Skip to main content
Article
On a Convex Set with Nondifferentiable Metric Projection
Mathematics and Statistics Faculty Publications and Presentations
  • Shyan S. Akmal, Portland State University
  • Nguyen Mau Nam, Portland State University
  • J. J. P. Veerman, Portland State University
Document Type
Pre-Print
Publication Date
8-1-2015
Subjects
  • Metric projections,
  • Directional derivatives
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.
Description

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

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/