Publisher： Cambridge University Press
E-ISSN： 1755-1633|51|1|55-72
ISSN： 0004-9727
Source： Bulletin of the Australian Mathematical Society, Vol.51, Iss.1, 1995-02, pp. : 55-72
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Abstract
Generalised second-order derivatives introduced by Rockafellar in the finite dimensional setting are extended to convex functions defined on reflexive Banach spaces. Our approach is based on the characterisation of convex generalised quadratic forms defined in reflexive Banach spaces, from the graph of the associated subdifferentials. The main result which is obtained is the exhibition of a particular generalised Hessian when the function admits a generalised second derivative. Some properties of the generalised second derivative are pointed out along with further justifications of the concept.
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