A branch-and-cut algorithm for a class of sum-of-ratios problems

Alireza M. Ashtiani and Paulo A.V. Ferreira

Applied Mathematics and Computation, 2015, vol. 268, issue C, 596-608

Abstract: The problem of maximizing a sum of concave–convex ratios over a convex set is addressed. The projection of the problem onto the image space of the functions that describe the ratios leads to the equivalent problem of maximizing a sum of elementary ratios subject to a linear semi-infinite inequality constraint. A global optimization algorithm that integrates a branch-and-bound procedure for dealing with nonconcavities in the image space and an efficient relaxation procedure for handling the semi-infinite constraint is proposed and illustrated through numerical examples. Comparative (computational) analyses between the proposed algorithm and two alternative algorithms for solving sum-of-ratios problems are also presented.

Keywords: Global optimization; Fractional programming; Semi-infinite optimization; Cutting plane; Branch-and-bound; Branch-and-cut (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:268:y:2015:i:c:p:596-608

DOI: 10.1016/j.amc.2015.06.089

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