GENERALIZED FRACTIONAL-PROGRAMMING AND CUTTING PLANE ALGORITHMS

In this paper, we introduce a variant of a cutting plane algorithm and show that this algorithm reduces to the well-known Dinkelbach-type pr ocedure of Crouzeix, Ferland, and Schaible if the optimization problem is a generalized fractional program. By this observation, an easy geo metrical interpretation of one of the most important algorithms in gen eralized fractional programming is obtained. Moreover, it is shown tha t the convergence of the Dinkelbach-type procedure is a direct consequ ence of the properties of this cutting plane method. Finally, a class of generalized fractional programs is considered where the standard po sitivity assumption on the denominators of the ratios of the objective function has to be imposed explicitly. It is also shown that, when us ing a Dinkelbach-type approach for this class of programs, the constra ints ensuring the positivity on the denominators can be dropped.