Fractional Programming. II, On Dinkelbach's Algorithm

Siegfried Schaible
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Siegfried Schaible: University of Cologne and Stanford University

Management Science, 1976, vol. 22, issue 8, 868-873

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.

Date: 1976
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