Weak local supportability and applications to approximation

Jonathan Borwein

Vol. 82 (1979), No. 2, 323–338

DOI: 10.2140/pjm.1979.82.323

Abstract

Perturbed optimization problems are studied using a weaker notion of local supportability than that developed by Ekeland and Lebourg. This weakening allows for a more comprehensive treatment of such problems. In particular we prove that nearest points exist densely for closed relatively weakly compact sets in spaces with locally uniformly convex norms and provide a simplified proof in this framework that a normed space with a Fréchet norm is an Asplund space.

Mathematical Subject Classification 2000

Primary: 46B99

Secondary: 41A25, 58C20, 90C30, 49A27

Milestones

Received: 30 March 1978

Published: 1 June 1979