Distributionally Robust Chance-Constrained Programmings for Non-Linear Uncertainties with Wasserstein Distance

In this paper, we study a distributionally robust chance-constrained programming (DRCCP) under Wasserstein ambiguity set, where the uncertain constraints require to be jointly satisfied with a probability of at least a given risk level for all the probability distributions of the uncertain parameters within a chosen Wasserstein distance from an empirical distribution. Differently from the previous results concentrating mainly on the linear uncertain constraints, we consider a DRCCP involving convex non-linear uncertain constraints. We investigate an equivalent reformulation and a deterministic approximation of such optimization problem. It is shown that this approximation is essentially exact under a certain condition and it can be reformulated as a tractable convex programming for a single DRCCP. We also demonstrate that the proposed approximation is equivalent to a tractable mixed-integer convex programming when the decision variables are binary and the uncertain constraints are linear. Numerical results show that the proposed mixed-integer convex reformulation can be solved efficiently.