j.est.2023.108795"},{"issue":"5","key":"1480_CR38","doi-asserted-by":"publisher","first-page":"4872","DOI":"10.1109\/TSG.2017.2673860","volume":"9","author":"A Papavasiliou","year":"2018","unstructured":"Papavasiliou, A.: Analysis of distribution locational marginal prices. IEEE Trans. Smart Grid 9(5), 4872\u20134882 (2018)","journal-title":"IEEE Trans. Smart Grid"},{"issue":"3","key":"1480_CR39","doi-asserted-by":"publisher","first-page":"2554","DOI":"10.1109\/TPWRS.2013.2255317","volume":"28","author":"M Farivar","year":"2013","unstructured":"Farivar, M., Low, S.H.: Branch flow model: relaxations and convexification\u00e2\u20ac \u201cPart I. IEEE Trans. Power Syst. 28(3), 2554\u20132564 (2013)","journal-title":"IEEE Trans. Power Syst."},{"issue":"1","key":"1480_CR40","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1109\/TAC.2014.2332712","volume":"60","author":"L Gan","year":"2015","unstructured":"Gan, L., Li, N., Topcu, U., Low, S.H.: Exact convex relaxation of optimal power flow in radial networks. IEEE Trans. Autom. Control 60(1), 72\u201387 (2015)","journal-title":"IEEE Trans. Autom. Control"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-025-01480-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10898-025-01480-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-025-01480-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T04:00:18Z","timestamp":1770609618000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10898-025-01480-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,25]]},"references-count":40,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["1480"],"URL":"https:\/\/doi.org\/10.1007\/s10898-025-01480-x","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,25]]},"assertion":[{"value":"6 June 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 February 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}