Second-Order Conic Programming Approach for Wasserstein Distributionally Robust Two-Stage Linear Programs

  title={Second-Order Conic Programming Approach for Wasserstein Distributionally Robust Two-Stage Linear Programs},
  author={Zhuolin Wang and Keyou You and Shiji Song and Yuli Zhang},
  journal={IEEE Transactions on Automation Science and Engineering},
This article proposes a second-order conic programming (SOCP) approach to solve distributionally robust two-stage linear programs over 1-Wasserstein balls. We start from the case with distribution uncertainty only in the objective function and then explore the case with distribution uncertainty only in constraints. The former program is exactly reformulated as a tractable SOCP problem, whereas the latter one is proved to be generally NP-hard as it involves a norm maximization problem over a… 

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