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<title lang=en>Ergodic convergence to a zero of the extended sum of two maximal monotone operators</title>
<creator>Moudafi, Abdellatif</creator>
<creator>Théra, Michel</creator>
<contributor>Département de Mathématiques et Informatique (D.M.I.) ; Université des Antilles et de la Guyane (UAG) - Université des Antilles (Pôle Guadeloupe) ; Université des Antilles (UA) - Université des Antilles (UA)</contributor>
<contributor>Laboratoire d'Arithmétique, de Calcul formel et d'Optimisation (LACO) ; Université de Limoges (UNILIM) - Centre National de la Recherche Scientifique (CNRS)</contributor>
<description>International audience</description>
<source>Studies in Computational Mathematics</source>
<identifier>hal-00778164</identifier>
<identifier>https://hal.univ-antilles.fr/hal-00778164</identifier>
<source>https://hal.univ-antilles.fr/hal-00778164</source>
<source>Studies in Computational Mathematics, 2001, 8, pp.369-379. 〈10.1016/S1570-579X(01)80022-7〉</source>
<identifier>DOI : 10.1016/S1570-579X(01)80022-7</identifier>
<relation>info:eu-repo/semantics/altIdentifier/doi/10.1016/S1570-579X(01)80022-7</relation>
<language>en</language>
<subject>[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>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.</description>
<date>2001-12-31</date>
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