  This paper develops a correspondence relating convex hulls of fractional
functions with those of polynomial functions over the same domain. Using this
result, we develop a number of new reformulations and relaxations for
fractional programming problems. First, we relate 0-1 problems involving a
ratio of affine functions with the boolean quadric polytope, and use
inequalities for the latter to develop tighter formulations for the former.
Second, we derive a new formulation to optimize a ratio of quadratic functions
over a polytope using copositive programming. Third, we show that univariate
fractional functions can be convexified using moment hulls. Fourth, we develop
a new hierarchy of relaxations that converges finitely to the simultaneous
convex hull of a collection of ratios of affine functions of 0-1 variables.
Finally, we demonstrate theoretically and computationally that our techniques
close a significant gap relative to state-of-the-art relaxations, require much
less computational effort, and can solve larger problem instances.
