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

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...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 268; pp. 596 - 608
Main Authors Ashtiani, Alireza M., Ferreira, Paulo A.V.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.10.2015
Subjects
Branch-and-bound
Branch-and-cut
Cutting plane
Fractional programming
Global optimization
Semi-infinite optimization
Branch-and-bound
Global optimization
Fractional programming
Semi-infinite optimization
Cutting plane
Branch-and-cut
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Summary: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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2015.06.089