Ergodic Convergence to a Zero of the Extended Sum

Abdellatif Moudafi (1) , Michel Théra (2)

1 D.M.I. - Département de Mathématiques et Informatique
2 LACO - Laboratoire d'Arithmétique, de Calcul formel et d'Optimisation

In this note we show that the splitting scheme of Passty [7] as well as the barycentric-proximal method of Lehdili & Lemaire [4] can be used to approximate a zero of the extended sum of maximal monotone operators. When the extended sum is maximal monotone, we extend the convergence result obtained by Lehdili & Lemaire for convex functions to the case of maximal monotone operators. Moreover, we recover the main convergence results by Passty and Lehdili & Lemaire when the pointwise sum of the involved operators is maximal monotone.

Mots clés: maximal monotone operators; Yosida regularization; enlargements; variational sum; extended sum; splitting methods

Domaines: Optimisation et contrôle [math.OC]

Abdellatif Moudafi, Michel Théra. Ergodic Convergence to a Zero of the Extended Sum. 2000. ⟨hal-00783905⟩