A NEW ALGORITHM FOR GENERALIZED FRACTIONAL PROGRAMS

A new dual problem for convex generalized fractional programs with no duality gap is presented and it is shown how this dual problem can be efficiently solved using a parametric approach, The resulting algorith m can be seen as ''dual'' to the Dinkelbach-type algorithm for general ized fractional programs since it approximates the optimal objective v alue of the dual (primal) problem from below, Convergence results for this algorithm are derived and an easy condition to achieve superlinea r convergence is also established, Moreover, under some additional ass umptions the algorithm also recovers at the same time an optimal solut ion of the primal problem, We also consider a variant of this new algo rithm, based on scaling the ''dual'' parametric function. The numerica l results, in case of quadratic-linear ratios and linear constraints, show that the performance of the new algorithm and its scaled version is superior to that of the Dinkelbach-type algorithms, From the comput ational results it also appears that contrary to the primal approach, the ''dual'' approach is less influenced by scaling.