Abstract
Convex functions with continuous epigraph in the sense of Gale and Klée have been studied recently by Auslender and Coutat in a finite-dimensional setting. Here, we provide characterizations of such functional in terms of the Legendre-Fenchel transformation in general locally convex spaces. Also, we show that the concept of continuous convex sets is of interest in these spaces. We end with a characterization of convex functions on Euclidean spaces with continuous level sets.
Original language | English |
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Pages (from-to) | 365-379 |
Journal | Journal of Optimization Theory and Applications |
Volume | 88 |
DOIs | |
Publication status | Published - 1 Jan 1996 |
Keywords
- Coercivity
- Continuous convex sets
- Convex duality
- Recession cones
- Support functions