Parametric approaches to fractional programs

Abstract

The fractional program P is defined by maxf(x)/g(x) subject tox∈X. A class of methods for solving P is based on the auxiliary problem Q(λ) with a parameter λ: maxf(x)−λg(x) subject tox∈X. Starting with two classical methods in this class, the Newton method and the binary search method, a number of variations are introduced and compared. Among the proposed methods. the modified binary search method is theoretically interesting because of its superlinear convergence and the capability to provide an explicit interval containing the optimum parameter value\(\bar \lambda \). Computational behavior is tested by solving fractional knapsack problems and quadratic fractional programs. The interpolated binary search method seems to be most efficient, while other methods also behave surprisingly well.