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Symmetric dual multiobjective fractional programming

Published online by Cambridge University Press:  09 April 2009

T. Weir
T. Weir
Affiliation:
13 Boehm Close Isaacs ACT 2607, Australia
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Abstract

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A pair of symmetric dual multiobjective fractional programming problems is formulated and appropriate duality theorems are established.

MSC classification

Secondary: 90C31: Sensitivity, stability, parametric optimization 90C32: Fractional programming
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 50 , Issue 1 , February 1991 , pp. 67 - 74
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Borwein, J. M., Optimization with respect to partial orderings, (D. Phil., Thesis, Oxford University, 1974).Google Scholar
[2]Chandra, S., Craven, B. D. and Mond, B., ‘Symmetric dual fractional programming’, Z. Oper. Res. 29 (1985), 59–64.Google Scholar
[3]Craven, B. D., ‘Lagrangian conditions and quasiduality’, Bull. Austral. Math. Soc. 16 (1977), 325–339.CrossRefGoogle Scholar
[4]Dantzig, G. G., Eisenberg, E. and Cottle, R. W., ‘Symmetric dual nonlinear programs’, Pacific J. Math. 15 (1965), 809–812.CrossRefGoogle Scholar
[5]Dorn, W. S., ‘A symmetric dual theorem for quadratic programs’, J. Oper. Res. Soc. Japan 2 (1960), 93–97.Google Scholar
[6]Geoffrion, A. M., ‘Proper efficiency and the theory of vector maximization’, J. Math. Anal. Appl. 22 (1968), 613–630.CrossRefGoogle Scholar
[7]Mond, B., ‘A symmetric dual theorem for nonlinear programming’, Quart. Appl. Math. 23 (1965), 265–269.CrossRefGoogle Scholar
[8]Mond, B. and Weir, T., ‘Generalized concavity and duality’, in Generalized Concavity in Optimization and Economics, edited by Schaible, S. and Ziemba, W. T., pp. 263–279, (Academic Press, New York, 1981).Google Scholar
[9]Weir, T., ‘Proper efficiency and duality for vector valued optimization problems’, J. Austral. Math. Soc. Ser. A 43 (1987), 21–35.CrossRefGoogle Scholar
[10]Weir, T. and Mond, B., ‘Symmetric and self duality in multiple objective programming’, Asia Pacific J. Oper. Res. 5 (1988), 124–133.Google Scholar