ISE Seminar Series

Chance constraints yield non-convex feasible regions in general. In particular, when the uncertain parameters are modeled by a Wasserstein ball, prior studies showed that the distributionally robust (pessimistic) chance constraint admits a mixed-integer representation. This study identifies sufficient conditions that lead to *convex* feasible regions of chance constraints with Wasserstein ambiguity. First, when uncertainty arises from the left-hand side of a pessimistic individual chance constraint, we derive a convex and conic representation if the Wasserstein ball is centered around a radial and symmetric distribution (e.g., Gaussian). Second, when uncertainty arises from the right-hand side of a pessimistic joint chance constraint, we show that the ensuing feasible region is convex if the Wasserstein ball is centered around a log-concave distribution. In addition, we propose a block coordinate ascent algorithm for this class of chance constraints and prove its convergence to global optimum. Furthermore, we extend these convexity results and conic representation to optimistic chance constraints. This is a joint work with Haoming Shen (IOE, University of Michigan).

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