On differentiability of metric projections in 𝑅ⁿ. I. Boundary case

Shapiro, Alexander

doi:10.1090/S0002-9939-1987-0866441-7

On differentiability of metric projections in $\textbf {R}^ n$. I. Boundary case
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Proc. Amer. Math. Soc. 99 (1987), 123-128 Request permission

Abstract:

This paper is concerned with metric projections onto a closed subset $S$ of a finite-dimensional normed space. Necessary and in a sense sufficient conditions for directional differentiability of a metric projection at a boundary point of $S$ are given in terms of approximating cones. It is shown that if $S$ is defined by a number of inequality constraints and a constraint qualification holds, then the approximating cone exists.

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