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Differentiability Properties of Metric Projections onto Convex Sets

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  • Alexander Shapiro

    (Georgia Institute of Technology)

Abstract

It is known that directional differentiability of metric projection onto a closed convex set in a finite-dimensional space is not guaranteed. In this paper, we discuss sufficient conditions ensuring directional differentiability of such metric projections. The approach is based on a general theory of sensitivity analysis of parameterized optimization problems.

Suggested Citation

  • Alexander Shapiro, 2016. "Differentiability Properties of Metric Projections onto Convex Sets," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 953-964, June.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:3:d:10.1007_s10957-016-0871-8
    DOI: 10.1007/s10957-016-0871-8
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    References listed on IDEAS

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    1. J. Frédéric Bonnans & Roberto Cominetti & Alexander Shapiro, 1998. "Sensitivity Analysis of Optimization Problems Under Second Order Regular Constraints," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 806-831, November.
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