Ergodic Convergence to a Zero of the Extended Sum

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

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