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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 with data-driven Wasserstein ambiguity sets. The proposed algorithmic and reformulation framework applies to distributionally robust optimization problems subjected to individual as well as joint chance constraints, with random right-hand side and technology vector, and under two types of uncertainties, called uncertain probabilities and continuum of realizations. For the uncertain probabilities case, we provide new mixed-integer linear programming reformulations for DRCCP problems and derive a set of precedence optimality cuts to strengthen the formulations. For the continuum of realizations case with random right-hand side, we propose an exact mixed-integer second-order cone programming (MISOCP) reformulation and a linear programming (LP) outer approximation. For the continuum of realizations case with random technology vector, we propose two MISOCP and LP outer approximations. We show that all proposed relaxations become exact reformulations when the decision variables are binary or bounded general integers. We evaluate the scalability and tightness of the proposed MISOCP and (MI)LP formulations on a distributionally robust chance-constrained knapsack problem.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 )

Citation:

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Entry Submitted: 07/04/2018
Entry Accepted: 07/04/2018
Entry Last Modified: 02/22/2020

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