Quadratic fractional programming under asymptotic analysis

This paper considers the quadratic fractional programming problem, which minimizes a ratio of two functions; a quadratic (not necessarily convex) function over an a affine function on an unbounded set. As is well-known, if the quadratic function is convex or quasiconvex, then the quadratic fractional function is pseudoconvex, a particular case of the quasiconvex minimization problem. Thus, we develop optimality conditions for the general case by introducing a generalized asymptotic function to deal with quasiconvexity. We established two characterization results for the nonemptiness and compactness for the set of minimizers of any quasiconvex function. In addition, an extension for the Frank-Wolfe theorem from the quadratic to the quadratic fractional problem will be given. Finally, applications to pseudoconvex quadratic fractional programming are also provided.