Convergence of interval-type algorithms for generalized fractional programming

The purpose of this paper is to analyze the convergence of interval-type algorithms for solving the generalized fractional program. They are characterized by an interval [LBk,UBk] including λ*, and the length of the interval is reduced at each iteration. A closer analysis of the bounds LBk and UBk allows to modify slightly the best known interval-type algorithm NEWMODM accordingly to prove its convergence and derive convergence rates similar to those for a Dinkelbach-type algorithm MAXMODM under the same conditions. Numerical results in the linear case indicate that the modifications to get convergence results are not obtained at the expense of the numerical efficiency since the modified version BFII is as efficient as NEWMODM and more efficient than MAXMODM.