  Convexification based on convex envelopes is ubiquitous in the non-linear
optimization literature. Thanks to considerable efforts of the optimization
community for decades, we are able to compute the convex envelopes of a
considerable number of functions that appear in practice, and thus obtain tight
and tractable approximations to challenging problems. We contribute to this
line of work by considering a family of functions that, to the best of our
knowledge, has not been considered before in the literature. We call this
family ray-concave functions. We show sufficient conditions that allow us to
easily compute closed-form expressions for the convex envelope of ray-concave
functions over arbitrary polytopes. With these tools, we are able to provide
new perspectives to previously known convex envelopes and derive a previously
unknown convex envelope for a function that arises in probability contexts.
