Author： Schaible Siegfried Shi Jianming
Publisher： Taylor & Francis Ltd
ISSN： 1055-6788
Source： Optimization Methods and Software, Vol.18, Iss.2, 2003-04, pp. : 219-229
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Abstract
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 $hbox{cal{NP}}$-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.
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