On Nonlinear Fractional Programming

Abstract

The main purpose of this paper is to delineate an algorithm for fractional programming with nonlinear as well as linear terms in the numerator and denominator. The algorithm presented is based on a theorem by Jagannathan (Jagannathan, R. 1966. On some properties of programming problems in parametric form pertaining to fractional programming. Management Sci. 12 609–615.) concerning the relationship between fractional and parametric programming. This theorem is restated and proved in a somewhat simpler way. Finally, it is shown how the given algorithm can be related to the method of Isbell and Marlow (Isbell, J. R., W. H. Marlow. 1956. Attrition games. Naval Res. Logist. Quart. 3 71–93.) for linear fractional programming and to the quadratic parametric approach by Ritter (Ritter, K. 1962. Ein Verfahren zur Lösung parameterabhängiger, nichtlinearer Maximum- Probleme. Unternehmensforschung, Band 6, S. 149–166.). The Appendix contains a numerical example.