  We present a framework to obtain valid inequalities for a reverse convex set:
the set of points in a polyhedron that lie outside a given open convex set.
Reverse convex sets arise in many models, including bilevel optimization and
polynomial optimization. An intersection cut is a well-known valid inequality
for a reverse convex set that is generated from a basic solution that lies
within the convex set. We introduce a framework for deriving valid inequalities
for the reverse convex set from basic solutions that lie outside the convex
set. We first propose an extension to intersection cuts that defines a two-term
disjunction for a reverse convex set, which we refer to as an intersection
disjunction. Next, we generalize this analysis to a multi-term disjunction by
considering the convex set's recession directions. These disjunctions can be
used in a cut-generating linear program to obtain valid inequalities for the
reverse convex set.
