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 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.