Twice Differentiable Characterizations of Convexity Notions for Functions on Full Dimensional Convex Sets

• Authors: Oliver Stein
• Languages of publication: PL

Abstracts

PL

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.

Keywords

PL

convexity, strict convexity, strong convexity, true convexity, differentiable characterization, full dimensional convex set

• Publisher: [unknown2]
• Journal: Schedae Informaticae
• Year: 2012
• Volume: 21

Dates

published

2012

online

21 - 05 - 2015

Contributors

author

Oliver Stein