Local characterization of strongly convex sets
Metric Geometry
2013-04-08 v2 Functional Analysis
Optimization and Control
Abstract
Strongly convex sets in Hilbert spaces are characterized by local properties. One quantity which is used for this purpose is a generalization of the modulus of convexity \delta_\Omega of a set \Omega. We also show that \lim_{\epsilon \to 0} \delta_\Omega(\epsilon)/\epsilon^2 exists whenever \Omega is closed and convex.
Cite
@article{arxiv.1207.4347,
title = {Local characterization of strongly convex sets},
author = {Alexander Weber and Gunther Reißig},
journal= {arXiv preprint arXiv:1207.4347},
year = {2013}
}