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H1-projection into the set of convex functions : a saddle-point formulation

Carlier, Guillaume; Lachand-Robert, Thomas; Maury, Bertrand (2001), H1-projection into the set of convex functions : a saddle-point formulation, ESAIM. Proceedings, 10, p. 277-289. http://dx.doi.org/10.1051/proc:2001017

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Type
Article accepté pour publication ou publié
Date
2001
Nom de la revue
ESAIM. Proceedings
Volume
10
Éditeur
EDP Sciences
Pages
277-289
Identifiant publication
Métadonnées
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Auteur(s)
Carlier, Guillaume
Lachand-Robert, Thomas
Maury, Bertrand
Résumé (EN)
We investigate numerical methods to approximate the projection-operator from H1 0 into the set of convex functions. We introduce a new formulation of the problem, based on gradient fi elds. It leads in a natural way to an in finite-dimensional saddle-point problem, which can be shown to be ill-posed in general. Existence and uniqueness of a saddle point is obtained for a Lagrangian de ned in suitable spaces. This well-posed formulation does not lead to an implementable algorithm. Yet, numerical experiments based on a discretization of the fi rst formulation exhibit a good behaviour.
Mots-clés
saddle point; Convex functions