  We present a framework for constructing strong mixed-integer programming
formulations for logical disjunctive constraints. Our approach is a
generalization of the logarithmically-sized formulations of Vielma and
Nemhauser for SOS2 constraints, and we offer a complete characterization of its
expressive power. We apply the framework to a variety of disjunctive
constraints, producing novel small and strong formulations for outer
approximations of multilinear terms, generalizations of special ordered sets,
piecewise linear functions over a variety of domains, and obstacle avoidance
constraints.
