Unique best approximation from a C²-manifold in Hilbert space

Theagenis Abatzoglou

Vol. 87 (1980), No. 2, 233–244

DOI: 10.2140/pjm.1980.87.233

Abstract

Given a C²-manifold in a Hilbert space we examine whether a critical point of the distance function to the manifold is actually a global best approximation. We establish a criterium for the above in terms of the curvature of the manifold.

Mathematical Subject Classification 2000

Primary: 58C07

Secondary: 41A52, 46C05, 58B20

Milestones

Received: 20 December 1978

Revised: 25 June 1979

Published: 1 April 1980