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On Distributionally Robust Chance Constrained Programs with Wasserstein Distance

Weijun Xie (wxie***at***vt.edu)

Abstract: This paper studies a distributionally robust chance constrained program (DRCCP) with Wasserstein ambiguity set, where the uncertain constraints should be satisfied with a probability at least a given threshold for all the probability distributions of the uncertain parameters within a chosen Wasserstein distance from an empirical distribution. In this work, we investigate equivalent reformulations and approximations of such problems. We first show that a DRCCP can be reformulated as a conditional value-at-risk constrained optimization problem, and thus admits tight inner and outer approximations. We also show that a DRCCP of bounded feasible region is mixed integer representable by introducing big-M coefficients and additional binary variables. For a DRCCP with pure binary decision variables, by exploring the submodular structure, we show that it admits a big-M free formulation and can be solved by a branch and cut algorithm. Finally, we present a numerical study to illustrate the effectiveness of the proposed formulations.

Keywords: Distributionally Robust; Chance Constraint; Wasserstein Ambiguity Set; Submodularity

Category 1: Stochastic Programming

Category 2: Robust Optimization

Citation: Submitted for publication

Download: [PDF]

Entry Submitted: 06/15/2018
Entry Accepted: 06/15/2018
Entry Last Modified: 02/14/2020

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