Fractional programming: Applications and algorithms

The paper deals with decision problems that give rise to the optimization of ratios subject to constraints. These so called fractional programs have been treated in a considerable number of papers. It is attempted to survey applications as well as solution methods in linear, quadratic and concave-convex fractional programming. In the first part we give a detailed outline on the major areas of applications of fractional programming. Following a brief review on some basic theoretical results like duality relations, in the second part we then discuss different algorithmic approaches. A primal, a dual and a parametric solution method is considered here. We try to determine for each method the kind of fractional programs that are solved by it suitably.