Abstract
Every lower semicontinuous convex function can be represented through its subdifferential by means of an "integration" formula introduced in [10] by Rockafellar. We show that in Banach spaces with the Radon-Nikodym property this formula can be significantly refined under a standard coercivity assumption. This yields an interesting application to the convexification of lower semicontinuous functions. © Heldermann Verlag.
Original language | English |
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Pages (from-to) | 255-265 |
Journal | Journal of Convex Analysis |
Volume | 12 |
Issue number | 2 |
Publication status | Published - 1 Dec 2005 |
Keywords
- Convex function
- Cusco mapping
- Epi-pointed function
- Strongly exposed point
- Subdifferential