Caractérisation d’une classe de convergences de fonctions convexes et application à la t-épi/hypo-convergence de fonctions convexes-concaves

Hajioui, K. El ; Mentagui, D.

Serdica Mathematical Journal, Tome 43 (2017) no. 3-4, pp. 267-292

Résumé

This paper focuses on a new characterization of a class of variational convergences which play a crucial role in optimization and variational analysis. When the functions under consideration are in Γ (X) or Γ (X^* ) where X is a normed linear space, this characterization is given in terms of infimal-convolution approximates associated to general kernels. When we are concerned by bivariate convex-concave saddle functions, a new convergence called t-epi/hypo-convergence is introduced and characterized first in terms of generalized augmented Lagrangians and then in terms of generalized inf-sup-convolution approximates associated to specified schemes of Legendre-Fenchel partial transforms. The proofs and results considered in this paper are original and displayed within the framework of variational analysis and the duality theory.

Détail

Mots-clés : Fonction convexe (convexe-concave), convergences variationnelles, t-convergence, t-épi/hypo-convergence, référentiel, approximation inf (inf–sup)-convolutive, Lagrangien augmenté, convergence simple, convergence uniforme sur les bornés, 49J45, 49J52, 49J40, 47N10