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Computational experiments are conducted using the setting of optimizing energy storage over a large transmission grid, which motivates both the spatial and temporal dimensions of our problem. Our numerical results indicate that the proposed methods exhibit significantly faster convergence than their classical counterparts, with greater gains observed for higher-dimensional problems.<\/jats:p>","DOI":"10.1137\/16m1072231","type":"journal-article","created":{"date-parts":[[2018,3,7]],"date-time":"2018-03-07T11:05:59Z","timestamp":1520420759000},"page":"575-595","source":"Crossref","is-referenced-by-count":39,"title":["Regularized Decomposition of High-Dimensional Multistage Stochastic Programs with Markov Uncertainty"],"prefix":"10.1137","volume":"28","author":[{"given":"Tsvetan","family":"Asamov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Warren B.","family":"Powell","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,3,6]]},"reference":[{"key":"atypb1","unstructured":"T. Asamov and W. B. Powell,\n                      Multistage Stochastic Optimization Methods Applied to Grid Energy Storage\n                      , tech. report, Department of Operations Research and Financial Engineering, Princeton University, 2015."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-014-0813-x"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01386316"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1287\/opre.33.5.989"},{"key":"atypb5","unstructured":"A. Chiralaksanakul and D. P. Morton,\n                      Assessing Policy Quality in Multi-stage Stochastic Programming\n                      , Humboldt-Universita\u0308t zu Berlin, Mathematisch-Naturwissenschaftliche Fakulta\u0308t II, Institut fu\u0308r Mathematik, 2004."},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2013.03.003"},{"key":"atypb7","first-page":"20","volume":"1","author":"Donohue C. J.","year":"2006","journal-title":"Algorithmic Oper. 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Nesterov,\n                      Introductory Lectures on Convex Optimization: A Basic Course\n                      , Appl. Optim. 87, Springer, 2004.","DOI":"10.1007\/978-1-4419-8853-9"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/BF01582895"},{"key":"atypb19","unstructured":"A. B. Philpott and V. L. De Matos,\n                      Dynamic Sampling Algorithms for Multistage Stochastic Programs with Risk Aversion\n                      , tech. report, Electric Power Optimization Centre, University of Auckland, 2011."},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2008.01.013"},{"key":"atypb21","doi-asserted-by":"crossref","unstructured":"W. B. Powell,\n                      Approximate Dynamic Programming: Solving the Curses of Dimensionality\n                      , John Wiley & Sons, 2011.","DOI":"10.1002\/9781118029176"},{"key":"atypb22","unstructured":"M. L. Puterman,\n                      Markov Decision Processes: Discrete Stochastic Dynamic Programming\n                      , John Wiley & Sons, 2014."},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1137\/0314056"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/BF01580883"},{"key":"atypb25","unstructured":"A. Ruszczyn\u0301ski,\n                      Regularized Decomposition of Stochastic Programs: Algorithmic Techniques and Numerical Results\n                      , Working paper WP-93-21, International Institute for Applied System Analysis, Laxenburg, Austria, 1993."},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1007\/BF02614323"},{"key":"atypb27","unstructured":"A. Ruszczyn\u0301ski,\n                      Nonlinear Optimization\n                      , Math. 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