A decomposition method for distributionally-robust two-stage stochastic mixed-integer conic programs

Fengqiao Luo, Sanjay Mehrotra*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We develop a decomposition algorithm for distributionally-robust two-stage stochastic mixed-integer convex conic programs, and its important special case of distributionally-robust two-stage stochastic mixed-integer second order conic programs. This generalizes the algorithm proposed by Sen and Sherali [Mathematical Programming 106(2): 203–223, 2006]. We show that the proposed algorithm is finitely convergent if the second-stage problems are solved to optimality at incumbent first stage solutions, and solution to an optimization problem to identify worst-case probability distribution is available. The second stage problems can be solved using a branch and cut algorithm, or a parametric cuts based algorithm presented in this paper. The decomposition algorithm is illustrated with an example. Computational results on a stochastic programming generalization of a facility location problem show significant solution time improvements from the proposed approach. Solutions for many models that are intractable for an extensive form formulation become possible. Computational results also show that for the same amount of computational effort the optimality gaps for distributionally robust instances and their stochastic programming counterpart are similar.

Original languageEnglish (US)
Pages (from-to)673-717
Number of pages45
JournalMathematical Programming
Issue number1-2
StatePublished - Nov 2022


  • Disjunctive programming
  • Distributionally robust optimization
  • Stochastic facility location
  • Two-stage stochastic mixed-integer conic programming
  • Two-stage stochastic mixed-integer second-order-cone programming

ASJC Scopus subject areas

  • Software
  • General Mathematics


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