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

0452988 - MÚ 2016 RIV DE eng J - Článek v odborném periodiku
Šilhavý, Miroslav
Differentiability of the metric projection onto a convex set with singular boundary points.
Journal of Convex Analysis. Roč. 22, č. 4 (2015), s. 969-997. ISSN 0944-6532. E-ISSN 0944-6532
Institucionální podpora: RVO:67985840
Klíčová slova: metric projection * Fréchet derivative * normal cone
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.786, rok: 2015
http://www.heldermann.de/JCA/JCA22/JCA224/jca22052.htm

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 ....
Trvalý link: http://hdl.handle.net/11104/0253882