SAMPLING UNCERTAIN CONSTRAINTS UNDER PARAMETRIC DISTRIBUTIONS

We consider optimization problems with uncertain constraints that need to be satisfied probabilistically. When data are available, a common method to obtain feasible solutions for such problems is to impose sampled constraints, following the so-called scenario generation (SG) approach. However, when the data size is small, the sampled constraints may not support a guarantee on the feasibility of the obtained solution. This paper studies how to leverage parametric information and the power of Monte Carlo simulation to obtain feasible solutions even when the data are not sufficient to support the use of SG. Our approach makes use of a distributionally robust optimization formulation that informs the Monte Carlo sample size needed to achieve our guarantee.

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