Combining penalty‐based and Gauss–Seidel methods for solving stochastic mixed‐integer problems

Fabricio Oliveira, Jeffrey Christiansen, Brian Dandurand, Andrew Eberhard

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)
30 Downloads (Pure)


In this paper, we propose a novel decomposition approach (named PBGS) for stochastic mixed‐integer programming (SMIP) problems, which is inspired by the combination of penalty‐based Lagrangian and block Gauss–Seidel methods. The PBGS method is developed such that the inherent decomposable structure that SMIP problems present can be exploited in a computationally efficient manner. The performance of the proposed method is compared with the progressive hedging (PH) method, which also can be viewed as a Lagrangian‐based method for obtaining solutions for SMIP problems. Numerical experiments performed using instances from the literature illustrate the efficiency of the proposed method in terms of computational performance and solution quality.
Original languageEnglish
Pages (from-to)494-524
Number of pages31
JournalInternational Transactions in Operational Research
Issue number1
Publication statusPublished - Jan 2020
MoE publication typeA1 Journal article-refereed


  • stochastic programming
  • decomposition methods
  • Lagrangian duality
  • penalty-based method
  • Gauss-Seidel method


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