Multi-Ratio Fractional Programing — A Survey

Nonlinear programming problems are considered where the objective function involves several ratios. We review recent results concerning three classes of multi-ratio fractional programs: 1) maximization of a sum of ratios, 2) maximization of the smallest of several ratios, and 3) multiobjective fractional programs. In addition to these results open problems are addressed as well.

[1]  S. Schaible,et al.  Simultaneous Optimization of Absolute and Relative Terms , 1984 .

[2]  Siegfried Schaible,et al.  Parameter-free convex equivalent and dual programs of fractional programming problems , 1974, Z. Oper. Research.

[3]  Siegfried Schaible,et al.  Duality in Fractional Programming: A Unified Approach , 1976, Oper. Res..

[4]  G. R. Bitran,et al.  The structure of admissible points with respect to cone dominance , 1979 .

[5]  Jean-Yves Potvin,et al.  Generalized fractional programming: Algorithms and numerical experimentation , 1985 .

[6]  R. E. Burkard.  Book reviewAnalyse und anwendungen von quotientenprogrammen: Ein Beitrag zur planung mit Hilfe der nichtlinearen programmierung: Siegfried SCHAIBLE Anton Hain, Meisenheim am Glan, 1978; 259 pages DM 26,- , 1980 .

[7]  S. Schaible.  A note on the sum of a linear and linear‐fractional function , 1977 .

[8]  Timothy J. Lowe,et al.  A Note on a Material Control Problem , 1983 .

[9]  Kanti Swarup,et al.  Duality in fractional programming , 1968, Unternehmensforschung.

[10]  Siegfried Schaible,et al.  Duality in generalized fractional programming via Farkas' lemma , 1983 .

[11]  I. Barrodale.  Best Rational Approximation and Strict Quasi-Convexity , 1973 .

[12]  Derek Atkins,et al.  Multicriteria Programming for Financial Planning , 1979 .

[13]  J. Neumann.  A Model of General Economic Equilibrium , 1945 .

[14]  Jacques A. Ferland,et al.  A note on an algorithm for generalized fractional programs , 1986 .

[15]  C. Scott,et al.  Conjugate duality in generalized fractional programming , 1989 .

[16]  Jacob Flachs,et al.  Generalized Cheney-Loeb-Dinkelbach-Type Algorithms , 1985, Math. Oper. Res..

[17]  Werner Dinkelbach.  On Nonlinear Fractional Programming , 1967 .

[18]  S. Schaible,et al.  An algorithm for generalized fractional programs , 1985 .

[19]  Jacques A. Ferland,et al.  Duality in generalized linear fractional programming , 1984, Math. Program..

[20]  S. Schaible.  Fractional Programming. II, On Dinkelbach's Algorithm , 1976 .

[21]  W. Ziemba,et al.  Generalized concavity in optimization and economics , 1981 .

[22]  Jean-Pierre Crouzeix,et al.  Convergence of a Dinkelbach-type algorithm in generalized fractional programming , 1987, Z. Oper. Research.

[23]  S. Schaible,et al.  Connectedness of the efficient set in three criteria , 1985 .