Accession Number : AD0719281

Title :   Fractional Programming: A Survey.

Descriptive Note : Technical rept.,

Corporate Author : FLORIDA UNIV GAINESVILLE DEPT OF INDUSTRIAL AND SYSTEMS ENGINEERING

Personal Author(s) : Grunspan,Marcel ; Thomas,M. E.

Report Date : JAN 1971

Pagination or Media Count : 57

Abstract : 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 Dantzig's simplex algorithm, a dual algorithm based on Lemke's dual simplex method, a parametric method and Charnes + Cooper's linear characterization of the problem is also reviewed. Some known results regarding the nonlinear fractional program are also reviewed. A bibliography is included. (Author)

Descriptors :   (*MATHEMATICAL PROGRAMMING, REVIEWS), LINEAR PROGRAMMING, NONLINEAR PROGRAMMING, STOCHASTIC PROCESSES, CONVEX SETS, MATRICES(MATHEMATICS), ECONOMICS, TRANSPORTATION, REPLACEMENT THEORY, MANAGEMENT PLANNING AND CONTROL, ALGORITHMS, CONVERGENCE, OPTIMIZATION

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE