Volume 19, Number 3, July-September 2013
|Page(s)||701 - 709|
|Published online||17 May 2013|
When some variational properties force convexity
Department of Mathematics, University of Avignon,
2 Institut de Mathématiques, Université Paul Sabatier, Toulouse, France
3 Faculty of Mathematics, University Al. I. Cuza, Iaşi, Romania
4 Octav Mayer Institute of Mathematics, Romanian Academy, Romania
Revised: 26 June 2012
The notion of adequate (resp. strongly adequate) function has been recently introduced to characterize the essentially strictly convex (resp. essentially firmly subdifferentiable) functions among the weakly lower semicontinuous (resp. lower semicontinuous) ones. In this paper we provide various necessary and sufficient conditions in order that the lower semicontinuous hull of an extended real-valued function on a reflexive Banach space is essentially strictly convex. Some new results on nearest (farthest) points are derived from this approach.
Mathematics Subject Classification: 46G05 / 49J50 / 46N10
Key words: Convex duality / well posed optimization problem / essential strict convexity / essential smoothness / best approximation
© EDP Sciences, SMAI, 2013
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