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On sufficiency of the Kuhn-Tucker conditions in nondifferentiable programming

Published online by Cambridge University Press:  17 April 2009

Fuan Zhao
Fuan Zhao
Affiliation:
Institute of Applied Mathematics, Academia Sinica Beijing 100080, Peoples Republic of China
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Abstract

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Some generalised invex conditions are given for a nondifferentiable constrained optimisation problem, generalising those of Hanson and Mond for differentiable problems. Some duality results are obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 3 , December 1992 , pp. 385 - 389
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Ben-Israel, A. and Mond, B., ‘What is invexity?’, J. Austral. Math. Soc., series B 28 (1968), 1–9.CrossRefGoogle Scholar
[2]Clarke, F.H., Nonsmooth analysis and optimization (Wiley, New York, 1983).Google Scholar
[3]Craven, B.D., ‘Nondifferentiable approximation by smooth approximations’, Optimization 17 (1986), 3–17.CrossRefGoogle Scholar
[4]Hanson, M.A., ‘On sufficiency of the Kuhn-Tucker conditions’, J. Math. Anal. Appl 80 (1981), 545–550.CrossRefGoogle Scholar
[5]Hanson, M.A. and Mond, B., ‘Necessary and sufficient conditions in constrained optimization’, Math. Programming 37 (1987), 51–58.CrossRefGoogle Scholar
[6]Hiriart-Urruty, J.-P., ‘On necessary optimality conditions in nondifferentiable programming’, Math. Programming 14 (1978), 73–86.CrossRefGoogle Scholar
[7]Hiriart-Urruty, J.-P., ‘Refinements of necessary optimality conditions in nondifferentiable programming’, Appl. Math. Optim. 5 (1979), 63–83.CrossRefGoogle Scholar
[8]Schechter, M., ‘A subgradient duality theorem’, J. Math. Anal. Appl. 61 (1977), 850–855.CrossRefGoogle Scholar
[9]Schechter, M., ‘More on subgradient duality’, J. Math. Anal. Appl. 71 (1979), 252–262.CrossRefGoogle Scholar