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.
Mots-clés : 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://www.numdam.org/articles/10.1051/cocv/2012029/}
}
TY - JOUR AU - Volle, M. AU - Hiriart-Urruty, J.-B. AU - Zălinescu, C. TI - When some variational properties force convexity JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 701 EP - 709 VL - 19 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2012029/ DO - 10.1051/cocv/2012029 LA - en ID - COCV_2013__19_3_701_0 ER -
%0 Journal Article %A Volle, M. %A Hiriart-Urruty, J.-B. %A Zălinescu, C. %T When some variational properties force convexity %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 701-709 %V 19 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2012029/ %R 10.1051/cocv/2012029 %G en %F COCV_2013__19_3_701_0
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. http://www.numdam.org/articles/10.1051/cocv/2012029/
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