Fractional Programming. II, On Dinkelbach's Algorithm

Abstract

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 posteriori error estimates are derived. Using those estimates and duality as introduced in Part I, a revised version of the algorithm is proposed. In addition, a similar algorithm is presented where, in contrast to Dinkelbach's procedure, the rate of convergence is still controllable. Error estimates are derived also for this algorithm.