North-Holland 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 A*, 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 r sults are not obtained at the expense of the numerical efficiency since the modified version BFII is as efficient as NEWMODM and more efficient han MAXMODM. Key words: Fractional programming, convergence, speed of convergence. 1