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Data-Driven Distributionally Robust Chance-Constrained Optimization with Wasserstein Metric

Ran Ji (rji2***at***gmu.edu)
Miguel Lejeune (mlejeune***at***gwu.edu)

Abstract: We study distributionally robust chance-constrained programming (DRCCP) optimization problems in which the ambiguity set is constructed with the Wasserstein metric via a data-driven approach. We investigate the DRCCP problems under two different types of uncertainties (uncertain probabilities and continuum of realizations) with two functional forms of the stochastic set (linear random right-hand side and linear random technology vector). We utilize the convex duality to derive the dual form of the worst-case expectation constraint with the indicator function. For the case of uncertain probabilities, we propose a set of deterministic mixed-integer linear programming inequalities to reformulate the DRCCP problem. For the case of continuum of realizations, we propose a set of mixed-integer second-order cone programming inequalities to reformulate and approximate the cases with uncertainties in the right-hand side and in the technology vector. We also provide the exactness conditions for the approximation method.

Keywords: Distributionally Robust Optimization, Chance-Constrained Programming, Wasserstein Metric

Category 1: Robust Optimization

Category 2: Stochastic Programming

Category 3: Linear, Cone and Semidefinite Programming (Second-Order Cone Programming )


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Entry Submitted: 07/04/2018
Entry Accepted: 07/04/2018
Entry Last Modified: 04/18/2019

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