MIDAS: A mixed integer dynamic approximation scheme

  • A. B. PhilpottEmail author
  • F. Wahid
  • J. F. Bonnans
Full Length Paper Series A


Mixed integer dynamic approximation scheme (MIDAS) is a new sampling-based algorithm for solving finite-horizon stochastic dynamic programs with monotonic Bellman functions. MIDAS approximates these value functions using step functions, leading to stage problems that are mixed integer programs. We provide a general description of MIDAS, and prove its almost-sure convergence to a \(2T\varepsilon \)-optimal policy for problems with T stages when the Bellman functions are known to be monotonic, and the sampling process satisfies standard assumptions.


Stochastic programming Approximate dynamic programming Sampling Mixed-integer programming 

Mathematics Subject Classification

90C15 90C39 



Funding was provided by PGMO, EDF, Meridian Energy Limited and the New Zealand Marsden Fund.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2019

Authors and Affiliations

  1. 1.Electric Power Optimization CentreUniversity of AucklandAucklandNew Zealand
  2. 2.Artelys ConsultingParisFrance
  3. 3.INRIA, Ecole PolytechniqueSaclayFrance

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