Parametric approaches to fractional programs (original) (raw)

Abstract

The fractional program P is defined by max_f(x)/g(x)_ subject to_x_∈X. A class of methods for solving P is based on the auxiliary problem Q(λ) with a parameter λ: max_f(x)−λ_g(x) subject to_x_∈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.

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  1. Toshihide Ibaraki
    Present address: Department of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, Japan

Authors and Affiliations

  1. Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, Tokyo, Japan
    Toshihide Ibaraki

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Ibaraki, T. Parametric approaches to fractional programs.Mathematical Programming 26, 345–362 (1983). https://doi.org/10.1007/BF02591871

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