Convergence of prox-regularization methods for generalized fractional programming

We analyze the convergence of the prox-regularization algorithms introduced by Gugat, to solve generalized fractional programs, without assuming that the optimal solutions set of the considered problem is nonempty, and since the objective functions are variable with respect to the iterations in the auxiliary problems generated by Dinkelbach-type algorithms DT1 and DT2, we consider that the regularizing parameter is also variable. On the other hand we study the convergence when the iterates are only ηk-minimizers of the auxiliary problems. This situation is more general than the one considered by Gugat. We also give some results concerning the rate of convergence of these algorithms, and show that it is linear and sometimes superlinear for some classes of functions.