Abstract

We show that if KK is a nonempty closed convex subset of a real Hilbert space HH, ee is a non-zero arbitrary vector in HH and for each t∈Rt\in \mathbb{R}, z(t)z(t) is the closest point in K+teK + te to the origin, then the angle z(t)z(t) makes with ee is a decreasing function of tt while z(t)≠0z(t)\neq 0, and the inner product of z(t)z(t) with ee is increasing.

Author information

Contact details are reproduced from the original publication and may be historical.

Renu Choudhary

Dept. of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand

renu@math.auckland.ac.nz

Keywords

  • Moving convex set
  • nearest point projection

Mathematics Subject Classification

46C05; 47H99, 41A65

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Suggested citation

R. Choudhary. “Direction of Movement of the Element of Minimal Norm in a Moving Convex Set.” Journal of Convex Analysis 14 (2007), No. 3, 455–463. https://doi.org/10.68381/jca14029

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Published by Heldermann Verlag, 2007. Rights now held by Banach Press LLC.