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A duality theorem for a multiple objective fractional optimization problem

Published online by Cambridge University Press:  17 April 2009

T. Weir
T. Weir
Affiliation:
Department of Mathematics, University College, Australian Defence Force Academy, Campbell, A.C.T. 2600.
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Abstract

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Characterizations of efficiency and proper efficiency are given for classes of multiple objective fractional optimization problems. These results are then applied to the case of multiple objective fractional linear problems. A dual problem is given for the multiple objective fractional problem and it is shown that for a properly efficient primal solution the dual solution is also properly efficient.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 3 , December 1986 , pp. 415 - 425
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Choo, E.U., “Proper Efficiency and the Linear Fractional Vector Maximization Problem”, Oper. Res., 32 (1984), 216–220.CrossRefGoogle Scholar
[2]Geoffrion, A.M., “Proper efficiency and the theory of vector maximization”, J. Math. Anal. Appl., 22 (1968), 618–630.CrossRefGoogle Scholar
[3]Kuhn, H.W. and Tucker, A.W., “Nonlinear Programming”, Proceedings Second Berkeley Symposium on Mathematical Statistics and Probability, (Univ. of California Press, Berkeley, California, 1950) 481–492.Google Scholar
[4]Mangasarian, O.L., Nonlinear programming, (McGraw-Hill, New York, 1969).Google Scholar
[5]Mond, B. and Weir, T., “Generalized concavity and duality”, 263–279 in: Schaible, S. and Ziemba, W.T. (eds), Generalized Concavity in Optimization and Economics, (Academic Press, New York, 1981).Google Scholar
[6]Mond, B. and Weir, T., “Duality for factional Programming with generalized convexity conditions”, J. Inform. Optim. Sci., 3 (1982), 105–124.Google Scholar
[7]Pareto, V., Cours d'economie Politique (Rouge, Lausanne, 1896).Google Scholar
[8]Schaible, S., “Fractional Programming. I. Duality”, Management Sci., 22 (1976), 858–867.CrossRefGoogle Scholar
[9]Weir, T., “Proper efficiency and duality for vector valued optimization problems”, Department of Mathematics, Royal Military College, Duntroon, Research Report No. 12/85; (submitted for publication)Google Scholar
[10]Wolfe, P., “A duality theorem for nonlinear programming”, Quart. Appl. Math., 19 (1961), 239–244.CrossRefGoogle Scholar