Ivan Shishkin, Rye (1878)

Problems/Hilbert and pre-Hilbert spaceUnreviewed

La projection sur un convexe fermé est 1-lipschitzienne

by beignet62·
44
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
·
Français
FrançaisAdd translation

Showing the Français version because no English translation exists yet. Add that translation.

Unreviewed. This problem has not been reviewed by trusted users yet.

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\|.

I solved itMark it doneAdd to my listKeep it in your list
I like this problem0 likes
Show related problems1

Specific to this problem

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

Hints

1

Hint 1

Open this only if you want a small nudge before looking at the solutions.

Solutions

0
Report

For an unclear, ambiguous, or possibly incorrect statement, please use the Discussion tab on the right. Report content that needs moderator intervention, such as dangerous, clearly non-mathematical, or plagiarized content.