Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-25T16:31:43.398Z Has data issue: false hasContentIssue false

Generalized fractional programming duablity: a ratio game approach

Published online by Cambridge University Press:  17 February 2009

S. Chandra
Affiliation:
Mathematics Department, Indian Institute of Technology, Hauz Khas, New Delhi–110016, India, and Mathematics Department, University of Melbourne, Parkville, Victoria 3052, Australia
B. D. Craven
Affiliation:
Mathematics Department, University of Melbourne, Parkville, Victoria 3052, Australia
B. Mond
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Victoria 3083, 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.

A ratio game approach to the generalized fractional programming problem is presented and duality relations established. This approach suggests certain solution procedures for solving fractional programs involving several ratios in the objective function.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Charnes, A. and Cooper, W. W., “Goal programming and multiobjective optimization, Part I,” European J. Oper. Res. 1 (1979), 3954.CrossRefGoogle Scholar
[2]Craven, B. D., Mathematical programming and control theory (Chapman and Hall, London, 1978).CrossRefGoogle Scholar
[3]Crouzeix, J. P., “A duality framework in quasiconvex programming,” in “Generalized concavity in optimization and economics, (eds.) Schaible, S. and Ziemba, W. T., (Academic Press, New York, 1981), 207225.Google Scholar
[4]Crouzeix, J. P., Ferland, J. A. and Schaible, S., “Duality in generalized fractional programming”, Math. Programming 27 (1983), 342354.CrossRefGoogle Scholar
[5]Crouzeix, J. P., Ferland, J. A. and Schaible, S., “An algorithm for generalized fractional programs”, J. Optim. Theory Appl. 47 (1975), 3549.CrossRefGoogle Scholar
[6]Dinkelbach, W., “On nonlinear fractional programming”, Management Sci. 13 (1967), 492498.CrossRefGoogle Scholar
[7]Fan, K., “Minimax theorems”, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 4247.CrossRefGoogle ScholarPubMed
[8]Jagannathan, R., “On some properties of programming problems in parametric form pertaining to fractional programming”, Management Sci. 12 (1966), 609615.CrossRefGoogle Scholar
[9]Jagannathan, R., “Duality for nonlinear fractional programs”, Zeits. Oper. Res. 17 (1973), 13.Google Scholar
[10]Jagannathan, R. and Schaible, S., “Duality in generalized fractional programming via Farkas lemma”, J. Optim. Theory Appl. 41 (1983), 417424.CrossRefGoogle Scholar
[11]Karlin, S., Mathematical methods and theory in games, programming and mathematical economics (Addison-Wesley, Reading, Mass., 1959).Google Scholar
[12]Lommis, L. H., “On a theory of von Neumann”, Proc. Nat. Acad. Sci. U.S.A. 32 (1946), 213215.CrossRefGoogle Scholar
[13]Mangasarian, O. L., Nonlinear programming (McGraw-Hill, New York, 1969).Google Scholar
[14]Schaible, S., “Bibliography in fractional programming”, Zeits. Oper. Res. 26 (1982), 211241.Google Scholar
[15]Schaible, S., “Fractional programming-invited survey”, Zeirs Oper. Res. 27 (1983), 3054.Google Scholar
[16]Schroeder, R. G., “Linear programming solutions to ratio games, Oper. Res. 18 (1970), 300305.CrossRefGoogle Scholar
[17]Shapley, L. S., “Stochastic games”, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 10951100.CrossRefGoogle ScholarPubMed
[18]Sion, M., “On general minimax theorems”, Pacific J. Math. 8 (1958), 171176.CrossRefGoogle Scholar
[19]von Neumann, J., “A model of general economic equilibrium”, Rev. Econom. Stud. 13 (1945), 19.CrossRefGoogle Scholar