Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T06:05:49.357Z Has data issue: false hasContentIssue false

On sufficiency of the Kuhn-Tucker conditions in nondifferentiable programming

Published online by Cambridge University Press:  17 April 2009

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

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
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), 19.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), 317.CrossRefGoogle Scholar
[4]Hanson, M.A., ‘On sufficiency of the Kuhn-Tucker conditions’, J. Math. Anal. Appl 80 (1981), 545550.CrossRefGoogle Scholar
[5]Hanson, M.A. and Mond, B., ‘Necessary and sufficient conditions in constrained optimization’, Math. Programming 37 (1987), 5158.CrossRefGoogle Scholar
[6]Hiriart-Urruty, J.-P., ‘On necessary optimality conditions in nondifferentiable programming’, Math. Programming 14 (1978), 7386.CrossRefGoogle Scholar
[7]Hiriart-Urruty, J.-P., ‘Refinements of necessary optimality conditions in nondifferentiable programming’, Appl. Math. Optim. 5 (1979), 6383.CrossRefGoogle Scholar
[8]Schechter, M., ‘A subgradient duality theorem’, J. Math. Anal. Appl. 61 (1977), 850855.CrossRefGoogle Scholar
[9]Schechter, M., ‘More on subgradient duality’, J. Math. Anal. Appl. 71 (1979), 252262.CrossRefGoogle Scholar