An Eaves Type Theorem for Quadratic Fractional Programming Problems and its Applications

Using the notions of asymptotic cone and function, Lara [J. Convex Analysis 26 (2019) 15--32] proposed necessary and sufficient conditions for the existence of minimizers of quadratic fractional programming (QFP) problems. This result could be seen as the first extension of the Frank-Wolfe theorem from the quadratic to the quadratic fractional case. However, the asymptotically linear assumption is quite strong and the denominator of the objective function must be linear. In this paper, we present a new class of convex sets, which contains the previous class of asymptotically linear sets. By using the obtained results we propose necessary and sufficient conditions for the existence of solutions of QFP problems. Finally, we use the above results to investigate the boundedness or unboundedness of the global solution set and the stability for global solution map of a class of QFP problems.