Twice Differentiable Characterizations of Convexity Notions for Functions on Full Dimensional Convex Sets
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RIS BIB ENDNOTETwice Differentiable Characterizations of Convexity Notions for Functions on Full Dimensional Convex Sets
Publication date: 20.12.2012
Schedae Informaticae, 2012, Volume 21, pp. 55 - 63
https://doi.org/10.4467/20838476SI.12.004.0814Authors
Twice Differentiable Characterizations of Convexity Notions for Functions on Full Dimensional Convex Sets
IWe derive C2 −characterizations for convex, strictly convex, as well as strongly convex functions on full dimensional convex sets. In the cases of convex and strongly convex functions this weakens the well-known openness assumption on the convex sets. We also show that, in a certain sense, the full dimensionality assumption cannot be weakened further. In the case of strictly convex functions we weaken the well-known sufficient C2 −condition for strict convexity to a characterization. Several examples illustrate the results.
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Information: Schedae Informaticae, 2012, Volume 21, pp. 55 - 63
Article type: Original article
Titles:
Twice Differentiable Characterizations of Convexity Notions for Functions on Full Dimensional Convex Sets
Twice Differentiable Characterizations of Convexity Notions for Functions on Full Dimensional Convex Sets
Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Published at: 20.12.2012
Article status: Open
Licence: None
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