On differentiability of metric projections in . I. Boundary case

Author:
Alexander Shapiro

Journal:
Proc. Amer. Math. Soc. **99** (1987), 123-128

MSC:
Primary 41A50; Secondary 41A65

DOI:
https://doi.org/10.1090/S0002-9939-1987-0866441-7

MathSciNet review:
866441

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Abstract: This paper is concerned with metric projections onto a closed subset 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 are given in terms of approximating cones. It is shown that if is defined by a number of inequality constraints and a constraint qualification holds, then the approximating cone exists.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1987-0866441-7

Keywords:
Metric projection,
normed space,
distance function,
directional differentiability,
approximating cone

Article copyright:
© Copyright 1987
American Mathematical Society