- Title
- Generic differentiability of order-bounded convex operators
- Creator
- Borwein, Jonathan M.
- Relation
- Journal of the Australian Mathematical Society: Series B: Applied Mathematics Vol. 28, Issue 1, p. 221-29
- Publisher Link
- http://dx.doi.org/10.1017/S0334270000005166
- Publisher
- Cambridge University Press
- Resource Type
- journal article
- Date
- 1986
- Description
- We give sufficient conditions for order-bounded convex operators to be generically differentiable (Gâteaux or Fréchet). When the range space is a countably order-complete Banach lattice, these conditions are also necessary. In particular, every order-bounded convex operator from an Asplund space into such a lattice is generically Fréchet differentiable, if and only if the lattice has weakly-compact order intervals, if and only if the lattice has strongly-exposed order intervals. Applications are given which indicate how such results relate to optimization theory.
- Subject
- order-bounded convex operators; convex analysis; non-linear analysis; Banach space
- Identifier
- http://hdl.handle.net/1959.13/1043573
- Identifier
- uon:14221
- Identifier
- ISSN:0334-2700
- Language
- eng
- Full Text
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