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Global Optimization Algorithm for the Nonlinear Sum of Ratios Problem

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Abstract

This article presents a branch-and-bound algorithm for globally solving the nonlinear sum of ratios problem (P). The algorithm economizes the required computations by conducting the branch-and-bound search in ℛp, rather than in ℛn, where p is the number of ratios in the objective function of problem (P) and n is the number of decision variables in problem (P). To implement the algorithm, the main computations involve solving a sequence of convex programming problems for which standard algorithms are available.

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Authors and Affiliations

  1. Warrington College of Business Administration, University of Florida, Gainesville, Florida

    H. P. Benson (Professor)

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  1. H. P. Benson
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Benson, H.P. Global Optimization Algorithm for the Nonlinear Sum of Ratios Problem. Journal of Optimization Theory and Applications 112, 1–29 (2002). https://doi.org/10.1023/A:1013072027218

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