Parametric approach for solving quadratic fractional optimization with a linear and a quadratic constraint

This paper studies a class of nonconvex fractional minimization problem in which the feasible region is the intersection of the unit ball with a single linear inequality constraint. First, using Dinkelbach’s idea, it is shown that finding the global optimal solution of the underlying problem is equivalent to find the unique root of a function. Then using a diagonalization technique, we present an efficient method to solve the indefinite quadratic minimization problem with the original problem’s constraints within a generalized Newton-based iterative algorithm. Our preliminary numerical experiments on several randomly generated test problems show that the new approach is much faster in finding the global optimal solution than the known semidefinite relaxation approach, especially when solving large-scale problems.