  We introduce new relaxation hierarchies for facial disjunctive programs (FD)
and concavo-convex programs, where the latter class of problems includes
disjoint bilinear programming (DBP) and concave minimization (CM) as special
cases. Meanwhile, FD restricts that feasible solutions belong to a collection
of faces of a Cartesian product of polytopes and generalizes 0-1 programs. We
construct these relaxation hierarchies by utilizing rational functions that are
barycentric coordinates for polytopes and derive these expressions using the
double-description (DD) procedure. The hierarchies, which have geometric and
algebraic underpinnings, converge to the convex hull for these problems at a
finite level. Our hierarchy provides the first unifying framework to analyze
and tighten relaxations from disjunctive programming (DP) and
reformulation-linearization technique (RLT) for these problem classes.
