  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 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.
