Ivan Shishkin, Rye (1878)

Problems/Hilbert and pre-Hilbert space

La projection sur un convexe fermé est 1-lipschitzienne

by beignet62·
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Soit HH un espace de Hilbert et CC un sous-ensemble convexe fermé de HH.

Montrer que l’application de projection sur CC est 11-lipschitzienne, c’est-à-dire :

∀x,y∈H,∥PC(x)−PC(y)∥≤∥x−y∥.\forall x,y\in H,\qquad \|P_C(x)-P_C(y)\|\leq \|x-y\|.

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32Une caractérisation du projeté sur un convexe ferméby beignet62 · exploration-specific / unlisted

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