Asymptotic behavior of second-order dissipative evolution equations combining potential with non-potential effects

Abstract : In the setting of a real Hilbert space H, we investigate the asymptotic behavior, as time t goes to infinity, of trajectories of second-order damped evolution equations, which are governed by the sum of the gradient operator of a convex differentiable potential function , and a maximal monotone operator which is assumed to be cocoercive. Under a sharp condition involving the viscous and the cocoercive parameters, it is proved that each trajectory weakly converges to an equilibrium. Passing from weak to strong convergence is obtained by introducing an asymptotically vanishing Tikhonov-like regularizing term. As special cases, we recover the asymptotic analysis of the heavy ball with friction dynamic attached to a convex potential, the second-order gradient-projection dynamic, and the second-order dynamic governed by the Yosida approximation of a general maximal monotone operator. The breadth and flexibility of the proposed framework is illustrated through applications in the areas of constrained optimization, dynamical approach to Nash equilibria for noncooperative games, and asymptotic stabilization in the case of a continuum of equilibria.
Type de document :
Article dans une revue
ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2010, 17, pp.836-857. 〈10.1051/cocv/2010024〉
Liste complète des métadonnées

Littérature citée [36 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00803774
Contributeur : Hedy Attouch <>
Soumis le : vendredi 22 mars 2013 - 17:55:22
Dernière modification le : lundi 23 octobre 2017 - 14:20:01
Document(s) archivé(s) le : dimanche 23 juin 2013 - 05:55:07

Fichier

ATTOUCH-MAINGE-09-04-2010-COCV...
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Hedy Attouch, Paul-Emile Maingé. Asymptotic behavior of second-order dissipative evolution equations combining potential with non-potential effects. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2010, 17, pp.836-857. 〈10.1051/cocv/2010024〉. 〈hal-00803774〉

Partager

Métriques

Consultations de
la notice

200

Téléchargements du document

77