Fractional Programming

An introduction to ratio optimization problems is provided which covers various applications as well as major theoretical and algorithmic developments. In addition to an extensive treatment of single-ratio fractional programming, three types of multi-ratio fractional programs are discussed: maximization of the smallest of several ratios, maximization of a sum of ratios and multi-objective fractional programs. Earlier as well as recent developments are discussed and open problems are identified. The article concludes with a comprehensive, up-to-date bibliography in fractional programming. Well over one thousand articles have appeared in more than thirty years of increasingly intensive research in fractional programming. The bibliography includes all references from the beginning until late 1993 to the extent they are known to the author at this time.