On a Convex Set with Nondifferentiable Metric Projection
Optimization and Control
2014-12-02 v1
Abstract
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.
Cite
@article{arxiv.1412.0058,
title = {On a Convex Set with Nondifferentiable Metric Projection},
author = {Shyan S. Akmal and Nguyen Mau Nam and J. J. P. Veerman},
journal= {arXiv preprint arXiv:1412.0058},
year = {2014}
}