  We extend Robust Optimization to fractional programming, where both the
objective and the constraints contain uncertain parameters. Earlier work did
not consider uncertainty in both the objective and the constraints, or did not
use Robust Optimization. Our contribution is threefold. First, we provide
conditions to guarantee that either a globally optimal solution, or a sequence
converging to the globally optimal solution, can be found by solving one or
more convex optimization problems. Second, we identify two cases for which an
exact solution can be obtained by solving a single optimization problem: (1)
when uncertainty in the numerator is independent from the uncertainty in the
denominator, and (2) when the denominator does not contain an optimization
variable. Third, we show that the general problem can be solved with an
(iterative) root finding method. The results are demonstrated on a
return-on-investment maximization problem, data envelopment analysis, and
mean-variance optimization. We find that the robust optimal solution is only
slightly more robust than the nominal solution. As a side-result, we use Robust
Optimization to show that two existing methods for solving fractional programs
are dual to each other.
