Duality and Sensitivity Analysis for Fractional Programs

In this paper we consider algorithms, duality and sensitivity analysis for optimization problems, called fractional, whose objective function is the ratio of two real-valued functions. We discuss a procedure suggested by Dinkelbach for solving the problem, its relation to certain approaches via variable transformations, and a variant of the procedure that has convenient convergence properties. The duality correspondences that are developed do not require either differentiability or the existence of an optimal solution. The sensitivity analysis applies to linear fractional problems, even when they “solve” at an extreme ray, and includes a primal-dual algorithm for parametric right-hand-side analysis.