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Journal Articles Studies in Computational Mathematics Year : 2001

Ergodic convergence to a zero of the extended sum of two maximal monotone operators

Abstract

In this note we show that the splitting scheme of Passty [13] as well as the barycentric-proximal method of Lehdili & Lemaire [8] can be used to approximate a zero of the extended sum of maximal monotone operators. When the extended sum is maximal monotone, we generalize a convergence result obtained by Lehdili & Lemaire for convex functions to the case of maximal monotone operators. Moreover, we recover the main convergence results of Passty and Lehdili & Lemaire when the pointwise sum of the involved operators in maximal monotone.
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Dates and versions

hal-00778164 , version 1 (18-01-2013)

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Abdellatif Moudafi, Michel Théra. Ergodic convergence to a zero of the extended sum of two maximal monotone operators. Studies in Computational Mathematics, 2001, 8, pp.369-379. ⟨10.1016/S1570-579X(01)80022-7⟩. ⟨hal-00778164⟩
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