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Invexity of supremum and infimum functions

Published online by Cambridge University Press:  17 April 2009

Nguyen Xuan Ha
Affiliation:
Institute of Cryptographic Technology, Hanoi, Vietnam
Do Van Luu
Affiliation:
P.O. Box 631, Bo Ho, 10000 Hanoi, Vietnam
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Abstract

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Under suitable assumptions we establish the formulas for calculating generalised gradients and generalised directional derivatives in the Clarke sense of the supremum and the infimum of an infinite family of Lipschitz functions. From these results we derive the results ensuring such a supremum or infimum are an invex function when all functions of the invex. Applying these results to a class of mathematical programs, we obtain necessary and sufficient conditions for optimality.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2002

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