Computational Optimization and Applications

, Volume 74, Issue 1, pp 1–42 | Cite as

On level regularization with normal solutions in decomposition methods for multistage stochastic programming problems

  • Wim van Ackooij
  • Welington de OliveiraEmail author
  • Yongjia Song


We consider well-known decomposition techniques for multistage stochastic programming and a new scheme based on normal solutions for stabilizing iterates during the solution process. The given algorithms combine ideas from finite perturbation of convex programs and level bundle methods to regularize the so-called forward step of these decomposition methods. Numerical experiments on a hydrothermal scheduling problem indicate that our algorithms are competitive with the state-of-the-art approaches such as multistage regularized decomposition, nested decomposition and stochastic dual dynamic programming.


Normal solution SDDP algorithm Stochastic optimization Nonsmooth optimization 



We would like to acknowledge the coordinating editor and two anonymous referees for their constructive suggestions that considerably improved the original version of this article. We also thank C. Wolf and A. Koberstein for providing us with some test problems and E. Finardi and F. Beltrán for the instances of the multistage hydro-thermal power generation planning problem. Finally, the first and the second authors would like to acknowledge the partial financial support of PGMO (Gaspard Monge Program for Optimization and operations research) of the Hadamard Mathematics Foundation, through the project “Models for planning energy investment under uncertainty”. The third author acknowledges partial support by the National Science Foundation (NSF) under grant CMMI 1854960. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.EDF R&D. OSIRIS 7Palaiseau CedexFrance
  2. 2.MINES ParisTech, PSL - Research University, CMA - Centre de Mathématiques AppliquéesSophia AntipolisFrance
  3. 3.Clemson UniversityClemsonUSA

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