Affordable Access

Approximation and regularization of arbitrary functions in Hilbert spaces by the Lasry-Lions method

Authors
Publication Date
Disciplines
  • Law

Abstract

Approximation and regularization of arbitrary functions in Hilbert spaces by the Lasry-Lions method ANNALES DE L’I. H. P., SECTION C H. ATTOUCH D. AZE Approximation and regularization of arbitrary functions in Hilbert spaces by the Lasry-Lions method Annales de l’I. H. P., section C, tome 10, no 3 (1993), p. 289-312. <http://www.numdam.org/item?id=AIHPC_1993__10_3_289_0> © Gauthier-Villars, 1993, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section C » (http://www.elsevier.com/locate/anihpc), implique l’accord avec les condi- tions générales d’utilisation (http://www.numdam.org/legal.php). Toute uti- lisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit conte- nir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Approximation and regularization of arbitrary functions in Hilbert spaces by the Lasry-Lions method H. ATTOUCH D. AZE Université de Montpellier 2, Mathematiques, place E. Bataillon, 34095 Montpellier Cedex 5, France Universite de Perpignan, Mathematiques, 52, Avenue de Villeneuve, 66860 Perpignan Cedex, France Ann. Inst. Henri Poincaré, Vol. 10, n° 3, 1993, p. 289-312. Analyse non linéaire ABSTRACT. - The Lasry-Lions regularization method is extended to arbitrary functions. In particular, to any proper lower semicontinuous function defined on a Hilbert space X and which is quadratically minorized (i. e. f (x) >_- - c (1 + ~ ~ x ( ~ 2) for some c ~ 0), is associ- ated a sequence of differentiable functions with Lipschitz continuous derivatives which approximate f from below. Some variants of the method are considered including the case of non quadratic kernels. Key words : Hilbert spaces, regularization, approximation, epigraphical sum, Moreau- Yosida approximation. RESUME. - La methode de regularisation de Lasry-Lions est etendue a des

There are no comments yet on this publication. Be the first to share your thoughts.