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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
Publication Date
  • Metric projections,
  • Directional derivatives,
  • Convex sets

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.


This is the pre-print of an article submitted for consideration to Optimization Letters. Copyright (2015) SpringerLink and can be found online at:

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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
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