# Convex Chance-Constrained Programs with Wasserstein Ambiguity

arXiv: https://arxiv.org/abs/2111.02486 · HTML: https://mlsanity.com/paper/2111.02486/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2021.

## Built on by (most cited first, 1 of 1)

- [Learning efficient representations of complex constraints for scalable optimization](https://mlsanity.com/paper/2603.08283/) (2026)

## Abstract (arXiv)

Chance constraints yield non-convex feasible regions in general. In particular, when the uncertain parameters are modeled by a Wasserstein ball, arXiv:1806.07418 and arXiv:1809.00210 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 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 α-concave distribution with α ≥ -1). In addition, we propose a block coordinate ascent algorithm and prove its convergence to global optimum, as well as the rate of convergence. Second, when uncertainty arises from the left-hand side of a pessimistic two-sided chance constraint, we show the convexity if the Wasserstein ball is centered around an elliptical and star-unimodal distribution. In addition, we propose a family of second-order conic inner approximations, and we bound their approximation error and prove their asymptotic exactness. Furthermore, we extend the convexity results to optimistic chance constraints.