Fractional Programming: Transformations, Duality and Algorithmic Aspects.

Abstract : Recently concave-convex fractional programs were related to parametric convex programs by Jagannathan, Dinkelbach and Geoffrion. It will be shown that these problems can also be represented by a single convex program. Thus basic duality theorems of convex programming can be extended to concave-convex fractional programs. In a more particular case an extension of a converse duality theorem of quadratic programming can be proved. Finally, for Dinkelbach's algorithm solving the equivalent parametric program, the rate of convergence as well as error-estimates are determined. Some modifications using duality also are proposed. (Author)