The problem of maximizing the sum of m concave-convex fractional functions on a convex set is shown to be equivalent to the one whose objective function f is the sum of m linear fractional functions defined on a suitable convex set; successively, f is transformed into the sum of one linear function and (m-1) linear fractional functions. As a special case, the problem of maximizing the sum of two linear fractional functions subject to linear constraints is considered. Theoretical properties are studied and an algorithm converging in a finite number of iterations is proposed.
