Fractional programming: The sum-of-ratios case

One of the most difficult fractional programs encountered so far is the sum-of-ratios problem. Contrary to earlier expectations it is much more removed from convex programming than other multi-ratio problems analyzed before. It really should be viewed in the context of global optimization. It proves...

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Bibliographic Details
Published in:Optimization methods & software 2003-04, Vol.18 (2), p.219-229
Main Authors: Schaible, Siegfried, Shi, Jianming
Format: Article
Language:English
Subjects:
Branch-and-bound
Fractional Programming
Multi-ratio Problems
Sum-of-ratios
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Summary:One of the most difficult fractional programs encountered so far is the sum-of-ratios problem. Contrary to earlier expectations it is much more removed from convex programming than other multi-ratio problems analyzed before. It really should be viewed in the context of global optimization. It proves to be essentially [Formula: See Text]-hard in spite of its special structure under the usual assumptions on numerators and denominators. The article provides a recent survey of applications, theoretical results and various algorithmic approaches for this challenging problem.
ISSN:1055-6788
1029-4937
DOI:10.1080/1055678031000105242