A Monotone+Skew Splitting Model for Composite Monotone Inclusions in Duality

Abstract : The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally monotone operator and a linear skew-adjoint operator. An algorithmic framework is developed for solving this generic problem in a Hilbert space setting. New primal-dual splitting algorithms are derived from this framework for inclusions involving composite monotone operators, and convergence results are established. These algorithms draw their simplicity and efficacy from the fact that they operate in a fully decomposed fashion in the sense that the monotone operators and the linear transformations involved are activated separately at each iteration. Comparisons with existing methods are made and applications to composite variational problems are demonstrated.
Type de document :
Article dans une revue
SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2011, 21 (4), pp.1230-1250. 〈10.1137/10081602X〉
Liste complète des métadonnées

https://hal.inria.fr/hal-00643797
Contributeur : Estelle Bouzat <>
Soumis le : mardi 22 novembre 2011 - 18:11:45
Dernière modification le : lundi 17 décembre 2018 - 01:28:21

Lien texte intégral

Identifiants

Citation

Luis M. Briceno-Arias, Patrick Louis Combettes. A Monotone+Skew Splitting Model for Composite Monotone Inclusions in Duality. SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2011, 21 (4), pp.1230-1250. 〈10.1137/10081602X〉. 〈hal-00643797〉

Partager

Métriques

Consultations de la notice

172