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An algorithm for generalized fractional programs. (English) Zbl 0548.90083

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.

MSC:

90C32 Fractional programming
65K05 Numerical mathematical programming methods
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References:

[1] Schaible, S.,Analyse and Anwendungen von Quotientenprogrammen, Hain-Verlag, Meisenheim, West Germany, 1978.
[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. · Zbl 0375.90079 · doi:10.1016/S0377-2217(77)81007-2
[3] Crouzeix, J. P., Ferland, J. A., andSchaible, S.,Duality in Generalized Linear Fractional Programming Mathematical Programming, Vol. 27, pp. 1-14, 1983. · Zbl 0526.90083 · doi:10.1007/BF02591908
[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. · Zbl 0502.90079 · doi:10.1007/BF00935361
[5] Schaible, S.,Fractional Programming, Zeitschrift für Operations Research, Vol. 27, pp. 39-54, 1983. · Zbl 0527.90094 · doi:10.1007/BF01916898
[6] Schaible, S., andIbaraki, T.,Fractional Programming, European Journal of Operational Research, Vol. 12, pp. 325-338, 1983. · Zbl 0529.90088 · doi:10.1016/0377-2217(83)90153-4
[7] Schaible, S.,Bibliography in Fractional Programming, Zeitschrift für Operations Research, Vol. 26, pp. 211-241, 1982. · Zbl 0494.90076 · doi:10.1007/BF01917115
[8] Dinkelbach, W.,On Nonlinear Fractional Programming, Management Science, Vol. 13, pp. 492-498, 1967. · Zbl 0152.18402 · doi:10.1287/mnsc.13.7.492
[9] Schaible, S.,Fractional Programming, II: On Dinkelbach’s Algorithm, Management Science, Vol. 22, pp. 868-873, 1976. · Zbl 0346.90052 · doi:10.1287/mnsc.22.8.868
[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.
[11] Ibaraki, T. Parametric Approaches to Fractional Programs, Mathematical Programming, Vol. 26, pp. 345-362, 1983. · Zbl 0506.90078 · doi:10.1007/BF02591871
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