Fractional Programming: A Survey.
FLORIDA UNIV GAINESVILLE DEPT OF INDUSTRIAL AND SYSTEMS ENGINEERING
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Although many fractional programming applications, theoretic results and algorithmic solutions have been published, there appears to be strong need for a central source of reference. The intent of this paper is to fill this need. The fractional programming problem has the special property the objective function can be expressed as a ratio of two functions. It is this special structure which invites special solutions. The paper is in two parts. In the first part we review publications in which problems were formulated as fractional programs. In the second part we review published results concerning the theory and algorithmic solutions of fractional programs. The hyperbolic program receives special attention. Four principal methods for attaining a solution are reviewed. These include an extension of Dantzigs simplex algorithm, a dual algorithm based on Lemkes dual simplex method, a parametric method and Charnes Coopers linear characterization of the problem is also reviewed. Some known results regarding the nonlinear fractional program are also reviewed. A bibliography is included. Author
- Operations Research