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Sufficient optimality criteria and duality for variational problems with generalised invexity

Published online by Cambridge University Press:  17 February 2009

B. Mond  and
I. Husain
B. Mond
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Melbourne, Victoria 3083.
I. Husain
Affiliation:
Department of Mathematics, Regional Engineering College, Hazratbal, India.
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Abstract

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A number of Kuhn-Tucker type sufficient optimality criteria for a class of variational problems under weaker invexity assumptions are presented. As an application of these optimality results, various Mond-Weir type duality results are proved under a variety of generalised invexity assumptions. These results generalise many well-known duality results of variational problems and also give a dynamic analogue of certain corresponding (static) results relating to duality with generalised invexity in mathematical programming.

Type
Research Article
Information
The ANZIAM Journal , Volume 31 , Issue 1 , July 1989 , pp. 108 - 121
Copyright
Copyright © Australian Mathematical Society 1989

References

[1] Bector, C. R., Chandra, S. and Husain, I., “Generalized Concavity and Duality in Continuous Programming”, Utilitas Mathematica 25 (1984) 171–190.Google Scholar
[2] Ben-Israel, A. and Mond, B., “What is Invexity?” J. Austral. Math, Soc. Ser. B 28 (1986) 1–9.CrossRefGoogle Scholar
[3] Chandra, S., Craven, B. D. and Husain, I., “A Class of Nondifferentiable Continuous Programming Problems”, J. Math. Anal. Appl. 107 (1985) 122–131.Google Scholar
[4] Craven, B. D., “Invex Functions and Constrained Local Minima”, Bull. Austral. Math. Soc. 24 (1981) 357–366.Google Scholar
[5] Craven, B. D. and Glover, B. B., “Invex Functions and Duality”, J. Austral. Math. Soc. Ser. A 39 (1985) 1–20.Google Scholar
[6] Hanson, M. A., “On Sufficiency of the Kuhn-Tucker Conditions”, J. Math. Anal. Appl. 80 (1981) 545–550.CrossRefGoogle Scholar
[7] Mangasarian, O. L., Nonlinear Programming (McGraw-Hill, New York, 1969).Google Scholar
[8] Mond, B., Chandra, S. and Husain, I., “Duality for Variational Problems with Invexity”, J. Math. Anal. Appl. 134 (1988) 322–328.Google Scholar
[9] Mond, B. and Hanson, M. A., “On Duality with Generalized Convexity”, Math. Operations-forsch. Statist. Ser. Optim. 15 (1984) 313–317.Google Scholar
[10] Mond, B. and Hanson, M. A., “Duality for Variational Problems”, J. Math. Anal. Appl. 18 (1967) 355–364.CrossRefGoogle Scholar
[11] 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
[12] Valentine, F. A., “The problem of Lagrange with differential inequalities as added side conditions”, in Contributions to the calculus of variations 1933–37, (University of Chicago Press, 1937) 407–448.Google Scholar