A Class of Fractional Programming Problems

The paper deals with problems of maximizing a sum of linear or concave-convex fractional functions on closed and bounded polyhedral sets. It shows that, under certain assumptions, problems of this type can be transformed into equivalent ones of maximizing multiparameter linear or concave functions subject to additional feasibility constraints. The problems are transformed into those finding roots of monotone-decreasing convex functions. Where the objective function is separable, such a root is unique, and any local optimum is a global one, i.e., the objective function is quasi-concave. In problems involving separable linear fractional functions, under some additional assumptions, the parametric presentation results in a combinational property. Where the number of terms in the objective function is equal or less than three, this property leads to an efficient algorithm.