Article
On a Convex Set with Nondifferentiable Metric Projection
Mathematics and Statistics Faculty Publications and Presentations
Sponsor
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.
Document Type
Pre-Print
Publication Date
8-1-2015
Subjects
- Metric projections,
- Directional derivatives,
- Convex sets
Disciplines
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.
DOI
10.1007/s11590-015-0847-x
Persistent Identifier
http://archives.pdx.edu/ds/psu/17507
Citation Information
Shyan S. Akmal, Nguyen Mau Nam and J. J. P. Veerman. "On a Convex Set with Nondifferentiable Metric Projection" Vol. 9 Iss. 6 (2015) p. 1039 - 1052 Available at: http://works.bepress.com/jj-veerman/4/
This is the pre-print of an article submitted for consideration to Optimization Letters. Copyright (2015) SpringerLink and can be found online at: http://dx.doi.org/10.1007/s11590-015-0847-x