untitled
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<identifier>oai:HAL:hal-00783905v1</identifier>
<datestamp>2018-01-11</datestamp>
<setSpec>type:REPORT</setSpec>
<setSpec>subject:math</setSpec>
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<metadata><dc>
<publisher>HAL CCSD</publisher>
<title lang=en>Ergodic Convergence to a Zero of the Extended Sum</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>
<identifier>hal-00783905</identifier>
<identifier>https://hal.univ-antilles.fr/hal-00783905</identifier>
<identifier>https://hal.univ-antilles.fr/hal-00783905/document</identifier>
<identifier>https://hal.univ-antilles.fr/hal-00783905/file/10.1.1.165.7044.pdf</identifier>
<source>https://hal.univ-antilles.fr/hal-00783905</source>
<source>2000</source>
<language>en</language>
<subject lang=en>maximal monotone operators</subject>
<subject lang=en>Yosida regularization</subject>
<subject lang=en>enlargements</subject>
<subject lang=en>variational sum</subject>
<subject lang=en>extended sum</subject>
<subject lang=en>splitting methods</subject>
<subject>[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]</subject>
<type>info:eu-repo/semantics/report</type>
<type>Reports</type>
<description lang=en>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.</description>
<date>2000</date>
</dc>
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