@article{58b3092a-2edd-4c1e-90ef-0378b4175a8f,
author = {Oliver Stein},
title = {Twice Differentiable Characterizations of Convexity Notions for Functions on Full Dimensional Convex Sets},
journal = {Schedae Informaticae},
volume = {2012},
number = {Volume 21},
year = {2012},
issn = {1732-3916},
pages = {55-63},keywords = {true convexity; differentiable characterization; full dimensional convex set.; convexity; strict convexity; strong convexity},
abstract = {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.},
doi = {10.4467/20838476SI.12.004.0814},
url = {https://ejournals.eu/en/journal/schedae-informaticae/article/twice-differentiable-characterizations-of-convexity-notions-for-functions-on-full-dimensional-convex-sets}
}