  This paper presents a canonical dual approach to the problem of minimizing
the sum of a quadratic function and the ratio of nonconvex function and
quadratic functions, which is a type of non-convex optimization problem subject
to an elliptic constraint. We first relax the fractional structure by
introducing a family of parametric subproblems. Under certain conditions, we
show that the canonical dual of each subproblem becomes a two-dimensional
concave maximization problem that exhibits no duality gap. Since the infimum of
the optima of the parameterized subproblems leads to a solution to the original
problem, we then derive some optimality conditions and existence conditions for
finding a global minimizer of the original problem.
