When some variational properties force convexity

M. Volle; J.-B. Hiriart-Urruty; C. Zălinescu

ESAIM: Control, Optimisation and Calculus of Variations (2013)

  • Volume: 19, Issue: 3, page 701-709
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Volle, M., Hiriart-Urruty, J.-B., and Zălinescu, C.. "When some variational properties force convexity." ESAIM: Control, Optimisation and Calculus of Variations 19.3 (2013): 701-709. <http://eudml.org/doc/272827>.

@article{Volle2013,
abstract = {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.},
author = {Volle, M., Hiriart-Urruty, J.-B., Zălinescu, C.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {convex duality; well posed optimization problem; essential strict convexity; essential smoothness; best approximation; convex function; convex analysis; lower semicontinuous function; essentially strictly convex function; essentially Gâteaux differentiable function; Chebyshev set; nearest point; farthest point; metric projection; antiprojection; uniquely remotal set; convexity of Chebyshev subsets; Tikhonov well-posedness},
language = {eng},
number = {3},
pages = {701-709},
publisher = {EDP-Sciences},
title = {When some variational properties force convexity},
url = {http://eudml.org/doc/272827},
volume = {19},
year = {2013},
}

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
PB - EDP-Sciences
VL - 19
IS - 3
SP - 701
EP - 709
AB - 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.
LA - eng
KW - convex duality; well posed optimization problem; essential strict convexity; essential smoothness; best approximation; convex function; convex analysis; lower semicontinuous function; essentially strictly convex function; essentially Gâteaux differentiable function; Chebyshev set; nearest point; farthest point; metric projection; antiprojection; uniquely remotal set; convexity of Chebyshev subsets; Tikhonov well-posedness
UR - http://eudml.org/doc/272827
ER -

References

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