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 procedure of Crouzeix, Ferland, and Schaible if the optimization problem is a generalized fractional program. By this observation, an easy geometrical interpretation of one of the most important algorithms in generalized fractional programming is obtained. Moreover, it is shown that the convergence of the Dinkelbach-type procedure is a direct consequence of the properties of this cutting plane method. Finally, a class of generalized fractional programs is considered where the standard positivity assumption on the denominators of the ratios of the objective function has to be imposed explicitly. It is also shown that, when using a Dinkelbach-type approach for this class of programs, the constraints ensuring the positivity on the denominators can be dropped.
|Keywords||boundedly lower subdifferentiable functions, cutting plane algorithms, generalized fractional programming|
|Persistent URL||dx.doi.org/10.1007/BF02192043, hdl.handle.net/1765/11537|
Frenk, J.B.G., & Barros, A.I.. (1995). Generalized fractional programming and cutting plane algorithms. Journal of Optimization Theory and Applications, 87(1), 103–120. doi:10.1007/BF02192043