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 |
|---|---|
| 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
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Cite this
Benoist, J., & Daniilidis, A. (2005). Subdifferential representation of convex functions: Refinements and applications. Journal of Convex Analysis, 12(2), 255-265.