Generalized Cheney-Loeb-Dinkelbach-Type Algorithms

We present a class of generalized Cheney-Loeb-Dinkelbach-type (i.e. DC-type) algorithms, together with the problems they solve, and discuss convergence properties. Our algorithms, which are as simple as the DC one, are applicable to classes of programs larger than fractional. In two particular cases, the first being an essentially max-min problem and the second a Pareto extremum, we prove 1.61 and second order convergence respectively. Applications are given to extended fractional max-min and fractional Pareto extremum problems.