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Global optimization of fractional programs

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Abstract

Dinkelbach's global optimization approach for finding the global maximum of the fractional programming problem is discussed. Based on this idea, a modified algorithm is presented which provides both upper and lower bounds at each iteration. The convergence of the lower and upper bounds to the global maximum function value is shown to be superlinear. In addition, the special case of fractional programming when the ratio involves only linear or quadratic terms is considered. In this case, the algorithm is guaranteed to find the global maximum to within any specified tolerance, regardless of the definiteness of the quadratic form.

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Authors and Affiliations

  1. Computer Science Department, The Pennsylvania State University, 16802, University Park, PA, U.S.A.

    P. M. Pardalos

  2. Computer Science Department, United States Naval Academy, 21402, Annapolis, MD, U.S.A.

    A. T. Phillips

Authors
  1. P. M. Pardalos
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  2. A. T. Phillips
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Pardalos, P.M., Phillips, A.T. Global optimization of fractional programs. J Glob Optim 1, 173–182 (1991). https://doi.org/10.1007/BF00119990

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  • DOI: https://doi.org/10.1007/BF00119990

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