Differentiability of the Metric Projection in Hilbert Space
نویسنده
چکیده
A study is made of differentiability of the metric projection P onto a closed convex subset K of a Hubert space H. When K has nonempty interior, the Gateaux or Fréchet smoothness of its boundary can be related with some precision to Gateaux or Fréchet differentiability properties of P. For instance, combining results in §3 with earlier work of R. D. Holmes shows that K has a C2 boundary if and only if P is C' in H \ K and its derivative P' has a certain invertibility property at each point. An example in §5 shows that if the C2 condition is relaxed even slightly then P can be nondifferentiable (Fréchet) in H \ K.
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