A characterization of convex and semicoercive functionals

Samir Adly (1) , Emil Ernst (2) , Michel Théra (1)

1 LACO - Laboratoire d'Arithmétique, de Calcul formel et d'Optimisation
2 IMAR - Institute of Mathematics of the Romanian Academy [Bucharest]

In this paper we prove that every proper convex and lower semicontinuous functional Φ defined on a real reflexive Banach space X is semicoercive if and only if every small uniform perturbation of Φ attains its minimum value on X.

Mots clés: convex analysis; barrier cone; support functional; recession analysis; semicoercive functional

Domaines: Mathématiques [math]

Samir Adly, Emil Ernst, Michel Théra. A characterization of convex and semicoercive functionals. Journal of Convex Analysis, 2001, 8, pp.127-148. ⟨hal-00068956⟩