We present a new primal-dual algorithm for computing the value of the Lagrangian dual of a stochastic mixed-integer program (SMIP) formed by relaxing its nonanticipativity constraints. This dual is widely used in decomposition methods for the solution of SMIPs. The algorithm relies on the well-known progressive hedging method, but unlike previous progressive hedging approaches for SMIP, our algorithm can be shown to converge to the optimal Lagrangian dual value. The key improvement in the new algorithm is an inner loop of optimized linearization steps, similar to those taken in the classical Frank--Wolfe method. Numerical results demonstrate that our new algorithm empirically outperforms the standard implementation of progressive hedging for obtaining bounds in SMIP.


  1. mixed-integer stochastic programming
  2. Lagrangian duality
  3. progressive hedging
  4. Frank--Wolfe method

MSC codes

  1. 90C06
  2. 90C11
  3. 90C15
  4. 90C46

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Information & Authors


Published In

cover image SIAM Journal on Optimization
SIAM Journal on Optimization
Pages: 1312 - 1336
ISSN (online): 1095-7189


Submitted: 20 May 2016
Accepted: 17 January 2018
Published online: 8 May 2018


  1. mixed-integer stochastic programming
  2. Lagrangian duality
  3. progressive hedging
  4. Frank--Wolfe method

MSC codes

  1. 90C06
  2. 90C11
  3. 90C15
  4. 90C46



Funding Information

Australian Research Council https://doi.org/10.13039/501100000923 : ARC DP140100985
Australian Research Council https://doi.org/10.13039/501100000923 : ARC DP140100985
National Science Foundation https://doi.org/10.13039/100000001 : 1634597
U.S. Department of Energy https://doi.org/10.13039/100000015 : DE-AC02-06CH11357

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