Geodesic
When some variational properties force convexity
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 3, pp. 701-709

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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.

DOI : 10.1051/cocv/2012029
Classification : 46G05, 49J50, 46N10
Keywords: convex duality, well posed optimization problem, essential strict convexity, essential smoothness, best approximation 
@article{COCV_2013__19_3_701_0,
     author = {Volle, M. and Hiriart-Urruty, J.-B. and Z\u{a}linescu, C.},
     title = {When some variational properties force convexity},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {701--709},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {3},
     year = {2013},
     doi = {10.1051/cocv/2012029},
     mrnumber = {3092358},
     zbl = {1277.46042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012029/}
}
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Volle, M.; Hiriart-Urruty, J.-B.; Zălinescu, C. When some variational properties force convexity. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 3, pp. 701-709. doi: 10.1051/cocv/2012029

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