Differentiability of the metric projection onto a convex set with singular boundary points

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F15%3A00452988" target="_blank" >RIV/67985840:_____/15:00452988 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Differentiability of the metric projection onto a convex set with singular boundary points

Popis výsledku v původním jazyce

The differentiability of the metric projection P onto a closed convex set K in ... is examined. The boundary K can have singular points of orders .... Here k=-1 corresponds to the interior points of K, k=0 to regular points of the boundary (i.e., faces),... edges and k=n-1 to vertices. It is assumed that for every k the set of all singular points forms an n-k-1 dimensional manifold ... (possibly empty) of class p2. Under a mild continuity assumption it is shown that then P is of class p-1 on an open set W whose complement has null Lebesgue measure. The set W is the union of the interiors of inverse images of ... under P. Moreover, a formula for the Fréchet derivative DP on each of these regions is given that relates DP to the second fundamental form (i.e., the curvature) of the manifold ....

Název v anglickém jazyce

Differentiability of the metric projection onto a convex set with singular boundary points

Popis výsledku anglicky

The differentiability of the metric projection P onto a closed convex set K in ... is examined. The boundary K can have singular points of orders .... Here k=-1 corresponds to the interior points of K, k=0 to regular points of the boundary (i.e., faces),... edges and k=n-1 to vertices. It is assumed that for every k the set of all singular points forms an n-k-1 dimensional manifold ... (possibly empty) of class p2. Under a mild continuity assumption it is shown that then P is of class p-1 on an open set W whose complement has null Lebesgue measure. The set W is the union of the interiors of inverse images of ... under P. Moreover, a formula for the Fréchet derivative DP on each of these regions is given that relates DP to the second fundamental form (i.e., the curvature) of the manifold ....

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Convex Analysis

ISSN

0944-6532

e-ISSN

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Svazek periodika

22

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

29

Strana od-do

969-997

Kód UT WoS článku

000369772300005

EID výsledku v databázi Scopus

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