%0 Journal Article
%T Twice Differentiable Characterizations of Convexity Notions for Functions on Full Dimensional Convex Sets
%A Stein, Oliver
%J Schedae Informaticae
%V 2012
%R 10.4467/20838476SI.12.004.0814
%N Volume 21
%P 55-63
%K true convexity, differentiable characterization, full dimensional convex set., convexity, strict convexity, strong convexity
%@ 1732-3916
%D 2012
%U https://ejournals.eu/en/journal/schedae-informaticae/article/twice-differentiable-characterizations-of-convexity-notions-for-functions-on-full-dimensional-convex-sets
%X 
	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.