An approach to fractional programming via D.C. optimization

Abstract

In this paper, we address the development of efficient global search methods for a sum of ratios (i.e. a fractional programming) problem. This is, in general, a nonconvex problem (with numerous local extremum) which belongs to a class of global optimization problems. We proved the reduction theorem for the fractional programming problem with the d.c. functions and one equation with the vector parameter that satisfy the nonnegativity assumption. This theorem allows a justified use of the Dinkelbach’s approach to solving fractional programming problems with the goal function given by d.c. functions.