TY - JOUR
TI - Twice Differentiable Characterizations of Convexity Notions for Functions on Full Dimensional Convex Sets
AU - Stein, Oliver
TI - Twice Differentiable Characterizations of Convexity Notions for Functions on Full Dimensional Convex Sets
AB - 
	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.
VL - 2012
IS - Volume 21
PY - 2012
SN - 1732-3916
C1 - 2083-8476
SP - 55
EP - 63
DO - 10.4467/20838476SI.12.004.0814
UR - https://ejournals.eu/en/journal/schedae-informaticae/article/twice-differentiable-characterizations-of-convexity-notions-for-functions-on-full-dimensional-convex-sets
KW - true convexity
KW - differentiable characterization
KW - full dimensional convex set.
KW - convexity
KW - strict convexity
KW - strong convexity