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Directionally nondifferentiable metric projection

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Abstract

A closed convex set inR 2 is constructed such that the associated metric projection onto that set is not everywhere directionally differentiable.

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References

  1. Zarantonello, E. H.,Projections on Convex Sets in Hilbert Space and Spectral Theory, Contributions to Nonlinear Functional Analysis, Academic Press, New York, New York, pp. 237–424, 1971.

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  2. Shapiro, A.,Sensitivity Analysis of Nonlinear Programs and Differentiability Properties of Metric Projections, SIAM Journal on Control and Optimization, Vol. 26, pp. 628–645, 1988.

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  3. Krusakl, J.,Two Convex Counterexamples: A Discontinuous Envelope Function and a Nondifferentiable Nearest-Point Mapping, Proceedings of the American Mathematical Society, Vol. 23, pp. 697–703, 1969.

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Authors and Affiliations

  1. School of Industrial and Systems Engineering, Georgia Institute of Technology, 30332-0205, Atlanta, Georgia

    A. Shapiro (Associate Professor)

Authors
  1. A. Shapiro
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Communicated by E. Polak

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Shapiro, A. Directionally nondifferentiable metric projection. J Optim Theory Appl 81, 203–204 (1994). https://doi.org/10.1007/BF02190320

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  • DOI: https://doi.org/10.1007/BF02190320

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