The quadratic fractional problem consists of minimizing a ratio of two functions, a quadratic function over an linear (affine) function. This problem has been mainly studied in the literature by its economics applications, like, among others, the minimization of cost/time or maximization of return/risk.
In this talk, we use generalized asymptotic functions to deal with the quadratic fractional minimization problem. An extension of the Frank-Wolfe theorem from the quadratic to the quadratic fractional problem will be given. We established a characterization for the nonemptiness and compactness of the solution set in terms of the first and second order asymptotic functions. Finally, necessary and sufficient conditions for the particular cases of the linear fractional and the quadratic minimization problems are also provide.