Geodesic
Global Maximum of a Convex Function: Necessary and Sufficient Conditions
Journal of convex analysis, Tome 13 (2006) no. 3, pp. 687-694

Voir la notice de l'article provenant de la source Heldermann Verlag

We prove that an extended-real-valued lower semi-continuous convex function Φ defined on a reflexive Banach space X achieves its supremum on every nonempty bounded and closed convex set of its effective domain Dom Φ, if and only if the restriction of Φ to Dom Φ is sequentially continuous with respect to the weak topology on the underlying space X.
Mots-clés : Global maximum of a convex function, optimality conditions 
@article{JCA_2006_13_3_JCA_2006_13_3_a11,
     author = {E. Ernst and M. Th\'era},
     title = {Global {Maximum} of a {Convex} {Function:} {Necessary} and {Sufficient} {Conditions}},
     journal = {Journal of convex analysis},
     pages = {687--694},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2006},
     url = {http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a11/}
}
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E. Ernst; M. Théra. Global Maximum of a Convex Function: Necessary and Sufficient Conditions. Journal of convex analysis, Tome 13 (2006) no. 3, pp. 687-694. http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a11/