An algorithm for generalized fractional programs
- 237 Downloads
An algorithm is suggested that finds the constrained minimum of the maximum of finitely many ratios. The method involves a sequence of linear (convex) subproblems if the ratios are linear (convex-concave). Convergence results as well as rate of convergence results are derived. Special consideration is given to the case of (a) compact feasible regions and (b) linear ratios.
Key WordsFractional programming multi-ratio programming convergence rate of convergence
Unable to display preview. Download preview PDF.
- 1.Schaible, S.,Analyse and Anwendungen von Quotientenprogrammen, Hain-Verlag, Meisenheim, West Germany, 1978.Google Scholar
- 2.Charnes, A., andCooper, W. W.,Goal Programming and Multi-Objective Optimization, Part I, European Journal of Operational Research, Vol. 1, pp. 39–54, 1977.Google Scholar
- 3.Crouzeix, J. P., Ferland, J. A., andSchaible, S.,Duality in Generalized Linear Fractional Programming Mathematical Programming, Vol. 27, pp. 1–14, 1983.Google Scholar
- 4.Jagannathan, R., andSchaible, S.,Duality in Generalized Fractional Programming via Farkas' Lemma, Journal of Optimization Theory and Applications, Vol. 41, pp. 417–424, 1983.Google Scholar
- 5.Schaible, S.,Fractional Programming, Zeitschrift für Operations Research, Vol. 27, pp. 39–54, 1983.Google Scholar
- 6.Schaible, S., andIbaraki, T.,Fractional Programming, European Journal of Operational Research, Vol. 12, pp. 325–338, 1983.Google Scholar
- 7.Schaible, S.,Bibliography in Fractional Programming, Zeitschrift für Operations Research, Vol. 26, pp. 211–241, 1982.Google Scholar
- 8.Dinkelbach, W.,On Nonlinear Fractional Programming, Management Science, Vol. 13, pp. 492–498, 1967.Google Scholar
- 9.Schaible, S.,Fractional Programming, II: On Dinkelbach's Algorithm, Management Science, Vol. 22, pp. 868–873, 1976.Google Scholar
- 10.Ibaraki, T.,Solving Mathematical Programs with Fractional Objective Functions, Generalized Concavity in Optimization and Economics, Edited by S. Schaible and W. T. Ziemba, Academic Press, New York, New York, pp. 441–472, 1981.Google Scholar
- 11.Ibaraki, T. Parametric Approaches to Fractional Programs, Mathematical Programming, Vol. 26, pp. 345–362, 1983.Google Scholar