Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-27T02:35:14.502Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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