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On differentiability of metric projections in $ {\bf R}\sp n$. I. Boundary case

Author: Alexander Shapiro
Journal: Proc. Amer. Math. Soc. 99 (1987), 123-128
MSC: Primary 41A50; Secondary 41A65
MathSciNet review: 866441
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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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Keywords: Metric projection, normed space, distance function, directional differentiability, approximating cone
Article copyright: © Copyright 1987 American Mathematical Society