On Generalized Linearity of Quadratic Fractional Functions

Quadratic fractional functions are proved to be quasilinear if and only if they are pseudo-linear. For these classes of functions, some characterizations are provided by means of the inertia of the quadratic form and the behavior of the gradient of the function itself. The study is then developed showing that generalized linear quadratic fractional functions share a particular structure. Therefore it is possible to suggest a sort of “canonical form” for those functions. A wider class of functions given by the sum of a quadratic fractional function and a linear one is also studied. In this case generalized linearity is characterized by means of simple conditions. Finally, it is deepened on the role played by generalized linear quadratic fractional functions in optimization problems.