Duality and Sensitivity Analysis for Fractional Programs (REVISED)

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 relationship to certain approaches via variable transformations, and a variant of the procedure which has convenient convergence properties. The duality correspondences that are developed do not require either differentiability or the existence of 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.Supported in part by the U.S. Army Research Office (Durham) under Contract No. DAHC04-73-C-0032 and Grant-In-Aid from Coca-Cola, U.S.A. administered at M.I.T. as OSP 2785