Differentiability Properties of Metric Projections onto Convex Sets

  • Alexander ShapiroEmail author


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.


Metric projection Directional differentiability Second-order regularity Cone reducibility Nondegeneracy 

Mathematics Subject Classification

90C30 90C31 



This research was partly supported by the NSF award CMMI 1232623.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Georgia Institute of TechnologyAtlantaUSA

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