The research of Nguyen Mau Nam was partially supported by the NSF under grant #1411817 and the Simons Foundation under grant #208785. The research of J.J.P. Veerman was partially supported by the European Union’s Seventh Framework Program (FP7-BEGPOT-2012-2013-1) under grant agreement n316165.
Metric projections, Directional derivatives
A remarkable example of a nonempty closed convex set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that construction to obtain a convex set with smooth boundary which possesses the same property.
Akmal, Shyan S.; Nam, Nguyen Mau; and Veerman, J. J. P., "On a Convex Set with Nondifferentiable Metric Projection" (2015). Mathematics and Statistics Faculty Publications and Presentations. 121.