This paper, which is presented in two parts, is a contribution to the theory of fractional programming, i.e., maximization of quotients subject to constraints. In Part I a duality theory for linear and concave-convex fractional programs is developed and related to recent results by Bector,...

Dinkelbach's algorithm [Dinkelbach, W. 1967. On nonlinear fractional programming. Management Sci. 13 492-498.] solving the parametric equivalent of a fractional program is investigated. It is shown that the algorithm converges superlinearly and often (locally) quadratically. A priori and a...