
Journal of Convex Analysis 14 (2007), No. 3, 455463 Copyright Heldermann Verlag 2007 Direction of Movement of the Element of Minimal Norm in a Moving Convex Set Renu Choudhary Dept. of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand renu@math.auckland.ac.nz [Abstractpdf] We show that if $K$ is a nonempty closed convex subset of a real Hilbert space $H$, $e$ is a nonzero arbitrary vector in $H$ and for each $t\in \mathbb{R}$, $z(t)$ is the closest point in $K + te$ to the origin, then the angle $z(t)$ makes with $e$ is a decreasing function of $t$ while $z(t)\neq 0$, and the inner product of $z(t)$ with $e$ is increasing. Keywords: Moving convex set, nearest point projection. MSC: 46C05; 47H99, 41A65 [ Fulltextpdf (101 KB)] for subscribers only. 