On quasiconvexity in fractional programming

Abstract

The purpose of this paper is to obtain quasiconcavity criteria for sums of linear fractional functions (SLFF) and for some fractional functions of more general type. The classes of SLFF are characterized for which the known necessary quasiconvexity condition (namely, the positive semidefiniteness of the second-order derivatives on a subspace) is also sufficient. These results are extended to the class of functions which can be represented as the ratio of polynomials of several variables. Thus the known quasiconvexity criteria for quadratic and cubic functions are essentially supplemented. The simplificated representations of quasiconvex SLFF is obtained; this allows to extend the known classes of quasiconvex SLFF.