On minimizing quadratically constrained ratio of two quadratic functions

We consider the nonconvex problem of minimizing the ratio of two quadratic functions over finitely many nonconvex quadratic inequalities. Relying on the homogenization technique we establish a sufficient condition that warrants the attainment of an optimal solution. Our result allows to extend and recover known conditions for some interesting special instances of the problem and to derive further results on its algorithmic and modeling aspects.