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On a convex set with nondifferentiable metric projection

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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 \(C^{1,1}\) boundary which possesses the same property.

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Acknowledgments

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-REGPOT-2012-2013-1) under Grant agreement n316165. The authors would like to thank the anonymous reviewers for their valuable comments that help improve the paper.

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Authors and Affiliations

  1. Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR, 97202, USA

    Shyan S. Akmal, Nguyen Mau Nam & J. J. P. Veerman

  2. CCQCN, Department of Physics, University of Crete, 71003, Heraklion, Greece

    J. J. P. Veerman

Authors
  1. Shyan S. Akmal
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  2. Nguyen Mau Nam
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  3. J. J. P. Veerman
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Correspondence to Nguyen Mau Nam.

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Akmal, S.S., Nam, N.M. & Veerman, J.J.P. On a convex set with nondifferentiable metric projection. Optim Lett 9, 1039–1052 (2015). https://doi.org/10.1007/s11590-015-0847-x

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  • DOI: https://doi.org/10.1007/s11590-015-0847-x

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