Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-13T14:59:18.377Z Has data issue: false hasContentIssue false
  • English
  • Français

Multiobjective fractional duality

Published online by Cambridge University Press:  17 April 2009

Richard R. Egudo
Richard R. Egudo
Affiliation:
School of Applied Science, Gippsland Institute of Advanced Education, Switchback Rd, Churchill Vic. 3852, Australia
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.

The concept of efficiency (Pareto optimum) is used to formulate duality for multiobjective fractional programming problems. We consider programs where the components of the objective function have non-negative and convex numerators while the denominators are concave and positive. For this case the Mond-Weir extension of Bector dual analogy is given. We also give the Schaible type vector dual. The case where functions are ρ-convex (weakly or strongly convex) is also considered.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 3 , June 1988 , pp. 367 - 378
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Bazaras, M.S. and Shetty, C.M., Nonlinear Programming: Theory and Algorithms (John Wily, 1979).Google Scholar
[2]Bector, C.R., ‘Duality in nonlinear fractional programming’, Z. Oper. Res. 17 (1973), 183–193.Google Scholar
[3]Chankong, V. and Haimes, Y.Y., Multiobjective Decision Making: Theory and Methodology. (North-Holland, New York, 1983).Google Scholar
[4]Egudo, R.R., ‘Efficiency and generalized convex duality for multiobjective programs’, J. Math. Anal. Appl. (to appear).Google Scholar
[5]Geoffrion, A.M., ‘Proper efficiency and the theory of vector maximization’, J. Math. Anal. Appl. 22 (1968), 618–630.CrossRefGoogle Scholar
[6]Mangasarian, O.L., Nonlinear Programming (McGraw-Hill, New York, 1969).Google Scholar
[7]Mond, B. and Weir, T., ‘Generalized concavity and duality’, in Generalised Concavity in Optiinization and Economics, ed. Schaible, S. and Ziemba, W.T., pp. 263–279 (Academic Press, 1981).Google Scholar
[8]Mond, B. and Weir, T., ‘Duality for fractional programming with generalized convexity conditions’, J. Inform. Optim. Sci. 3 (1982), 105–124.Google Scholar
[9]Schaible, S., ‘Fractional programming. 1. Duality’, Management Sci. 22 (1976), 858–867.CrossRefGoogle Scholar
[10]Schaible, S., ‘Duality in fractional programming: a unified approach’, Oper. Res. 24 (1976), 452–461.CrossRefGoogle Scholar
[11]Singh, C., ‘A class of multiple-criteria fractional programming problems’, J. Math. Anal. Appl. 115 (1968), 202–213.CrossRefGoogle Scholar
[12]Vial, J.P., ‘Strong convexity of sets and functions’, J. Math. Econom. 9 (1982), 187–205.CrossRefGoogle Scholar
[13]Vial, J.P., ‘Strong and weak convexity of sets and functions’, Math. Oper. Res. 8 (1983), 231–259.CrossRefGoogle Scholar
[14]Weir, T., ‘A duality theorem for a multiobjective fractional optimization problem’, Bull. Austral. Math. Soc. 34 (1986), 415–425.CrossRefGoogle Scholar
[15]Weir, T., ‘A dual for a multiple objective fractional programming problem’, J. Inform. Optim. Sci. 7 (1986), 261–269.Google Scholar