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Duality with generalized convexity

Published online by Cambridge University Press:  17 February 2009

R. R. Egudo  and
B. Mond
R. R. Egudo
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Vic. 3083Australia.
B. Mond
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Vic. 3083, Australia.
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Recently, Hanson and Mond formulated a type of generalized convexity and used it to establish duality between the nonlinear programming problem and the Wolfe dual. Elsewhere, Mond and Weir gave an alternate dual, different from the Wolfe dual, that allowed the weakening of the convexity requirements. Here we establish duality between the nonlinear programming problem and the Mond-Weir dual using Hanson-Mond generalized convexity conditions.

Type
Research Article
Information
The ANZIAM Journal , Volume 28 , Issue 1 , July 1986 , pp. 10 - 21
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Gulati, T. R., and Craven, B. D., “A strict converse duality theorem in nonlinear programming,” J. Inform. Optim. Sci. 4 (1983), 301–306.Google Scholar
[2]Hanson, M. A. and Mond, B., “Further generalizations of convexity in mathematical programming,” J. Inform. Optim. Sci. 3 (1982), 25–32.Google Scholar
[3]Kuhn, H. W. and Tucker, A. W.,“Nonlinear programming,” Prov. 2nd Berkeley Symposium on Mathematical Statistics and Probability, (University of California Press 1951), 481–492.Google Scholar
[4]Mangasarian, O. L., Nonlinear programming (McGraw-Hill, New York, London, Sydney, 1969).Google Scholar
[5]Mond, B., “Generalized convexity in mathematical programming,” Bull. Austral. Math. Soc. 27 (1983), 185–202.CrossRefGoogle Scholar
[6]Mond, B. and Egudo, R. R., “On strict converse duality in nonlinear programming,” J. Inform. Optim. Sci. 6 (1985), 113–16.Google Scholar
[7]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
[8]Weir, T., “Generalized convexity and duality in mathematical programming”, Ph.D. thesis, La Trobe University, Bundoora, Melbourne, Australia, 1982.Google Scholar
[9]Wolfe, P., “A duality theorem for nonlinear programming,” Quart. Appl. Math. 19 (1961), 239–244.Google Scholar