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A chain rule for nonsmooth composite functions via minimisation

Published online by Cambridge University Press:  17 April 2009

D. Ralph
D. Ralph
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Vic. 3052, Australia
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Abstract

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Nonsmooth calculus using the approximate subdifferential of Mordukhovich and loffe admits a sharper chain rule, hence sharper applications in optimisation, than does the generalised gradient of Clarke. We observe, however, that at a local minimum point of the composition of nonsmooth vector valued and real valued functions, the generalised gradient admits a special, relatively sharp chain rule, that yields sharper results than have been seen before in the context of the generalised gradient.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 1 , February 1994 , pp. 129 - 137
Copyright
Copyright © Australian Mathematical Society 1994

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