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Semi-invex functions and their subdifferentials

Published online by Cambridge University Press:  17 April 2009

J. Dutta ,
V. Vetrivel  and
S. Nanda
J. Dutta
Affiliation:
Department of MathematicsIndian Institute of TechnologyKharagpur 721 302India
V. Vetrivel
Affiliation:
Department of MathematicsIndian Institute of TechnologyKharagpur 721 302India
S. Nanda
Affiliation:
Department of MathematicsIndian Institute of TechnologyKharagpur 721 302India
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Abstract

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We introduce the notion of semi-invex function (non-smooth) and the associated subdifferential. We study their properties and establish the conditions for optimality in constrained and unconstrained minimisation problems.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 3 , December 1997 , pp. 385 - 393
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Clarke, F.H., Optimization and nonsmooth analysis (Wiley Interscience, New York, 1983).Google Scholar
[2]Craven, B.D., ‘Nondifferentiable optimization by smooth approximation’, Optimization 17 (1986), 3–17.CrossRefGoogle Scholar
[3]Hanson, M.A., ‘On the sufficiency of Kuhn-Tucker conditions’, J. Math. Anal. Appl. 80 (1981), 545–550.CrossRefGoogle Scholar
[4]Mohan, S. and Neogy, S., ‘On invex sets and pre-invex functions’, J. Math. Anal. Appl. 189 (1995), 901–908.CrossRefGoogle Scholar
[5]Penot, J., ‘Calcul sous-differentiel et optimisation’, J. Funct. Anal. 27 (1978), 248–276.CrossRefGoogle Scholar
[6]Pini, R., ‘Invexity and generalised convexity’, Optimization 22 (1991), 513–525.CrossRefGoogle Scholar
[7]Rockafellar, R.T., Convex analysis (Princeton University Press, Princeton, NJ, 1970).CrossRefGoogle Scholar
[8]Yang, X.Q. and Craven, B.D., ‘Necessary optimality conditions with modified subdifferential’, Optimization 22 (1991), 387–400.CrossRefGoogle Scholar