  We describe a factor-revealing convex optimization problem for the
integrality gap of the maximum-cut semidefinite programming relaxation: for
each $n \geq 2$ we present a convex optimization problem whose optimal value is
the largest possible ratio between the value of an optimal rank-$n$ solution to
the relaxation and the value of an optimal cut. This problem is then used to
compute lower bounds for the integrality gap.
