Convex Chance-Constrained Programs with Wasserstein Ambiguity

Haoming Shen(hmshenumich.edu)
Ruiwei Jiang(ruiweiumich.edu)

Abstract: Chance constraints yield non-convex feasible regions in general. In particular, when the uncertain parameters are modeled by a Wasserstein ball, [Xie19] and [CKW18] showed that the distributionally robust (pessimistic) chance constraint admits a mixed-integer conic representation. This paper 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 Gaussian distribution. 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 (or, more generally, an $\alpha$-concave distribution with $\alpha \geq −1$). 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 the convexity results and conic representation to optimistic chance constraints.

Keywords: Chance constraints; Convexity; Wasserstein ambiguity; Distributionally robust optimization; Distributionally optimistic optimization

Category 1: Stochastic Programming

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Entry Submitted: 11/03/2021
Entry Accepted: 11/03/2021
Entry Last Modified: 11/03/2021

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