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essential strict convexity

ESAIM: Control, Optimisation and Calculus of Variations (1)

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When some variational properties forceconvexity
M. Volle, J.-B. Hiriart-Urruty, C. Zălinescu
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 19 / Issue 3 / July 2013

Published online by Cambridge University Press:

17 May 2013, pp. 701-709

Print publication:

July 2013
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The notion of adequate (resp. strongly adequate) function has been recently introduced tocharacterize the essentially strictly convex (resp. essentially firmly subdifferentiable)functions among the weakly lower semicontinuous (resp. lower semicontinuous) ones. In thispaper we provide various necessary and sufficient conditions in order that the lowersemicontinuous hull of an extended real-valued function on a reflexive Banach space isessentially strictly convex. Some new results on nearest (farthest) points are derivedfrom this approach.