The stochastic dual dynamic programming (SDDP) algorithm has become one of the main tools used to address convex multistage stochastic optimal control problems. Recently a large amount of work has been devoted to improving the convergence speed of the algorithm through cut selection and regularization, and to extending the field of applications to nonlinear, integer, or risk-averse problems. However, one of the main downsides of the algorithm remains the difficulty in giving an upper bound of the optimal value, usually estimated through Monte Carlo methods and therefore difficult to use in the stopping criterion of the algorithm. In this paper we present a dual SDDP algorithm that yields a converging exact upper bound for the optimal value of the optimization problem. As an easy consequence of our approach, we show how to compute an alternative control policy based on an inner approximation of Bellman value functions instead of the outer approximation given by the standard SDDP algorithm. We illustrate the approach on an energy production problem involving zones of production and transportation links between the zones. The numerical experiments we carry out on this example show the effectiveness of the method.


  1. stochastic programming
  2. dynamic programming
  3. SDDP
  4. Fenchel conjugacy

MSC codes

  1. 90C15
  2. 90C39
  3. 49N15

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Information & Authors


Published In

cover image SIAM Journal on Optimization
SIAM Journal on Optimization
Pages: 1223 - 1250
ISSN (online): 1095-7189


Submitted: 29 April 2019
Accepted: 24 February 2020
Published online: 28 April 2020


  1. stochastic programming
  2. dynamic programming
  3. SDDP
  4. Fenchel conjugacy

MSC codes

  1. 90C15
  2. 90C39
  3. 49N15



Funding Information

Êlectricité de France https://doi.org/10.13039/501100006289
Fondation Mathématique Jacques Hadamard https://doi.org/10.13039/501100007493

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