# Differentiability Properties of Metric Projections onto Convex Sets

#### 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.

DOI: 10.1007/s10957-016-0871-8

### Cite this paper

@article{Shapiro2016DifferentiabilityPO, title={Differentiability Properties of Metric Projections onto Convex Sets}, author={Alexander Shapiro}, journal={J. Optimization Theory and Applications}, year={2016}, volume={169}, pages={953-964} }