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Nonlinear programming duality and matrix game equivalence

Published online by Cambridge University Press:  17 February 2009

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

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Certain well known results on linear programming duality and matrix game equivalence are extended to nonlinear and fractional programming problems.

Type
Research Article
Information
The ANZIAM Journal , Volume 26 , Issue 4 , April 1985 , pp. 422 - 429
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Bector, C. R. and Bhat, S. K., “Pseudo-monotonic interval programming”, Naval Res. Logist. Quart. 25 (1978), 309–314.CrossRefGoogle Scholar
[2]Bhat, S. K., “Linearization techniques for linear fractional and pseudomonotonic programming revisited”, Cahiers Centre Études Rech. Opér. 23 (1981), 53–56.Google Scholar
[3]Chandra, S., Craven, B. D. and Mood, B., “Generalized concavity and duality with a square root term”, Optimization (1985), to appear.CrossRefGoogle Scholar
[4]Craven, B. D., Mathematical programming and control theory (Chapman and Hall, London, 1978).CrossRefGoogle Scholar
[5]Dantzig, G. B., “A proof of the equivalence of the programming problem and the game problem”, in Activity analysis of production and allocation (ed. Koopmans, T. C.), Cowles Commission Monograph No. 13, (John Wiley and Sons, 1951), 330–335.Google Scholar
[6]Frank, M. and Wolfe, P., “An algorithm for quadratic programming”, Naval Res. Logist. Quart. 3 (1956), 95–110.CrossRefGoogle Scholar
[7]Forgó, F., “The relationship between continuous zero-sum two person games and linear programming”, Res. Rep. 1969–1, Dept. of Mathematics, Karl Marx University of Economics, Budapest.Google Scholar
[8]Gass, S., Linear programming (McGraw-Hill and Kogakusha, 1964).Google Scholar
[9]Karlin, S., Mathematical methods and theory in games, programming and mathematical economics (Addison-Wesley, Reading, Mass., 1959).Google Scholar
[10]Kortanek, K. O. and Evans, J. P., “Pseudo-concave programming and convex Lagrange regularity”, Oper. Res. 15 (1967), 882–891.CrossRefGoogle Scholar
[11]Mangasarian, O. L., “Nonlinear fractional programming”, J. Oper. Res. Soc. Japan 12 (1969), 1–10.Google Scholar
[12]Mond, B. and Weir, T., ‘Generalized concavity and duality’, in Generalized concavity in optimization and economics (eds. Schaible, S. and Ziemba, W. T.), (Academic Press, 1981), 263–279.Google Scholar
[13]Tijs, S. H., “Semi-infinite linear programs and semi-infinite matrix games”, Nieuw Arch. Wisk. 27 (1969), 197–214.Google Scholar